ATLAS: Mathieu group M23

Order = 10200960.
Mult = 1.
Out = 1.

Standard generators

Standard generators of the Mathieu group M23 are a and b where a has order 2, b has order 4, ab has order 23, and ababababbababbabb has order 8.

Black box algorithms

To find standard generators for M23:


The representations available are as follows. They should be in Atlas order, defined by setting ab in 23B, abababb in 15A, abababbb in 7A and ababababb in 11B.

Maximal subgroups

The maximal subgroups of M23 are as follows.

Conjugacy classes

A set of generators for the maximal cyclic subgroups can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements. Problems of algebraic conjugacy are not yet dealt with.
- Last updated 23.03.99