About this representation
| Group |
M24 |
| Group generators |
Standard generators |
| Number of
points |
24 |
| Primitivity
information |
Primitive |
|
Transitivity degree |
5 |
| Rank |
2 |
| Suborbit
lengths |
1, 23 |
|
Character |
1 + 23 |
| Point
stabiliser |
M23 |
| Notes |
This representation is 5-transitive, acting on a S(5, 8,
24) Steiner system. There are 759 blocks, one of which is
{1, 2, 3, 4, 5, 11, 17, 24}. You can find the others in
GAP with the command:
B := [1, 2, 3, 4, 5, 11, 17, 24];
G := Group(b11, b21);
O := Orbit(G, B, OnSets);
|
| Contributed
by |
Not recorded |
Download
This representation is available in the following
formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A |
24 |
|
| 2A |
8 |
28 |
| 2B |
0 |
212 |
| 3A |
6 |
36 |
| 3B |
0 |
38 |
| 4A |
0 |
24, 44 |
| 4B |
4 |
22, 44 |
| 4C |
0 |
46 |
| 5A |
4 |
54 |
| 6A |
2 |
22, 32,
62 |
| 6B |
0 |
64 |
| 7A |
3 |
73 |
| 7B |
3 |
73 |
| 8A |
2 |
2, 4, 82 |
| 10A |
0 |
22, 102 |
| 11A |
2 |
112 |
| 12A |
0 |
2, 4, 6, 12 |
| 12B |
0 |
122 |
| 14A |
1 |
2, 7, 14 |
| 14B |
1 |
2, 7, 14 |
| 15A |
1 |
3, 5, 15 |
| 15B |
1 |
3, 5, 15 |
| 21A |
0 |
3, 21 |
| 21B |
0 |
3, 21 |
| 23A |
1 |
23 |
| 23B |
1 |
23 |
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 |