ATLAS: Fischer group F24

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

Standard generators

Standard generators of the Fischer group F24' 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 3F24 are pre-images A and B where A has order 2, and AB has order 29.
Standard generators of the automorphism group F24':2 are c and d where c is in class 2C, d is in class 8D, cd has order 29.
Standard generators of 3F24:2 are preimages C and D, where D ???.
A pair of generators conjugate to a, b can be obtained as
a' = (cdd)^{10}, b' = (cdcdd)^{-10}(cdcdcddcdcdd)^8(cdcdd)^{10}.

Representations

The representations of F24' available are The representations of 3F24' available are The representations of F24':2 available are The representations of 3F24:2 available are

Maximal subgroups

The maximal subgroups of the simple group F24' are The maximal subgroups of the automorphism group F24':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.
- Return to main ATLAS page. - Last updated 29.10.99

- R.A.Wilson@bham.ac.uk
- richard@ukonline.co.uk