ATLAS: Mathieu group M24

Order = 244823040 = 210.33.5.7.11.23.
Mult = 1.
Out = 1.

Standard generators

Standard generators of the Mathieu group M24 are a and b where a is in class 2B, b is in class 3A, ab has order 23 and abababbababbabb has order 4.

Black box algorithms

To find standard generators for M24:

Presentation

A presentation of M24 on its standard generators is given below.

< a, b | a2 = b3 = (ab)23 = [a, b]12 = [a, bab]5 = (ababab-1)3(abab-1ab-1)3 = (ab(abab-1)3)4 = 1 >.


Representations

The representations of M24 available are:

Maximal subgroups

The maximal subgroups of M24 are as follows. Words provided by Peter Walsh, implemented and checked by Ibrahim Suleiman.

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.
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Last updated 21st December 1999,
R.A.Wilson, R.A.Parker and J.N.Bray