ATLAS: Exceptional group F4(2)

Order = 3311126603366400 =
Mult = 2.
Out = 2.

Standard generators

Standard generators of F4(2) are a and b where a is in class 2C, b is in class 3C, ab has order 17 and ababababbababbabb has order 13.
Standard generators of the double cover 2.F4(2) are preimages A and B where B has order 3 and AB has order 17.

Standard generators of F4(2):2 are c and d where c is in class 2E, d is in class 3AB, cd has order 40 (in fact this is in class 40B) and abababb has order 10.
Standard generators of either of the double covers 2.F4(2).2 are preimages C and D where D has order 3.


An image of (a, b) under an outer automorphism is given by ((ab)^-5a(ab)^5, (abb)^-3bb(abb)^3).


The representations of F4(2) available are: The representations of 2.F4(2) available are: The representation of F4(2).2 available is: The representations of 2.F4(2).2 available are: The representations of 2.F4(2).4 = 2.(F4(2) × 2).2 available are:

Maximal subgroups

Maximal subgroups of F4(2) include:
Main ATLAS page Go to main ATLAS (version 2.0) page.
Exceptional groups page Go to exceptional groups page.
Old F4(2) page Go to old F4(2) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 17th April 2000.
Last updated 07.08.01 by JNB.
Information checked to Level 0 on 17.04.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.