ATLAS: Exceptional group ^2E6(2)

Order = 76532479683774853939200.
Mult = 2 x 2 x 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 pre-images 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 pre-images 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 pre-images E and F where EF has order 19.
Standard generators of 2.^2E6(2):2 are pre-images E and F where EF has order 19.

An automorphism of order 3 may be obtained by mapping (a,b) to ((ab)^-2bab,(abb)^-6b(abb)^6).
An automorphism of order 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:
- Return to main ATLAS page. - Last updated 01.10.98

- R.A.Wilson@bham.ac.uk
- richard@ukonline.co.uk