ATLAS: Higman-Sims group HS

Order = 44352000 = 29.32.53.7.11.
Mult = 2.
Out = 2.

Standard generators

Standard generators of the Higman-Sims group HS are a and b where a is in class 2A, b is in class 5A, and ab has order 11.
Standard generators of the double cover 2HS are pre-images A and B where B has order 5, and AB has order 11.
Standard generators of the automorphism group HS:2 are c and d where c is in class 2C, d is in class 5C, and cd has order 30.
Standard generators of 2HS:2 are pre-images C and D where D has order 5.
A pair generators conjugate to a, b can be obtained as
a' = (cd)^{-1}(cdd)^{10}cd, b' = (cdcdd)^{-4}(cdd)^4(cdcdd)^4.

Black box algorithms

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

Representations

The representations of HS available are The representations of 2HS available are The representations of HS:2 available are The representations of 2HS:2 available are

Maximal subgroups

The maximal subgroups of the Higman-Sims group are as follows. Words provided by Suleiman and Wilson. The maximal subgroups of HS:2 are as follows. Words provided by Suleiman and Wilson.

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 09.08.99

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