ATLAS: Symplectic group S_{4}(11)
Order = 12860654400 = 2^{6}.3^{2}.5^{2}.11^{4}.61.
Mult = 2.
Out = 2.
Standard generators of S_{4}(11) are a and b where
a is in class 2B, b has order 3, ab has order 61 and
ababb has order 10. (This last condition implies that b is
in class 3B.)
Standard generators of 2.S_{4}(11) are preimages A and B
where B has order 3 and AB has order 61.
Standard generators of S_{4}(11):2 are not yet defined.
Standard generators of 2.S_{4}(11):2 are not yet defined.
To find standard generators for S_{4}(11):
 Find an element of even order and power it up to give an involution
a.
 Look for an element z such that [a, z] has
order greater than 11. If we find such an element,
then a is in class 2B. Otherwise, go back to step 1.
 Find an element s of order 60, and
let t=s^{30}, c=s^{20}.
 Check the order of [t, y] for a few random
elements y.
If any of these commutators has order greater than 11, then
c is in class 3A, so go back to step 3.
 Look for a conjugate b of c such that ab has
order 61 and ababb has order 10. If no such conjugate can be
found, then c is probably in class 3A, so go back to step 3.
 The elements a and b are standard generators.
The representations of S_{4}(11) available are:

Permutations on 1464[a] points  action on points (Sp_{4}(11)):
a and
b (GAP).

Permutations on 1464[b] points  action on isotropic lines (Sp_{4}(11)):
a and
b (GAP).

Permutations on 2928 points (imprimitive):
a and
b (GAP).
 Some faithful irreducibles in characteristic 0
 Dimension 122 over Z (reducible over Q(b11)):
a and b (GAP).
The representations of 2.S_{4}(11) = Sp_{4}(11) available are:
Go to main ATLAS (version 2.0) page.
Go to classical groups page.
Anonymous ftp access is also available on
for.mat.bham.ac.uk.
Version 2.0 created on 21st June 2004.
Last updated 21.06.04 by SJN.