About this representation
Group
 M_{23}

Group generators
 Standard generators

Number of points
 23

Primitivity information
 Primitive

Transitivity degree
 4

Rank
 2

Suborbit lengths
 1, 22

Character
 1 + 22

Point stabiliser
 M_{22}

Notes
 This representation is 4transitive, and acts on an S(4, 7, 23) Steiner system. There are 253 blocks, one of which is {1, 2, 3, 4, 5, 11, 17}. You can find the rest in GAP as follows:
G := Group(b11,b21);
B := [1, 2, 3, 4, 5, 11, 17];
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
 23


2A
 7
 2^{8}

3A
 5
 3^{6}

4A
 3
 2^{2}, 4^{4}

5A
 3
 5^{4}

6A
 1
 2^{2}, 3^{2}, 6^{2}

7A
 2
 7^{3}

7B
 2
 7^{3}

8A
 1
 2, 4, 8^{2}

11A
 1
 11^{2}

11B
 1
 11^{2}

14A
 0
 2, 7, 14

14B
 0
 2, 7, 14

15A
 0
 3, 5, 15

15B
 0
 3, 5, 15

23A
 0
 23

23B
 0
 23

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

Semipresentation
 Check against a semipresentation. If this fails, then the representation is not on standard generators, and may generate the wrong group. Note that the semipresentation 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
