The groups of order 64

# The groups of order 64

It contains information about the groups of order 64, as
• presentation (PC-representation)
• order distribution of the elements
• number of conjugacy classes
• nilpotency class
• centre and commutator subgroup
• automorphism and inner automorphism group
• lower central series

For the groups 64/261 - 64/267 no information about their automorphism group is given. This information could not be computed in reasonable time.
The groups are numbered according to their numbering in GAP.
```64/1
((a1,a2,a3,a4,a5,a6;a1^2=a2,a2^2=a3,a3^2=a4,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
1 elements of order 2
2 elements of order 4
4 elements of order 8
8 elements of order 16
16 elements of order 32
32 elements of order 64

ABELIAN

--------------------------------------------------------------
64/2
((a1,a2,a3,a4,a5,a6;a1^2=a3,a2^2=a4,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
12 elements of order 4
48 elements of order 8

ABELIAN

group is isomorphic to 8/1 x 8/1

--------------------------------------------------------------
64/3
((a1,a2,a3,a4,a5,a6;a1^2=a3,a2^2=a4,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
12 elements of order 4
48 elements of order 8

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/3
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 512
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/3 --- 2/1 --- 1/1

--------------------------------------------------------------
64/4
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5 ] , type 4/2
Automorphism Group of size 256
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/4 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/5
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5 ] , type 4/2
Automorphism Group of size 256
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/5 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/6
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
20 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a3, a5 ] , type 4/1
Automorphism Group of size 128
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/6 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/7
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
28 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a3, a5 ] , type 4/1
Automorphism Group of size 128
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/7 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/8
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 128
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/8 --- 8/2 --- 4/2 --- 1/1

--------------------------------------------------------------
64/9
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 128
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/9 --- 8/2 --- 4/2 --- 1/1

--------------------------------------------------------------
64/10
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a6,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
20 elements of order 4
32 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/10 --- 8/2 --- 4/2 --- 1/1

--------------------------------------------------------------
64/11
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a6,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
28 elements of order 4
32 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/11 --- 8/2 --- 4/2 --- 1/1

--------------------------------------------------------------
64/12
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a6,a4^2=a5*a6,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
12 elements of order 4
32 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/12 --- 8/2 --- 4/2 --- 1/1

--------------------------------------------------------------
64/13
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a6,a4^2=a5*a6,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
28 elements of order 4
32 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/13 --- 8/2 --- 4/2 --- 1/1

--------------------------------------------------------------
64/14
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a6,a3^2=a6,a4^2=a5*a6,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
28 elements of order 4
32 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/14 --- 8/2 --- 4/2 --- 1/1

--------------------------------------------------------------
64/15
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a3,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
12 elements of order 4
48 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a3, a5 ] , type 4/1
Automorphism Group of size 256
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/15 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/16
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a3*a5,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
12 elements of order 4
48 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a3, a5 ] , type 4/1
Automorphism Group of size 256
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/16 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/17
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a3 ] , type 2/1
Automorphism Group of size 512
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/17 --- 2/1 --- 1/1

--------------------------------------------------------------
64/18
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/1
Commutator subgroup generated by [ a3, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 16/3
Nilpotency class 2
Lower Central Series:  64/18 --- 4/1 --- 1/1

--------------------------------------------------------------
64/19
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a6,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
48 elements of order 8

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/1
Commutator subgroup generated by [ a3, a6 ] , type 4/1
Automorphism Group of size 1536
Inner automorphism group type 16/3
Nilpotency class 2
Lower Central Series:  64/19 --- 4/1 --- 1/1

--------------------------------------------------------------
64/20
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3*a5, a4, a6 ] , type 8/2
Commutator subgroup generated by [ a3, a6 ] , type 4/1
Automorphism Group of size 256
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/20 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/21
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3*a5, a4, a6 ] , type 8/3
Commutator subgroup generated by [ a3, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/21 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/22
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a6,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
48 elements of order 8

28 conjugacy classes
Centre generated by [ a3*a5, a4, a6 ] , type 8/2
Commutator subgroup generated by [ a3, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/22 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/23
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a3,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/23 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/24
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/24 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/25
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a3,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/1
Commutator subgroup generated by [ a3, a6 ] , type 4/2
Automorphism Group of size 256
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/25 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/26
((a1,a2,a3,a4,a5,a6;a1^2=a3,a2^2=a4,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
12 elements of order 4
16 elements of order 8
32 elements of order 16

ABELIAN

group is isomorphic to 4/1 x 16/1

--------------------------------------------------------------
64/27
((a1,a2,a3,a4,a5,a6;a1^2=a3,a2^2=a4,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
12 elements of order 4
16 elements of order 8
32 elements of order 16

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/2
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 256
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/27 --- 2/1 --- 1/1

--------------------------------------------------------------
64/28
((a1,a2,a3,a4,a5,a6;a1^2=a3,a2^2=a4,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
12 elements of order 4
16 elements of order 8
32 elements of order 16

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/1
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 128
Inner automorphism group type 16/3
Nilpotency class 2
Lower Central Series:  64/28 --- 4/1 --- 1/1

--------------------------------------------------------------
64/29
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=1,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=a3,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
16 elements of order 8
32 elements of order 16

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/2
Commutator subgroup generated by [ a3 ] , type 2/1
Automorphism Group of size 128
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/29 --- 2/1 --- 1/1

--------------------------------------------------------------
64/30
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=1,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=a3,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
16 elements of order 8
32 elements of order 16

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/1
Commutator subgroup generated by [ a3, a6 ] , type 4/2
Automorphism Group of size 128
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/30 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/31
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a6,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
16 elements of order 8
32 elements of order 16

28 conjugacy classes
Centre generated by [ a3*a4, a5, a6 ] , type 8/1
Commutator subgroup generated by [ a3, a6 ] , type 4/1
Automorphism Group of size 64
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/31 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/32
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a3,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

13 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/3
Automorphism Group of size 128
Inner automorphism group type 32/46
Nilpotency class 4
Lower Central Series:  64/32 --- 8/3 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/33
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a6,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a3,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

13 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/3
Automorphism Group of size 128
Inner automorphism group type 32/46
Nilpotency class 4
Lower Central Series:  64/33 --- 8/3 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/34
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
44 elements of order 4

13 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/46
Nilpotency class 4
Lower Central Series:  64/34 --- 8/2 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/35
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a6,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
52 elements of order 4

13 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/46
Nilpotency class 4
Lower Central Series:  64/35 --- 8/2 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/36
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
20 elements of order 4
32 elements of order 8

13 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/46
Nilpotency class 4
Lower Central Series:  64/36 --- 8/2 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/37
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a6,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a5*a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
28 elements of order 4
32 elements of order 8

13 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/46
Nilpotency class 4
Lower Central Series:  64/37 --- 8/2 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/38
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a5*a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a5*a6,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
20 elements of order 4
8 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 256
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/38 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/39
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a6,a3^2=a5*a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a5*a6,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
36 elements of order 4
8 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 256
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/39 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/40
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a5*a6,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a5*a6,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
12 elements of order 4
24 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 128
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/40 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/41
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5*a6,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
28 elements of order 4
8 elements of order 8
16 elements of order 16

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 128
Inner automorphism group type 32/27
Nilpotency class 4
Lower Central Series:  64/41 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/42
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=a5,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5*a6,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
4 elements of order 4
24 elements of order 8
16 elements of order 16

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 256
Inner automorphism group type 32/27
Nilpotency class 4
Lower Central Series:  64/42 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/43
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a6,a3^2=a5,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5*a6,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
20 elements of order 4
24 elements of order 8
16 elements of order 16

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 256
Inner automorphism group type 32/27
Nilpotency class 4
Lower Central Series:  64/43 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/44
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a3,a3^2=1,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=a3,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
12 elements of order 4
16 elements of order 8
32 elements of order 16

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/2
Commutator subgroup generated by [ a3 ] , type 2/1
Automorphism Group of size 128
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/44 --- 2/1 --- 1/1

--------------------------------------------------------------
64/45
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a3,a3^2=a6,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=a3*a6,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
12 elements of order 4
16 elements of order 8
32 elements of order 16

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/1
Commutator subgroup generated by [ a3, a6 ] , type 4/1
Automorphism Group of size 128
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/45 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/46
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a3,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5*a6,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
20 elements of order 4
24 elements of order 8
16 elements of order 16

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 128
Inner automorphism group type 32/30
Nilpotency class 4
Lower Central Series:  64/46 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/47
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a3*a5,a3^2=a5*a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
36 elements of order 4
8 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 512
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/47 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/48
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a3*a5*a6,a3^2=a5*a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
36 elements of order 4
8 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 512
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/48 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/49
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a3*a5,a3^2=a5*a6,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a3*a5,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
4 elements of order 4
40 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/1
Commutator subgroup generated by [ a3, a5, a6 ] , type 8/1
Automorphism Group of size 256
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/49 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/50
((a1,a2,a3,a4,a5,a6;a1^2=a3,a2^2=1,a3^2=a4,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
4 elements of order 4
8 elements of order 8
16 elements of order 16
32 elements of order 32

ABELIAN

group is isomorphic to 2/1 x 32/1

--------------------------------------------------------------
64/51
((a1,a2,a3,a4,a5,a6;a1^2=a3,a2^2=1,a3^2=a4,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
4 elements of order 4
8 elements of order 8
16 elements of order 16
32 elements of order 32

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/1
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 64
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/51 --- 2/1 --- 1/1

--------------------------------------------------------------
64/52
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a4*a5,a4^2=a5*a6,a5^2=a6,a6^2=1
,[a1,a2]=a3*a4,[a1,a3]=a4*a5,[a1,a4]=a5*a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a4*a5,[a2,a4]=a5*a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
33 elements of order 2
2 elements of order 4
4 elements of order 8
8 elements of order 16
16 elements of order 32

19 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a4, a5, a6 ] , type 16/1
Automorphism Group of size 512
Inner automorphism group type 32/49
Nilpotency class 5
Lower Central Series:  64/52 --- 16/1 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/53
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a4*a5,a4^2=a5*a6,a5^2=a6,a6^2=1
,[a1,a2]=a3*a4,[a1,a3]=a4*a5,[a1,a4]=a5*a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a4*a5,[a2,a4]=a5*a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
17 elements of order 2
18 elements of order 4
4 elements of order 8
8 elements of order 16
16 elements of order 32

19 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a4, a5, a6 ] , type 16/1
Automorphism Group of size 256
Inner automorphism group type 32/49
Nilpotency class 5
Lower Central Series:  64/53 --- 16/1 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/54
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=a4*a5,a4^2=a5*a6,a5^2=a6,a6^2=1
,[a1,a2]=a3*a4,[a1,a3]=a4*a5,[a1,a4]=a5*a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a4*a5,[a2,a4]=a5*a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
1 elements of order 2
34 elements of order 4
4 elements of order 8
8 elements of order 16
16 elements of order 32

19 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a3, a4, a5, a6 ] , type 16/1
Automorphism Group of size 512
Inner automorphism group type 32/49
Nilpotency class 5
Lower Central Series:  64/54 --- 16/1 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/55
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

ABELIAN

group is isomorphic to 4/1 x 4/1 x 4/1

--------------------------------------------------------------
64/56
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/5
Commutator subgroup generated by [ a4 ] , type 2/1
Automorphism Group of size 12288
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/56 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/18

--------------------------------------------------------------
64/57
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a4 ] , type 2/1
Automorphism Group of size 12288
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/57 --- 2/1 --- 1/1

--------------------------------------------------------------
64/58
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a4 ] , type 2/1
Automorphism Group of size 2048
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/58 --- 2/1 --- 1/1

group is isomorphic to 4/1 x 16/9

--------------------------------------------------------------
64/59
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a4*a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a4 ] , type 2/1
Automorphism Group of size 2048
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/59 --- 2/1 --- 1/1

group is isomorphic to 4/1 x 16/10

--------------------------------------------------------------
64/60
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
32 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 12288
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/60 --- 4/2 --- 1/1

--------------------------------------------------------------
64/61
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/61 --- 4/2 --- 1/1

--------------------------------------------------------------
64/62
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 4096
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/62 --- 4/2 --- 1/1

--------------------------------------------------------------
64/63
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a5,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 4096
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/63 --- 4/2 --- 1/1

--------------------------------------------------------------
64/64
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4*a5,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 6144
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/64 --- 4/2 --- 1/1

--------------------------------------------------------------
64/65
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 12288
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/65 --- 4/2 --- 1/1

--------------------------------------------------------------
64/66
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/66 --- 4/2 --- 1/1

--------------------------------------------------------------
64/67
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4*a6,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/67 --- 4/2 --- 1/1

--------------------------------------------------------------
64/68
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/68 --- 4/2 --- 1/1

--------------------------------------------------------------
64/69
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4*a6,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/69 --- 4/2 --- 1/1

--------------------------------------------------------------
64/70
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/70 --- 4/2 --- 1/1

--------------------------------------------------------------
64/71
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4*a6,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/71 --- 4/2 --- 1/1

--------------------------------------------------------------
64/72
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4*a5*a6,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/72 --- 4/2 --- 1/1

--------------------------------------------------------------
64/73
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
32 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 3072
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/73 --- 8/3 --- 1/1

--------------------------------------------------------------
64/74
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 3072
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/74 --- 8/3 --- 1/1

--------------------------------------------------------------
64/75
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/75 --- 8/3 --- 1/1

--------------------------------------------------------------
64/76
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 3072
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/76 --- 8/3 --- 1/1

--------------------------------------------------------------
64/77
((a1,a2,a3,a4,a5,a6;a1^2=a4*a5,a2^2=a4,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 1536
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/77 --- 8/3 --- 1/1

--------------------------------------------------------------
64/78
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/78 --- 8/3 --- 1/1

--------------------------------------------------------------
64/79
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/79 --- 8/3 --- 1/1

--------------------------------------------------------------
64/80
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4*a5,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 3072
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/80 --- 8/3 --- 1/1

--------------------------------------------------------------
64/81
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4*a5,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/81 --- 8/3 --- 1/1

--------------------------------------------------------------
64/82
((a1,a2,a3,a4,a5,a6;a1^2=a4*a5*a6,a2^2=a4*a5,a3^2=a4,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

22 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 10752
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/82 --- 8/3 --- 1/1

--------------------------------------------------------------
64/83
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

ABELIAN

group is isomorphic to 2/1 x 4/1 x 8/1

--------------------------------------------------------------
64/84
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 2048
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/84 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/19

--------------------------------------------------------------
64/85
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=1,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a2, a4, a5, a6 ] , type 16/3
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 1024
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/85 --- 2/1 --- 1/1

group is isomorphic to 4/1 x 16/11

--------------------------------------------------------------
64/86
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a5,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a1, a4, a5, a6 ] , type 16/2
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 512
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/86 --- 2/1 --- 1/1

--------------------------------------------------------------
64/87
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a4 ] , type 2/1
Automorphism Group of size 1024
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/87 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/20

--------------------------------------------------------------
64/88
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/88 --- 4/2 --- 1/1

--------------------------------------------------------------
64/89
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/89 --- 4/2 --- 1/1

--------------------------------------------------------------
64/90
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/90 --- 4/2 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/46

--------------------------------------------------------------
64/91
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/1
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/91 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/92
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
8 elements of order 4
32 elements of order 8

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/92 --- 4/2 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/47

--------------------------------------------------------------
64/93
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/93 --- 4/2 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/48

--------------------------------------------------------------
64/94
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/1
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/9
Nilpotency class 3
Lower Central Series:  64/94 --- 4/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/95
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 1024
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/95 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/27

--------------------------------------------------------------
64/96
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 1024
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/96 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/28

--------------------------------------------------------------
64/97
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/97 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/98
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/98 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/99
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/99 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/100
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/100 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/101
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 256
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/101 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/31

--------------------------------------------------------------
64/102
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/1
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/102 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/103
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a4 ] , type 2/1
Automorphism Group of size 1024
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/103 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/21

--------------------------------------------------------------
64/104
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/104 --- 4/2 --- 1/1

--------------------------------------------------------------
64/105
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/105 --- 4/2 --- 1/1

--------------------------------------------------------------
64/106
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 2048
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/106 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/30

--------------------------------------------------------------
64/107
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4*a6,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 2048
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/107 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/29

--------------------------------------------------------------
64/108
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 1024
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/108 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/109
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/109 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/110
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=1,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
48 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/110 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/32

--------------------------------------------------------------
64/111
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=1,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
48 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/1
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/111 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/112
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a4,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/3
Commutator subgroup generated by [ a4 ] , type 2/1
Automorphism Group of size 512
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/112 --- 2/1 --- 1/1

--------------------------------------------------------------
64/113
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a4,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/113 --- 4/2 --- 1/1

--------------------------------------------------------------
64/114
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a4,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 256
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/114 --- 4/2 --- 1/1

--------------------------------------------------------------
64/115
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
20 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/2
Commutator subgroup generated by [ a4 ] , type 2/1
Automorphism Group of size 256
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/115 --- 2/1 --- 1/1

group is isomorphic to 8/1 x 8/4

--------------------------------------------------------------
64/116
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
20 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 128
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/116 --- 4/2 --- 1/1

--------------------------------------------------------------
64/117
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
20 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 256
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/117 --- 4/2 --- 1/1

--------------------------------------------------------------
64/118
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/118 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 4/1 x 16/12

--------------------------------------------------------------
64/119
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 256
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/119 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 4/1 x 16/13

--------------------------------------------------------------
64/120
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a5*a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/120 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 4/1 x 16/14

--------------------------------------------------------------
64/121
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a6,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/121 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/122
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a6,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/122 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/123
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a5*a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a6,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/123 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/124
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a5,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
20 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a5, a6 ] , type 8/1
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 128
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/124 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/125
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a5,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a6,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
20 elements of order 4
32 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/1
Commutator subgroup generated by [ a4, a6 ] , type 4/1
Automorphism Group of size 128
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/125 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/126
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=a4*a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
28 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/2
Commutator subgroup generated by [ a4 ] , type 2/1
Automorphism Group of size 768
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/126 --- 2/1 --- 1/1

group is isomorphic to 8/1 x 8/5

--------------------------------------------------------------
64/127
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a4,a3^2=a4*a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
28 elements of order 4
32 elements of order 8

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a4, a6 ] , type 4/2
Automorphism Group of size 256
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/127 --- 4/2 --- 1/1

--------------------------------------------------------------
64/128
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
16 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/128 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/129
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/129 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/130
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/130 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/131
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/131 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/132
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/132 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/133
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/133 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/134
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
27 elements of order 2
20 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/33
Nilpotency class 3
Lower Central Series:  64/134 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/135
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/33
Nilpotency class 3
Lower Central Series:  64/135 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/136
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/33
Nilpotency class 3
Lower Central Series:  64/136 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/137
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/33
Nilpotency class 3
Lower Central Series:  64/137 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/138
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
27 elements of order 2
36 elements of order 4

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 384
Inner automorphism group type 32/33
Nilpotency class 3
Lower Central Series:  64/138 --- 8/3 --- 2/1 --- 1/1

--------------------------------------------------------------
64/139
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
44 elements of order 4

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/3
Automorphism Group of size 384
Inner automorphism group type 32/33
Nilpotency class 3
Lower Central Series:  64/139 --- 8/3 --- 2/1 --- 1/1

--------------------------------------------------------------
64/140
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
27 elements of order 2
20 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/140 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/141
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4,a3^2=a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/141 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/142
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/142 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/143
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4,a3^2=a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/143 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/144
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4*a6,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/144 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/145
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4*a6,a3^2=a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/145 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/146
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/146 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/147
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4*a6,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/147 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/148
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4*a6,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/148 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/149
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/149 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/150
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4*a6,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/150 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/151
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4*a6,a3^2=1,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/151 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/152
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4,a3^2=1,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5*a6,[a1,a4]=a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 128
Inner automorphism group type 32/36
Nilpotency class 3
Lower Central Series:  64/152 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/153
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4*a6,a3^2=1,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5*a6,[a1,a4]=a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
8 elements of order 4
32 elements of order 8

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/36
Nilpotency class 3
Lower Central Series:  64/153 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/154
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4*a6,a3^2=1,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5*a6,[a1,a4]=a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
24 elements of order 4
32 elements of order 8

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 32/36
Nilpotency class 3
Lower Central Series:  64/154 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/155
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/155 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/156
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4,a3^2=a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/156 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/157
((a1,a2,a3,a4,a5,a6;a1^2=a4*a6,a2^2=a4,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/157 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/158
((a1,a2,a3,a4,a5,a6;a1^2=a4*a6,a2^2=a4,a3^2=a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/158 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/159
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4*a6,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/159 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/160
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4*a6,a3^2=a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/160 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/161
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a4,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/161 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/162
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a4*a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/162 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/163
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=a4,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/163 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/164
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a4,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/164 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/165
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a4*a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/165 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/166
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=a4,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=a6,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

19 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 256
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/166 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/167
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5,a3^2=a4,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5*a6,[a1,a4]=a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a4*a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/167 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/168
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a5,a3^2=a4,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5*a6,[a1,a4]=a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a4*a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/168 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/169
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5*a6,a3^2=a4,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5*a6,[a1,a4]=a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a4*a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/169 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/170
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5,a3^2=a4,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5*a6,[a1,a4]=a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a4*a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/170 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/171
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5*a6,a3^2=a4,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5*a6,[a1,a4]=a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a4*a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/171 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/172
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a5*a6,a3^2=a4,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5*a6,[a1,a4]=a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a4*a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/172 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/173
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 2048
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/173 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/174
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4*a6,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
35 elements of order 2
12 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 4096
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/174 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/175
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4*a6,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 4096
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/175 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/176
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4,a3^2=a5*a6,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
28 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/176 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/177
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a4,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
27 elements of order 2
20 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/177 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/178
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a4,a3^2=a5,a4^2=a6,a5^2=1,a6^2=1
,[a1,a2]=a4*a6,[a1,a3]=a5,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
36 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/178 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/179
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 2048
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/179 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/180
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4*a6,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/180 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/181
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4,a3^2=a5*a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 2048
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/181 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/182
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=a4,a3^2=a5,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a4,[a1,a3]=a5*a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
44 elements of order 4
16 elements of order 8

16 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/2
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/182 --- 8/2 --- 2/1 --- 1/1

--------------------------------------------------------------
64/183
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=1,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
16 elements of order 8
32 elements of order 16

ABELIAN

group is isomorphic to 2/1 x 2/1 x 16/1

--------------------------------------------------------------
64/184
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=1,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
16 elements of order 8
32 elements of order 16

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/2
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 256
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/184 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/22

--------------------------------------------------------------
64/185
((a1,a2,a3,a4,a5,a6;a1^2=a4,a2^2=1,a3^2=1,a4^2=a5,a5^2=a6,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
8 elements of order 4
16 elements of order 8
32 elements of order 16

40 conjugacy classes
Centre generated by [ a1, a4, a5, a6 ] , type 16/1
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 192
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/185 --- 2/1 --- 1/1

--------------------------------------------------------------
64/186
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=a5*a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a5,[a1,a3]=1,[a1,a4]=a5*a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5*a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
35 elements of order 2
4 elements of order 4
8 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/1
Automorphism Group of size 1024
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/186 --- 8/1 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/49

--------------------------------------------------------------
64/187
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=a5*a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a5,[a1,a3]=1,[a1,a4]=a5*a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5*a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
20 elements of order 4
8 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/1
Automorphism Group of size 512
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/187 --- 8/1 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/50

--------------------------------------------------------------
64/188
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=1,a4^2=a5*a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a5,[a1,a3]=1,[a1,a4]=a5*a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5*a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
36 elements of order 4
8 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/2
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/1
Automorphism Group of size 1024
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/188 --- 8/1 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/51

--------------------------------------------------------------
64/189
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a6,a4^2=a5*a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a5,[a1,a3]=1,[a1,a4]=a5*a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5*a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
20 elements of order 4
8 elements of order 8
16 elements of order 16

22 conjugacy classes
Centre generated by [ a3, a6 ] , type 4/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/1
Automorphism Group of size 256
Inner automorphism group type 16/12
Nilpotency class 4
Lower Central Series:  64/189 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/190
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=a5*a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a5,[a1,a3]=a6,[a1,a4]=a5*a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5*a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
27 elements of order 2
12 elements of order 4
8 elements of order 8
16 elements of order 16

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/1
Automorphism Group of size 256
Inner automorphism group type 32/23
Nilpotency class 4
Lower Central Series:  64/190 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/191
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=1,a4^2=a5*a6,a5^2=a6,a6^2=1
,[a1,a2]=a4*a5,[a1,a3]=a6,[a1,a4]=a5*a6,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5*a6,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
28 elements of order 4
8 elements of order 8
16 elements of order 16

16 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a4, a5, a6 ] , type 8/1
Automorphism Group of size 256
Inner automorphism group type 32/23
Nilpotency class 4
Lower Central Series:  64/191 --- 8/1 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/192
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

ABELIAN

group is isomorphic to 2/1 x 2/1 x 4/1 x 4/1

--------------------------------------------------------------
64/193
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
32 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/5
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 49152
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/193 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 2/1 x 16/9

--------------------------------------------------------------
64/194
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a5,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/5
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 49152
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/194 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 2/1 x 16/10

--------------------------------------------------------------
64/195
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 8192
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/195 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/16

--------------------------------------------------------------
64/196
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 4096
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/196 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 4/1 x 8/4

--------------------------------------------------------------
64/197
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a5,a3^2=a5*a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 12288
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/197 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 4/1 x 8/5

--------------------------------------------------------------
64/198
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a6,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/3
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 3072
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/198 --- 2/1 --- 1/1

group is isomorphic to 4/1 x 16/8

--------------------------------------------------------------
64/199
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

34 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 4096
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/199 --- 2/1 --- 1/1

--------------------------------------------------------------
64/200
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a5,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

34 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 12288
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/200 --- 2/1 --- 1/1

--------------------------------------------------------------
64/201
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=1,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

34 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5 ] , type 2/1
Automorphism Group of size 3072
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/201 --- 2/1 --- 1/1

--------------------------------------------------------------
64/202
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
39 elements of order 2
24 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 12288
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/202 --- 4/2 --- 1/1

group is isomorphic to 2/1 x 32/33

--------------------------------------------------------------
64/203
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
32 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 4096
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/203 --- 4/2 --- 1/1

group is isomorphic to 2/1 x 32/36

--------------------------------------------------------------
64/204
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a5,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 4096
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/204 --- 4/2 --- 1/1

group is isomorphic to 2/1 x 32/37

--------------------------------------------------------------
64/205
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 4096
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/205 --- 4/2 --- 1/1

group is isomorphic to 2/1 x 32/38

--------------------------------------------------------------
64/206
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/206 --- 4/2 --- 1/1

--------------------------------------------------------------
64/207
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 8192
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/207 --- 4/2 --- 1/1

group is isomorphic to 2/1 x 32/39

--------------------------------------------------------------
64/208
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 8192
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/208 --- 4/2 --- 1/1

group is isomorphic to 2/1 x 32/40

--------------------------------------------------------------
64/209
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5*a6,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 6144
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/209 --- 4/2 --- 1/1

group is isomorphic to 2/1 x 32/41

--------------------------------------------------------------
64/210
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/210 --- 4/2 --- 1/1

--------------------------------------------------------------
64/211
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
39 elements of order 2
24 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 49152
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/211 --- 4/2 --- 1/1

group is isomorphic to 2/1 x 32/34

--------------------------------------------------------------
64/212
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a5,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 16384
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/212 --- 4/2 --- 1/1

group is isomorphic to 2/1 x 32/35

--------------------------------------------------------------
64/213
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a6,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/213 --- 4/2 --- 1/1

--------------------------------------------------------------
64/214
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a6,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

28 conjugacy classes
Centre generated by [ a4, a5, a6 ] , type 8/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 8/3
Nilpotency class 2
Lower Central Series:  64/214 --- 4/2 --- 1/1

--------------------------------------------------------------
64/215
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
32 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/215 --- 4/2 --- 1/1

--------------------------------------------------------------
64/216
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
32 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/216 --- 4/2 --- 1/1

--------------------------------------------------------------
64/217
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/217 --- 4/2 --- 1/1

--------------------------------------------------------------
64/218
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/218 --- 4/2 --- 1/1

--------------------------------------------------------------
64/219
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/219 --- 4/2 --- 1/1

--------------------------------------------------------------
64/220
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/220 --- 4/2 --- 1/1

--------------------------------------------------------------
64/221
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/221 --- 4/2 --- 1/1

--------------------------------------------------------------
64/222
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/222 --- 4/2 --- 1/1

--------------------------------------------------------------
64/223
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5*a6,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/223 --- 4/2 --- 1/1

--------------------------------------------------------------
64/224
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 6144
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/224 --- 4/2 --- 1/1

--------------------------------------------------------------
64/225
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a5,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
56 elements of order 4

22 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/225 --- 4/2 --- 1/1

--------------------------------------------------------------
64/226
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
35 elements of order 2
28 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/226 --- 4/2 --- 1/1

group is isomorphic to 8/4 x 8/4

--------------------------------------------------------------
64/227
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
27 elements of order 2
36 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/227 --- 4/2 --- 1/1

--------------------------------------------------------------
64/228
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
44 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/228 --- 4/2 --- 1/1

--------------------------------------------------------------
64/229
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
44 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1536
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/229 --- 4/2 --- 1/1

--------------------------------------------------------------
64/230
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a5,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
52 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 3072
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/230 --- 4/2 --- 1/1

group is isomorphic to 8/4 x 8/5

--------------------------------------------------------------
64/231
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5,a3^2=a5,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
27 elements of order 2
36 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 3072
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/231 --- 4/2 --- 1/1

--------------------------------------------------------------
64/232
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
44 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/232 --- 4/2 --- 1/1

--------------------------------------------------------------
64/233
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
52 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/233 --- 4/2 --- 1/1

--------------------------------------------------------------
64/234
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5*a6,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
44 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 512
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/234 --- 4/2 --- 1/1

--------------------------------------------------------------
64/235
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a5*a6,a3^2=1,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
52 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/235 --- 4/2 --- 1/1

--------------------------------------------------------------
64/236
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=a5,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
44 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/236 --- 4/2 --- 1/1

--------------------------------------------------------------
64/237
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a5*a6,a3^2=a5,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
52 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/237 --- 4/2 --- 1/1

--------------------------------------------------------------
64/238
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a5,a3^2=a6,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
60 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 3072
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/238 --- 4/2 --- 1/1

--------------------------------------------------------------
64/239
((a1,a2,a3,a4,a5,a6;a1^2=a5*a6,a2^2=a5,a3^2=a6,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
60 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 18432
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/239 --- 4/2 --- 1/1

group is isomorphic to 8/5 x 8/5

--------------------------------------------------------------
64/240
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a5*a6,a3^2=a6,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
44 elements of order 4

25 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 2048
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/240 --- 4/2 --- 1/1

--------------------------------------------------------------
64/241
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5*a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5*a6,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
27 elements of order 2
36 elements of order 4

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1536
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/241 --- 4/2 --- 1/1

--------------------------------------------------------------
64/242
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a5,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5*a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5*a6,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
27 elements of order 2
36 elements of order 4

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 9216
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/242 --- 4/2 --- 1/1

--------------------------------------------------------------
64/243
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5*a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5*a6,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
19 elements of order 2
44 elements of order 4

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/243 --- 4/2 --- 1/1

--------------------------------------------------------------
64/244
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a5,a3^2=a5,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5*a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5*a6,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
11 elements of order 2
52 elements of order 4

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 1024
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/244 --- 4/2 --- 1/1

--------------------------------------------------------------
64/245
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=a6,a3^2=a6,a4^2=a5,a5^2=1,a6^2=1
,[a1,a2]=a5,[a1,a3]=a6,[a1,a4]=a5*a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a5*a6,[a2,a4]=a5,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
3 elements of order 2
60 elements of order 4

19 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/2
Automorphism Group of size 15360
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/245 --- 4/2 --- 1/1

--------------------------------------------------------------
64/246
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

ABELIAN

group is isomorphic to 2/1 x 2/1 x 2/1 x 8/1

--------------------------------------------------------------
64/247
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 6144
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/247 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 2/1 x 16/11

--------------------------------------------------------------
64/248
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

40 conjugacy classes
Centre generated by [ a1, a4, a5, a6 ] , type 16/2
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 1536
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/248 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/17

--------------------------------------------------------------
64/249
((a1,a2,a3,a4,a5,a6;a1^2=a5,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
16 elements of order 4
32 elements of order 8

34 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/1
Commutator subgroup generated by [ a6 ] , type 2/1
Automorphism Group of size 1536
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/249 --- 2/1 --- 1/1

--------------------------------------------------------------
64/250
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
39 elements of order 2
8 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a4, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 12288
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/250 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 2/1 x 16/12

--------------------------------------------------------------
64/251
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a4, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 6144
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/251 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 2/1 x 16/13

--------------------------------------------------------------
64/252
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
7 elements of order 2
40 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a4, a6 ] , type 8/3
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 12288
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/252 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 2/1 x 16/14

--------------------------------------------------------------
64/253
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a6,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

28 conjugacy classes
Centre generated by [ a3, a4, a6 ] , type 8/2
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 1024
Inner automorphism group type 8/4
Nilpotency class 3
Lower Central Series:  64/253 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/26

--------------------------------------------------------------
64/254
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
16 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/254 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/44

--------------------------------------------------------------
64/255
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/2
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 1024
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/255 --- 4/1 --- 2/1 --- 1/1

group is isomorphic to 2/1 x 32/45

--------------------------------------------------------------
64/256
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=a6,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=a6,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a4, a6 ] , type 4/1
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 512
Inner automorphism group type 16/6
Nilpotency class 3
Lower Central Series:  64/256 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/257
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
16 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 768
Inner automorphism group type 32/8
Nilpotency class 3
Lower Central Series:  64/257 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/258
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
24 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 384
Inner automorphism group type 32/8
Nilpotency class 3
Lower Central Series:  64/258 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/259
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a5*a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=a6,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=a6,[a2,a6]=1
,[a3,a4]=a6,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
32 elements of order 4
16 elements of order 8

22 conjugacy classes
Centre generated by [ a6 ] , type 2/1
Commutator subgroup generated by [ a5, a6 ] , type 4/1
Automorphism Group of size 768
Inner automorphism group type 32/8
Nilpotency class 3
Lower Central Series:  64/259 --- 4/1 --- 2/1 --- 1/1

--------------------------------------------------------------
64/260
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
32 elements of order 4

ABELIAN

group is isomorphic to 2/1 x 2/1 x 2/1 x 2/1 x 4/1

--------------------------------------------------------------
64/261
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
47 elements of order 2
16 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/5
Commutator subgroup generated by [ a6 ] , type 2/1
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/261 --- 2/1 --- 1/1

--------------------------------------------------------------
64/262
((a1,a2,a3,a4,a5,a6;a1^2=a6,a2^2=a6,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
15 elements of order 2
48 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/5
Commutator subgroup generated by [ a6 ] , type 2/1
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/262 --- 2/1 --- 1/1

--------------------------------------------------------------
64/263
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
32 elements of order 4

40 conjugacy classes
Centre generated by [ a3, a4, a5, a6 ] , type 16/4
Commutator subgroup generated by [ a6 ] , type 2/1
Inner automorphism group type 4/2
Nilpotency class 2
Lower Central Series:  64/263 --- 2/1 --- 1/1

--------------------------------------------------------------
64/264
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
39 elements of order 2
24 elements of order 4

34 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a6 ] , type 2/1
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/264 --- 2/1 --- 1/1

--------------------------------------------------------------
64/265
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=a6,a3^2=a6,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
23 elements of order 2
40 elements of order 4

34 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/2
Commutator subgroup generated by [ a6 ] , type 2/1
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/265 --- 2/1 --- 1/1

--------------------------------------------------------------
64/266
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=a6,a6^2=1
,[a1,a2]=a6,[a1,a3]=1,[a1,a4]=a6,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=a6,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
31 elements of order 2
32 elements of order 4

34 conjugacy classes
Centre generated by [ a5, a6 ] , type 4/1
Commutator subgroup generated by [ a6 ] , type 2/1
Inner automorphism group type 16/5
Nilpotency class 2
Lower Central Series:  64/266 --- 2/1 --- 1/1

--------------------------------------------------------------
64/267
((a1,a2,a3,a4,a5,a6;a1^2=1,a2^2=1,a3^2=1,a4^2=1,a5^2=1,a6^2=1
,[a1,a2]=1,[a1,a3]=1,[a1,a4]=1,[a1,a5]=1,[a1,a6]=1
,[a2,a3]=1,[a2,a4]=1,[a2,a5]=1,[a2,a6]=1
,[a3,a4]=1,[a3,a5]=1,[a3,a6]=1
,[a4,a5]=1,[a4,a6]=1
,[a5,a6]=1

))
63 elements of order 2

ABELIAN

```