About this representation
| Group |
M12 |
| Group generators |
Standard generators |
| Number of
points |
12 |
|
Distinguishing letter |
b |
| Primitivity
information |
Primitive |
|
Transitivity degree |
5 |
| Rank |
2 |
| Suborbit
lengths |
1, 11 |
| Point
stabiliser |
M11 |
| Notes |
This representation acts 5-transitively on the points of
an S(5, 6, 12) Steiner system. One of the 132 blocks is
{1, 2, 3, 4, 5, 6}, and the others can be found with the
GAP commands:
G := Group(b11, b21);
B := [1, 2, 3, 4, 5, 6];
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 |
12 |
|
| 2A |
0 |
26 |
| 2B |
4 |
24 |
| 3A |
3 |
33 |
| 3B |
0 |
34 |
| 4A |
4 |
42 |
| 4B |
0 |
22, 42 |
| 5A |
2 |
52 |
| 6A |
0 |
62 |
| 6B |
1 |
2, 3, 6 |
| 8A |
2 |
2, 8 |
| 8B |
0 |
4, 8 |
| 10A |
0 |
2, 10 |
| 11A |
1 |
11 |
| 11B |
1 |
11 |
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 |