ATLAS: Fischer group Fi24'

Order = 1255205709190661721292800 = 221.316.52.73.11.13.17.23.29.
Mult = 3.
Out = 2.

The following information is available for Fi24':


Standard generators

Standard generators of the Fischer group Fi24' are a and b where a is in class 2A, b is in class 3E, ab has order 29 and abababb has order 33.
Standard generators of the triple cover 3.Fi24' are preimages A and B where A has order 2 and AB has order 29.

Standard generators of the automorphism group Fi24 = Fi24':2 are c and d where c is in class 2C, d is in class 8D and cd has order 29.
Standard generators of 3.Fi24':2 are preimages C and D where D has order 29.

A pair of generators conjugate to a, b can be obtained as
a' = (cdd)10, b' = (cdcdd)−10(cdcdcddcdcdd)8(cdcdd)10.


Black box algorithms

Finding generators

To find standard generators for Fi24':

This algorithm is available in computer readable format: finder for Fi24'.

To find standard generators of Fi24 = Fi24':2:

This algorithm is available in computer readable format: finder for Fi24':2.

Checking generators

To check that elements x and y of Fi24' are standard generators:

This algorithm is available in computer readable format: checker for Fi24'.

To check that elements x and y of Fi24':2 are standard generators:

This algorithm is available in computer readable format: checker for Fi24':2.

Representations

The representations of Fi24' available are: The representations of 3.Fi24' available are: The representations of Fi24 = Fi24':2 available are: The representations of 3.Fi24':2 available are:

Maximal subgroups

The maximal subgroups of the simple group Fi24' are: The maximal subgroups of the automorphism group Fi24 = Fi24':2 are:

Conjugacy classes

A set of generators for the maximal cyclic subgroups up to automorphism can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements, or their images under an outer automorphism. Problems of algebraic conjugacy are also not dealt with.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Sporadic groups page Go to sporadic groups page.
Old Fi24\' page Go to old Fi24' page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 16th June 2000.
Last updated 16.05.06 by JNB.
Information checked to Level 0 on 16.06.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.