About this representation
| Group |
M11 |
| Group generators |
Standard generators |
| Number of
points |
11 |
| Primitivity
information |
Primitive |
|
Transitivity degree |
4 |
| Rank |
2 |
| Suborbit
lengths |
1, 10 |
|
Character |
1 + 10a |
| Point
stabiliser |
M10 =
A6.23 |
| Notes |
This representation acts 4-transitively and preserves an
S(4, 5, 11) Steiner system. One of the 66 blocks is {1,
2, 3, 4, 5}, and the others can be found with the GAP
commands:
G := Group(a, b); # Where a and b are the generators
B := [1, 2, 3, 4, 5];
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 |
11 |
|
| 2A |
3 |
24 |
| 3A |
2 |
33 |
| 4A |
3 |
42 |
| 5A |
1 |
52 |
| 6A |
0 |
2, 3, 6 |
| 8A |
1 |
2, 8 |
| 8B |
1 |
2, 8 |
| 11A |
0 |
11 |
| 11B |
0 |
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 |