ATLAS: Symplectic group S10(2)

Order = 24815256521932800 =
Mult = 1.
Out = 1.

The following information is available for S10(2):

Standard generators

Standard generators of S10(2) are a and b where a is in class 2A, b has order 11 and ab has order 15.
NB: Class 2A is the class of transvections in the natural 10­dimensional representation of S10(2).

Black box algorithms

Finding generators

To find standard generators for S10(2): This algorithm is available in computer readable format: finder for S10(2).

Checking generators

To check that elements x and y of S10(2) are standard generators:

This algorithm is available in computer readable format: checker for S10(2).


A presentation for S10(2) in terms of its standard generators is given below.

< a, b | a2 = b11 = (ab)15 = (ab5)18 = [a, b]3 = [a, b2]2 = [a, b3]2 = [a, b4]2 = [a, b5]3 = [a, (ab)5]2 = 1 >.

This presentation is available in Magma format as follows: S10(2) on a and b.


The representations of S10(2) available are:

Maximal subgroups

The maximal subgroups of S10(2) include the following.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old S10(2) page Go to old S10(2) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 22nd May 1999.
Last updated 13.01.05 by SJN.
Information checked to Level 1 on 22.05.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.