ATLAS: Conway group Co1

Order = 4157776806543360000 =
Mult = 2.
Out = 1.

The following information is available for Co1:

Standard generators

Standard generators of the Conway group Co1 are a and b where a is in class 2B, b is in class 3C, ab has order 40 and ababb has order 6.
Standard generators of the double cover 2.Co1 = Co0 are preimages A and B where B has order 3 and ABABABABBABABBABB has order 33.

Black box algorithms

Finding generators

To find standard generators for Co1:

This algorithm is available in computer readable format: finder for Co1.

Checking generators

To check that elements x and y of Co1 are standard generators: This algorithm is available in computer readable format: checker for Co1.


The representations of Co1 available are: The representations of 2.Co1 available are:

Maximal subgroups

The maximal subgroups of Co1 are as follows.

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.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Sporadic groups page Go to sporadic groups page.
Old Co1 page Go to old Co1 page - ATLAS version 1.
ftp access Anonymous ftp access is also available on, user atlasftp, password atlasftp. Files can be found in directory v2.0 and subdirectories.

Version 2.0 created on 1st June 1999.
Last updated 6.1.05 by SJN.
Information checked to Level 1 on 11.06.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.