ATLAS: Exceptional group E6(2)
Order = 214841575522005575270400 =
236.36.52.73.13.17.31.73.
Mult = 1.
Out = 2.
Standard generators
Standard generators of E6(2) and E6(2):2 are not defined.
At present two sets of generators are in use: the set (a, b)
is labelled G1, and the set (x, y) is labelled G0 below.
We may obtain (a conjugate in E6(2):2 of) (a, b) by setting a = ((xyxy2)6)^(y5xy6x2y4) and b = x.
Representations
The representations of E6(2) available are:
-
Dimension 27 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 27 over GF(2) - the dual of the above:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 78 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 27 over GF(2):
x and
y (Meataxe),
x and
y (Meataxe binary),
x and
y (GAP).
-
Dimension 27 over GF(2) - the dual of the above:
x and
y (Meataxe),
x and
y (Meataxe binary),
x and
y (GAP).
-
Dimension 78 over GF(2):
x and
y (Meataxe),
x and
y (Meataxe binary),
x and
y (GAP).
Maximal subgroups
Taken from:
Peter Kleidman and Robert Wilson,
The maximal subgroups of E6(2) and Aut(E6(2)),
Proc London Math Soc 60 (1990), 266-294.
- 216:O10+(2) - two classes.
- 25+20:(S3 × L5(2)) - two classes.
- 21+20:L6(2).
- [229]:(S3 × L3(2) × L3(2)).
- F4(2).
- S3 × L6(2).
- 3.(32:Q8 × L3(4)).S3.
- L3(8):3.
- (L3(2) × L3(2) × L3(2)):S3.
- L3(2) × G2(2).
- 73:31+2:2A4.
- G2(2) - two classes.
Go to main ATLAS (version 2.0) page.
Go to exceptional groups page.
Go to old E6(2) page - ATLAS version 1.
Anonymous ftp access is also available on
sylow.mat.bham.ac.uk.
Version 2.0 created on 21st April 1999.
Last updated 17.05.00 by JNB.
Information checked to
Level 0 on 21.04.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.