ATLAS: Symplectic group S6(3)

Order = 4585351680 = 29.39.5.7.13.
Mult = 2.
Out = 2.

Standard generators

Standard generators of S6(3) are a and b where a is in class 2A, b has order 5, ab has order 13 and abb has order 14.
Standard generators of the double cover 2.S6(3) are preimages A and B where B has order 5 and AB has order 13.

Standard generators of S6(3):2 are c and d where c is in class 2A, d is in class 4F, cd has order 20 and cdd has order 8.
Standard generators of either 2.S6(3).2 are preimages C and D where CDCDCDCDDCDDD has order 13.

WARNING: The standard generators in v2.0 for S6(3):2 and 2.S6(3).2 were defined on 27.06.00. The representations in v2.0 for S6(3):2 and 2.S6(3).2 are in these standard generators. There are [or were] no standard generators in v1 for S6(3):2 or 2.S6(3).2. The reprsentations of S6(3):2 and 2.S6(3).2 in v1 are NOT in standard generators as we have defined them above.


Representations

The representations of S6(3) available are: The representations of 2.S6(3) available are: The representations of S6(3):2 available are: The representations of 2.S6(3):2 available are:

Maximal subgroups

The maximal subgroups of S6(3) are as follows: The maximal subgroups of S6(3):2 are as follows:
Main ATLAS page Go to main ATLAS (version 2.0) page.
Classical groups page Go to classical groups page.
Old S6(3) page Go to old S6(3) 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 11.01.02 by RAW.
Information checked to Level 0 on 07.06.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.