ATLAS: Conway group Co3

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

The following information is available for Co3:

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

Finding generators

To find standard generators for Co3:

This algorithm is available in computer readable format: finder for Co3.

Checking generators

To check that elements x and y of Co3 are standard generators: This algorithm is available in computer readable format: checker 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 have been dealt with - the class names are consistent with the mod 3 character table in GAP.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Sporadic groups page Go to sporadic groups page.
Old Co3 page Go to old Co3 page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 14th June 2000.
Last updated 6.1.05 by SJN.
Information checked to Level 0 on 14.06.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.