About this representation
| Group |
McL |
| Group generators |
Standard generators |
| Number of
points |
15400 |
|
Distinguishing letter |
a |
|
Description |
Cosets of
31+42S5 |
| Primitivity
information |
Primitive |
|
Transitivity degree |
1 |
| Rank |
5 |
| Suborbit
lengths |
1, 90, 1215, 2430, 11664 |
|
Character |
1 + 252 + 4500 + 5103 + 5544 |
| Point
stabiliser |
31+4:2.S5 |
| Contributed
by |
Not recorded |
Download
This representation is available in the following
formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A |
15400 |
|
| 2A |
56 |
27672 |
| 3A |
91 |
35103 |
| 3B |
10 |
35130 |
| 4A |
12 |
222, 43836 |
| 5A |
25 |
53075 |
| 5B |
0 |
53080 |
| 6A |
11 |
240, 315,
62544 |
| 6B |
2 |
24, 318,
62556 |
| 7A |
0 |
72200 |
| 7B |
0 |
72200 |
| 8A |
2 |
25, 411,
81918 |
| 9A |
1 |
330, 91701 |
| 9B |
1 |
330, 91701 |
| 10A |
1 |
212, 511,
101532 |
| 11A |
0 |
111400 |
| 11B |
0 |
111400 |
| 12A |
3 |
24, 33,
420, 66, 121272 |
| 14A |
0 |
78, 141096 |
| 14B |
0 |
78, 141096 |
| 15A |
1 |
38, 518,
151019 |
| 15B |
1 |
38, 518,
151019 |
| 30A |
1 |
52, 64,
108, 153, 30508 |
| 30B |
1 |
52, 64,
108, 153, 30508 |
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 |