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:
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
|