About this representation

Group M24
Group generators Standard generators
Number of points 2024
Primitivity information Primitive
Transitivity degree 1
Rank 5
Suborbit lengths 1, 63, 210, 630, 1120
Character 1 + 23 + 252 + 483 + 1265
Point stabiliser L3(4):3:22 = M21:S3
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 2024
2A 120 2952
2B 0 21012
3A 26 3666
3B 8 3672
4A 0 260, 4476
4B 12 254, 4476
4C 0 4506
5A 4 5404
6A 6 210, 338, 6314
6B 0 24, 6336
7A 1 7289
7B 1 7289
8A 2 25, 427, 8238
10A 0 22, 10202
11A 0 11184
12A 0 23, 45, 619, 12157
12B 0 42, 12168
14A 1 717, 14136
14B 1 717, 14136
15A 1 3, 55, 15133
15B 1 3, 55, 15133
21A 1 7, 2196
21B 1 7, 2196
23A 0 2388
23B 0 2388

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