ATLAS: Symplectic group S8(2)
Order = 47377612800 = 216.35.52.7.17.
Mult = 1.
Out = 1.
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.
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 >.
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].
-
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.