ATLAS: Symplectic group S_{8}(2)
Order = 47377612800 = 2^{16}.3^{5}.5^{2}.7.17.
Mult = 1.
Out = 1.
Standard generators of S_{8}(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.
A presentation for S_{8}(2) on its standard generators is given below.
< a, b  a^{2} = b^{5} = (ab)^{17} = [a, b]^{3} = [a, b^{2}]^{4} = [a, bab]^{3} = [a, b^{2}abab^{2}]^{2} = [a, b^{2}ab^{2}]^{3} = [a, (ab^{2})^{4}]^{2} = [a, babab]^{3} = (ababab^{2}ab^{1}ab^{2})^{4} = 1 >.
The representations of S_{8}(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].

Dimension 35 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 50 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 35 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 51 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 35 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 51 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 35 over GF(17):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 51 over GF(17):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
 Some faithful irreducibles in characteristic 0
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.