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.
An image of (a,b) under the outer automorphism is given by ((ab)^-5a(ab)^5, (abb)^-3bb(abb)^3).
Standard generators of the double cover 2.F4(2) are pre-images 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 the double cover 2.F4(2):2 are pre-images C and D where D has order 3.


The representations of F4(2) available are The representation of F4(2).2 available is The representations of 2.F4(2) available are The representations of 2.F4(2).2 available are

Maximal subgroups

Maximal subgroups of F4(2) include:
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