ATLAS: Exceptional group F4(2)
Order = 3311126603366400 = 224.36.52.72.13.17.
Mult = 2.
Out = 2.
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:
-
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.F4(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 F4(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.F4(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.F4(2).4 = 2.(F4(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 F4(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.