# 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.