ATLAS: Symplectic group S_{4}(9)
Order = 1721606400 = 2^{8}.3^{8}.5^{2}.41.
Mult = 2.
Out = 2^{2}.
Standard generators of S_{4}(9) are a and b where
a is in class 2B, b is in class 4B, ab has order 41 and
ababbb has order 5.
Standard generators of 2.S_{4}(9) are not yet defined.
Standard generators of the other decorations of S_{4}(9)
are not yet defined.
To find standard generators for S_{4}(9):
 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 9. If we find such an element,
then a is in class 2B. Otherwise, go back to step 1.
 Find an element of order 8, 12, 20, 24 or 40,
and power it up to give an involution t and an element
c of order 4.
 Check the order of [t, y] for a few random
elements y.
If any of these commutators has order greater than 19, then
c is in class 4A, so go back to step 3.
 Look for a conjugate b of c such that ab has
order 41 and abab^{3} has order 5. If no such conjugate can be
found, then c is probably in class 4A, so go back to step 3.
 The elements a and b are standard generators.
The representations of S_{4}(9) available are:

Permutations on 820[a] points  action on points (Sp_{4}(9)):
a and
b (GAP).

Permutations on 820[b] points  action on isotropic lines (Sp_{4}(9)):
a and
b (GAP).

Permutations on 1640 points (imprimitive):
a and
b (GAP).
 Some faithful irreducibles in characteristic 0
 Dimension 41a over Z:
a and b (GAP).
 Dimension 41b over Z:
a and b (GAP).
The representations of 2.S_{4}(9) = Sp_{4}(9) 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 22.06.04 by SJN.