About this representation

Group M23
Group generators Standard generators
Number of points 1771
Primitivity information Primitive
Transitivity degree 1
Rank 8
Suborbit lengths 1, 20, 60, 90, 160, 4803
Character 1 + 22 + 2.230 + 253 + 1035
Point stabiliser 24:(3 A5):2
Contributed by Not recorded

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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 1771
2A 91 2840
3A 16 3585
4A 7 242, 4420
5A 1 5354
6A 4 26, 329, 6278
7A 0 7253
7B 0 7253
8A 1 23, 421, 8210
11A 0 11161
11B 0 11161
14A 0 713, 14120
14B 0 713, 14120
15A 1 53, 15117
15B 1 53, 15117
23A 0 2377
23B 0 2377

Checks applied

Check Description Date Checked by Result
Presentation Check against the relations in a presentation. If this test passes, then the group is of the correct isomorphism type, and the generators are those stated. Note that the presentation itself is not checked here. Aug 2, 2006 certify.pl version 0.05 Pass
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 18, 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