ATLAS: Fischer group Fi22

Order = 64561751654400 = 217.39.52.7.11.13.
Mult = 6.
Out = 2.

Standard generators and automorphisms

Standard generators of the Fischer group Fi22 are a and b where a is in class 2A, b has order 13, ab has order 11 and ababababbababbabb has order 12.

The outer automorphism may be realised by mapping (a, b) to a, (ab)^4bb(ab)^-4.

Standard generators of the automorphism group Fi22:2 are c and d where c is in class 2A, d is in class 18E and cd has order 42.


Black box algorithms

To find standard generators for Fi22: To find standard generators for Fi22.2:

Representations

Representations are available for groups isoclinic to one of the following:
[Actually, representations of 6.Fi22:2 are not yet available.]

The representations of Fi22 available are

The representations of 2.Fi22 available are The representations of 3.Fi22 available are The representations of 6.Fi22 available are The representations of Fi22:2 available are The representations of 2.Fi22:2 available are The representations of 3.Fi22:2 available are The representations of 6.Fi22:2 available are

Maximal subgroups

The maximal subgroups of Fi22 are The maximal subgroups of Fi22:2 are We add here some subgroups which may be useful for condensation purposes:

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.
- Return to main ATLAS page. - Last updated 01.02.00

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