ATLAS: Exceptional group F_{4}(2)
Order = 3311126603366400 = 2^{24}.3^{6}.5^{2}.7^{2}.13.17.
Mult = 2.
Out = 2.
Standard generators of F_{4}(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 F_{4}(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.F_{4}(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 F_{4}(2) available are:

Dimension 26 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 69888 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of 2.F_{4}(2) available are:

Permutations on 139776 points:
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 52 over GF(3):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 2380 over GF(3):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 52 over GF(5):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 52 over GF(37):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 52 over Z:
A and B (Magma).
The representation of F_{4}(2).2 available is:

Dimension 52 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
The representations of 2.F_{4}(2).2 available are:

Dimension 52 over GF(25):
C and
D (Meataxe),
C and
D (Meataxe binary),
C and
D (GAP).
The representations of 2.F_{4}(2).4 = 2.(F_{4}(2) × 2).2 available are:

Dimension 52 over GF(5):
C and
D (Meataxe),
C and
D (Meataxe binary),
C and
D (GAP).
Maximal subgroups of F_{4}(2) include:
Go to main ATLAS (version 2.0) page.
Go to exceptional groups page.
Go to old F4(2) page  ATLAS version 1.
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.