ATLAS: Mathieu group M24

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

The following information is available for M24:

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

Finding generators

To find standard generators for M24: This algorithm is available in computer readable format: finder for M24.

Checking generators

To check that elements x and y of M24 are standard generators: This algorithm is available in computer readable format: checker for M24.


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 >.

This presentation is available in Magma format as follows: M24 on a and b.


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.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Sporadic groups page Go to sporadic groups page.
Old M24 page Go to old M24 page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 7th June 2000.
Last updated 21.12.04 by SJN.
Information checked to Level 0 on 07.06.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.