About this representation

Group M24
Group generators Standard generators
Number of points 3795
Primitivity information Primitive
Transitivity degree 1
Rank 5
Suborbit lengths 1, 42, 56, 1008, 2688
Character 1 + 252 + 483 + 1035a + 2024
Point stabiliser 26:(L3(2) × S3)
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 3795
2A 99 21848
2B 75 21860
3A 15 31260
3B 15 31260
4A 19 240, 4924
4B 7 246, 4924
4C 7 234, 4930
5A 0 5759
6A 3 26, 332, 6614
6B 3 26, 324, 6618
7A 1 7542
7B 1 7542
8A 1 23, 423, 8462
10A 0 515, 10372
11A 0 11345
12A 1 2, 36, 43, 613, 12307
12B 1 2, 32, 43, 611, 12309
14A 1 714, 14264
14B 1 714, 14264
15A 0 53, 15252
15B 0 53, 15252
21A 1 72, 21180
21B 1 72, 21180
23A 0 23165
23B 0 23165

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