About this representation

Group Co3
Group generators Standard generators
Number of points 48600
Primitivity information Primitive
Transitivity degree 1
Rank 8
Suborbit lengths 1, 253, 506, 1771, 7590, 8855, 14168, 15456
Character 1+23+253b+275+2024+5544+8855+31625c
Point stabiliser M23
Contributed by Not recorded

Download

This representation is available in the following formats:

MeatAxe a b
MeatAxe binary a b
GAP a b
GAP a, b
Magma a, b

On conjugacy classes

Conjugacy class Fixed points Cycle type
1A 48600
2A 1080 223760
2B 0 224300
3A 0 316200
3B 162 316146
3C 0 316200
4A 0 2540, 411880
4B 48 2516, 411880
5A 0 59720
5B 20 59716
6A 0 3360, 67920
6B 0 3360, 67920
6C 18 272, 3354, 67896
6D 0 281, 68073
6E 0 68100
7A 6 76942
8A 0 224, 4258, 85940
8B 0 224, 4258, 85940
8C 4 222, 4258, 85940
9A 0 95400
9B 0 95400
10A 0 5216, 104752
10B 0 210, 104858
11A 2 114418
11B 2 114418
12A 0 6180, 123960
12B 0 316, 6172, 123960
12C 0 29, 436, 6177, 123948
14A 2 22, 7154, 143394
15A 0 153240
15B 2 36, 532, 153228
18A 0 9120, 182640
20A 0 10108, 202376
20B 0 10108, 202376
21A 0 32, 212314
22A 0 2, 222209
22B 0 2, 222209
23A 1 232113
23B 1 232113
24A 0 68, 1286, 241980
24B 0 68, 1286, 241980
30A 0 1572, 301584

Checks applied

Check Description Date Checked by Result
Semi-presentation Check against a semi-presentation. If this fails, then the representation is not on standard generators, and may generate the wrong group. Note that the semi-presentation itself is not checked here. Jul 4, 2006 certify.pl version 0.05 Pass
Order Check that the elements generate a group of the correct order. Jul 4, 2006 permanalyse version 0.03 Pass
Number of points Check whether the permutation representation is acting on the stated number of points. Jul 4, 2006 certify.pl version 0.05 Pass
Files exist Check whether files exist (where stated). Jul 4, 2006 certify.pl version 0.05 Pass