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

2E6(2):2 and covers

2E6(2):3 and covers

2E6(2):S3 and covers


Maximal subgroups

The maximal subgroups of 2E6(2) include: The maximal subgroups of 2E6(2):2 include:
Main ATLAS page Go to main ATLAS (version 2.0) page.
Exceptional groups page Go to exceptional groups page.
Old 2E6(2) page Go to old 2E6(2) page - ATLAS version 1.
ftp access 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.