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
|