About this representation
| Group |
HS:2 |
| Group generators |
Standard generators |
| Number of
points |
352 |
| Primitivity
information |
Transitive but imprimitive |
|
Transitivity degree |
1 |
| Rank |
4 |
| Suborbit
lengths |
1, 50, 126, 175 |
| Contributed
by |
Not recorded |
Download
This representation is available in the following
formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A |
352 |
|
| 2A |
32 |
2160 |
| 2B |
24 |
2164 |
| 3A |
10 |
3114 |
| 4A |
32 |
480 |
| 4B |
0 |
216, 480 |
| 4C |
8 |
212, 480 |
| 5A |
2 |
570 |
| 5B |
12 |
568 |
| 5C |
2 |
570 |
| 6A |
6 |
22, 36,
654 |
| 6B |
2 |
24, 310,
652 |
| 7A |
2 |
750 |
| 8A |
0 |
48, 840 |
| 8B |
4 |
22, 46,
840 |
| 10A |
2 |
56, 1032 |
| 10B |
4 |
24, 54,
1032 |
| 11A |
0 |
1132 |
| 12A |
2 |
310, 42,
1226 |
| 15A |
0 |
34, 52,
1522 |
| 20A |
2 |
56, 2016 |
| 2C |
0 |
2176 |
| 2D |
0 |
2176 |
| 4D |
0 |
216, 480 |
| 4E |
0 |
216, 480 |
| 4F |
0 |
212, 482 |
| 6C |
0 |
25, 657 |
| 6D |
0 |
25, 657 |
| 6E |
0 |
25, 657 |
| 8C |
0 |
48, 840 |
| 8D |
0 |
48, 840 |
| 10C |
0 |
26, 1034 |
| 10D |
0 |
2, 1035 |
| 12B |
0 |
2, 42, 65,
1226 |
| 14A |
0 |
2, 1425 |
| 20B |
0 |
22, 42,
102, 2016 |
| 20C |
0 |
2, 103,
2016 |
| 20D |
0 |
2, 103,
2016 |
| 30A |
0 |
62, 10,
3011 |
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 |