About this representation
| Group |
HS |
| Group generators |
Standard generators |
| Number of
points |
1100 |
|
Distinguishing letter |
b |
| Primitivity
information |
Primitive |
|
Transitivity degree |
1 |
| Rank |
5 |
| Suborbit
lengths |
1, 28, 105, 336, 630 |
| Point
stabiliser |
S8 |
| Contributed
by |
Not recorded |
Download
This representation is available in the following
formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A |
1100 |
|
| 2A |
60 |
2520 |
| 2B |
32 |
2534 |
| 3A |
11 |
3363 |
| 4A |
40 |
210, 4260 |
| 4B |
16 |
222, 4260 |
| 4C |
4 |
228, 4260 |
| 5A |
0 |
5220 |
| 5B |
10 |
5218 |
| 5C |
0 |
5220 |
| 6A |
5 |
23, 39,
6177 |
| 6B |
3 |
24, 319,
6172 |
| 7A |
1 |
7157 |
| 8A |
2 |
27, 411,
8130 |
| 8B |
0 |
22, 414,
8130 |
| 8C |
0 |
22, 414,
8130 |
| 10A |
0 |
512, 10104 |
| 10B |
2 |
24, 56,
10106 |
| 11A |
0 |
11100 |
| 11B |
0 |
11100 |
| 12A |
1 |
2, 313, 42,
63, 1286 |
| 15A |
1 |
33, 52,
1572 |
| 20A |
0 |
58, 102,
2052 |
| 20B |
0 |
58, 102,
2052 |
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 |