About this representation
| Group |
M22 |
| Group generators |
Standard generators |
| Number of
points |
22 |
| Primitivity
information |
Primitive |
|
Transitivity degree |
3 |
| Rank |
2 |
| Suborbit
lengths |
1, 21 |
| Notes |
The group M22 acts 3-transitively on the 22 points of a
S(3, 6, 22) Steiner system. One of the 77 blocks is {1,
2, 3, 10, 18, 20}, and the others can be found with the
GAP commands:
G := Group(b11, b21);
B := [1, 2, 3, 10, 18, 20];
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 |
22 |
|
| 2A |
6 |
28 |
| 3A |
4 |
36 |
| 4A |
2 |
22, 44 |
| 4B |
2 |
22, 44 |
| 5A |
2 |
54 |
| 6A |
0 |
22, 32,
62 |
| 7A |
1 |
73 |
| 7B |
1 |
73 |
| 8A |
0 |
2, 4, 82 |
| 11A |
0 |
112 |
| 11B |
0 |
112 |
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 |