ATLAS: Symplectic group S4(4)
Order = 979200.
Mult = 1.
Out = 4.
Standard generators and automorphisms
Standard generators of S4(4) are
a
and b where
a is in class 2A or 2B, b is in class 5E,
ab has order 17
and ababb has order 15.
An outer automorphism of order 2 maps (a,b) to
(a,(abb)^-3b(abb)^3).
Standard generators of S4(4):2 are
c
and d where
c is in class 2D, d is in class 4C or 4D,
cd has order 17,
and cdd has order 4.
A further automorphism of order 2 maps (c,d) to
((cd)^-2c(cd)^2,(cdcdd)^-1(cdcdcddcd)^3cdcdd).
Standard generators of S4(4).4 are not defined.
Representations
The representations of S4(4) available are
- a and
b as
4 x 4 matrices over GF(4) - the natural representation.
- a and
b as
18 x 18 matrices over GF(3).
- a and
b as
18 x 18 matrices over GF(5).
- a and
b as
33 x 33 matrices over GF(5).
- a and
b as
18 x 18 matrices over GF(17).
- a and
b as
permutations on 85 points.
- a and
b as
permutations on 120 points.
The representation of S4(4):2 available is
- c and
d as
8 x 8 matrices over GF(2).
The representation of S4(4):4 available is
- e and
f as
16 x 16 matrices over GF(2).
Maximal subgroups
The maximal subgroups of S4(4) are as follows. Words calculated by Ibrahim Suleiman.
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Last updated 02.09.99
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk