About this representation

Group M23
Group generators Standard generators
Number of points 1288
Primitivity information Primitive
Transitivity degree 1
Rank 4
Suborbit lengths 1, 165, 330, 792
Character 1 + 22 + 230 + 1035
Point stabiliser M11
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 1288
2A 56 2616
3A 10 3426
4A 4 226, 4308
5A 3 5257
6A 2 24, 318, 6204
7A 0 7184
7B 0 7184
8A 2 2, 413, 8154
11A 1 11117
11B 1 11117
14A 0 78, 1488
14B 0 78, 1488
15A 0 3, 52, 1585
15B 0 3, 52, 1585
23A 0 2356
23B 0 2356

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