# ATLAS: Exceptional group 2E6(2)

Order = 76532479683774853939200 = 236.39.52.72.11.13.17.19.
Mult = 22 × 3.
Out = S3.

### Standard generators and automorphisms

Standard generators of 2E6(2) are a and b where a is in class 2B, b is in class 3C, ab has order 19 and abababb has order 33.
Standard generators of the double cover 2.2E6(2) are preimages A and B where B has order 3, AB has order 19 and ABABABB has order 33.
Standard generators of the triple cover 3.2E6(2) are preimages A and B where A has order 2 and AB has order 19.

Standard generators of 2E6(2):2 are e and f where e is in class 2D, f is in class 8R, ef has order 19, and efeff has order 30.
Standard generators of 3.2E6(2):2 are preimages E and F where EF has order 19.
Standard generators of 2.2E6(2):2 are preimages E and F where EF has order 19.

Standard generators for the other groups below are not defined.

### Automorphisms

An automorphism of order 3 of 2E6(2) may be obtained by mapping (a, b) to ((ab)^-2bab, (abb)^-6b(abb)^6).
An automorphism of order 2 of 2E6(2) may be obtained by mapping (a, b) to (a, (abb)^-9b(abb)^9).

### Representations

#### 2E6(2) and covers

• The representations of 2E6(2) available are:
• Dimension 78 over GF(2): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 1705 (structure 1702.(1+1+1)) over GF(2): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• The representation of 2.2E6(2) available is:
• The representation of 22.2E6(2) available is:
• The representation of 3.2E6(2) available is:

#### 2E6(2):2 and covers

• The representation of 2E6(2):2 available is:
• The representation of 3.2E6(2):2 available is:
• The representations of 2.2E6(2):2 available are:

#### 2E6(2):3 and covers

• The representation of 2E6(2):3 available is:
• The representation of 3.2E6(2).3 available is:

#### 2E6(2):S3 and covers

• The representation of 2E6(2):S3 available is:
• The representation of 3.2E6(2):S3 available is:

### Maximal subgroups

The maximal subgroups of 2E6(2) include:
The maximal subgroups of 2E6(2):2 include:

Go to main ATLAS (version 2.0) page.
Go to exceptional groups page.
Go to old 2E6(2) page - ATLAS version 1.
Anonymous ftp access is also available. See here for details.

Version 2.0 created on 26th April 2000.
Last updated 06.01.04 by RAW.
Information checked to Level 0 on 23.05.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.