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
|
Download
This representation is available in the following formats:
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
|