ATLAS: Conway group Co3

Order = 495766656000 =
Mult = 1.
Out = 1.

Standard generators

Standard generators of the Conway group Co3 are a and b where a is in class 3A, b is in class 4A, and ab has order 14.

Black box algorithms

To find standard generators for Co3:


The representations of Co3 available are:

Maximal subgroups

The maximal subgroups of Co3 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.
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Last updated 14th September 1999,
R.A.Wilson, R.A.Parker and J.N.Bray