About this representation
| Group |
M24 |
| Group generators |
Standard generators |
| Number of
points |
1288 |
| Primitivity
information |
Primitive |
|
Transitivity degree |
1 |
| Rank |
3 |
| Suborbit
lengths |
1, 495, 792 |
|
Character |
1 + 252 + 1035a |
| Point
stabiliser |
M12:2 |
| Contributed
by |
Not recorded |
Download
This representation is available in the following
formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A |
1288 |
|
| 2A |
56 |
2616 |
| 2B |
48 |
2620 |
| 3A |
10 |
3426 |
| 3B |
7 |
3427 |
| 4A |
8 |
224, 4308 |
| 4B |
4 |
226, 4308 |
| 4C |
4 |
222, 4310 |
| 5A |
3 |
5257 |
| 6A |
2 |
24, 318,
6204 |
| 6B |
3 |
22, 315,
6206 |
| 7A |
0 |
7184 |
| 7B |
0 |
7184 |
| 8A |
2 |
2, 413,
8154 |
| 10A |
3 |
59, 10124 |
| 11A |
1 |
11117 |
| 12A |
2 |
32, 42,
68, 12102 |
| 12B |
1 |
2, 3, 4, 67,
12103 |
| 14A |
0 |
78, 1488 |
| 14B |
0 |
78, 1488 |
| 15A |
0 |
3, 52, 1585 |
| 15B |
0 |
3, 52, 1585 |
| 21A |
0 |
7, 2161 |
| 21B |
0 |
7, 2161 |
| 23A |
0 |
2356 |
| 23B |
0 |
2356 |
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 |