ATLAS: Symplectic group S8(2)

Order = 47377612800 = 216.35.52.7.17.
Mult = 1.
Out = 1.

Standard generators

Standard generators of S8(2) are a and b where a is in class 2B, b is in class 5B, ab has order 17 and abb has order 21.

Presentation

A presentation for S8(2) on its standard generators is given below.

< a, b | a2 = b5 = (ab)17 = [a, b]3 = [a, b2]4 = [a, bab]3 = [a, b2abab2]2 = [a, b2ab2]3 = [a, (ab2)4]2 = [a, babab]3 = (ababab2ab-1ab-2)4 = 1 >.

Representations

The representations of S8(2) available are:
• Some faithful permutation representations [all transitive].
• Permutations on 120 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 136 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 240 points - imprimitive: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 255 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 272 points - imprimitive: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 2295 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 5355 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Some faithful representations in characteristic 2 [all irreducible].
• Dimension 8 over GF(2) - the natural representation: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 16 over GF(2): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 26 over GF(2): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 48 over GF(2): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Some faithful representations in characteristic > 2 [all irreducible].
• Some faithful irreducibles in characteristic 0

Maximal subgroups Go to main ATLAS (version 2.0) page. Go to classical groups page. Go to old S8(2) page - ATLAS version 1. Anonymous ftp access is also available. See here for details.

Version 2.0 created on 7th June 2000.
Last updated 03.03.04 by SJN.
Information checked to Level 0 on 07.06.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.