About this representation

Group M23
Group generators Standard generators
Number of points 253
Distinguishing letter a
Primitivity information Primitive
Transitivity degree 1
Rank 3
Suborbit lengths 1, 42, 210
Character 1 + 22 + 230
Point stabiliser L3(4):22
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 253
2A 29 2112
3A 10 381
4A 5 212, 456
5A 3 550
6A 2 24, 39, 636
7A 1 736
7B 1 736
8A 1 22, 46, 828
11A 0 1123
11B 0 1123
14A 1 74, 1416
14B 1 74, 1416
15A 0 3, 52, 1516
15B 0 3, 52, 1516
23A 0 2311
23B 0 2311

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