ATLAS: Baby Monster group B

Order = 4154781481226426191177580544000000 = 241.313.
Mult = 2.
Out = 1.

The following information is available for B:

Standard generators

Standard generators of the Baby Monster are a and b where a is in class 2C, b is in class 3A, ab has order 55 and ababababbababbabb has order 23.

Black box algorithms

Finding generators

To find standard generators for B: This algorithm is available in computer readable format: finder for B.

Checking generators

To check that elements x and y of B are standard generators:

This algorithm is available in computer readable format: checker for B.


The representations of B available are:

Maximal subgroups

The maximal subgroups include the following, in decreasing order of size. (This list is now (since 15th January 1997) believed to be complete.)

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, for example by running this program afterwards.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Sporadic groups page Go to sporadic groups page.
Old B page Go to old B page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 20th December 2000.
Last updated 12.05.06 by JNB.
Information checked to Level 0 on 20.12.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.