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 The representation of S4(4):2 available is The representation of S4(4):4 available is

Maximal subgroups

The maximal subgroups of S4(4) are as follows. Words calculated by Ibrahim Suleiman.
- Return to main ATLAS page. - Last updated 02.09.99

- R.A.Wilson@bham.ac.uk
- richard@ukonline.co.uk