group size
16
autgroup size
64
Autgroup [ 64, 138 ]
inner autgroup size
4
16 symmetries, 11 types

1
[ (5,6), (1,2)(3,4), (2,4), (1,3)(2,4) ] -> [ (5,6), (1,2)(3,4)(5,6), (2,4), (1,3)(2,4) ]

1	1	maps to		1	1
2	2	maps to		2	2
4	3	maps to		4	3
5	4	maps to		7	5
7	5	maps to		5	4
9	6	maps to		9	6
10	7	maps to		10	7
12	8	maps to		13	8
14	9	maps to		15	10
15	10	maps to		14	9
16	11	maps to		16	11

2
[ (5,6), (1,2)(3,4), (2,4), (1,3)(2,4) ] -> [ (5,6), (1,4)(2,3)(5,6), (2,4), (1,3)(2,4) ]

1	1	maps to		1	1
2	2	maps to		2	2
4	3	maps to		4	3
5	4	maps to		8	5
7	5	maps to		6	4
9	6	maps to		9	6
10	7	maps to		10	7
12	8	maps to		12	8
14	9	maps to		15	10
15	10	maps to		14	9
16	11	maps to		16	11

3
[ (5,6), (1,2)(3,4), (2,4), (1,3)(2,4) ] -> [ (5,6), (1,2)(3,4)(5,6), (1,3), (1,3)(2,4) ]

1	1	maps to		1	1
2	2	maps to		3	2
4	3	maps to		4	3
5	4	maps to		7	5
7	5	maps to		5	4
9	6	maps to		9	6
10	7	maps to		11	7
12	8	maps to		13	8
14	9	maps to		15	10
15	10	maps to		14	9
16	11	maps to		16	11

4
[ (5,6), (1,2)(3,4), (2,4), (1,3)(2,4) ] -> [ (5,6), (1,4)(2,3)(5,6), (1,3), (1,3)(2,4) ]

1	1	maps to		1	1
2	2	maps to		3	2
4	3	maps to		4	3
5	4	maps to		8	5
7	5	maps to		6	4
9	6	maps to		9	6
10	7	maps to		11	7
12	8	maps to		12	8
14	9	maps to		15	10
15	10	maps to		14	9
16	11	maps to		16	11


Subgroup of the autgroup compatible with sym structure: Size: 8
Quotient: Z2