ATLAS: Symplectic group S6(2)

Order = 1451520 =
Mult = 2.
Out = 1.

The following information is available for S6(2):

Standard generators

Standard generators of S6(2) are a and b where a is in class 2A, b has order 7 and ab has order 9.
Standard generators of the double cover 2.S6(2) are preimages A and B where B has order 7 and AB has order 9.


A presentation of S6(2) on its standard generators is given below.

< a, b | a2 = b7 = (ab)9 = (ab2)12 = [a, b]3 = [a, b2]2 = 1 >.

A shorter, and more coset enumeration friendly, presentation may be obtained by replacing (ab2)12 = 1 with [a, babab]2 = 1.

This presentation, and that of the covering group 2.S6(2), is available in Magma format as follows: S6(2) on a and b and 2S6(2) on A and B.


The representations of S6(2) available are: The representations of 2.S6(2) available are:

Maximal subgroups

The maximal subgroups of S6(2) are as follows.

Conjugacy classes

Representatives of the 30 conjugacy classes of S6(2) are given below. These are available here, and generators for the maximal cyclic subgroups are available here
Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old S6(2) page Go to old S6(2) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 7th June 2000.
Last updated 16.11.04 by JNB.
Information checked to Level 0 on 07.06.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.