ATLAS: Symplectic group S4(13)
Order = 68518981440 = 26.32.5.72.134.17.
Mult = 2.
Out = 2.
Standard generators of S4(13) are a and b where
a is in class 2B, b has order 3, ab has order 85 and
ababb has order 14. (This last condition implies that b is
in class 3B.)
Standard generators of 2.S4(13) are not yet defined.
Standard generators of S4(13):2 are not yet defined.
Standard generators of 2.S4(13):2 are not yet defined.
To find standard generators for S4(13):
- 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 13. If we find such an element,
then a is in class 2B. Otherwise, go back to step 1.
- Find an element s of order 84, and
let t=s42, c=s28.
- Check the order of [t, y] for a few random
elements y.
If any of these commutators has order greater than 13, then
c is in class 3A, so go back to step 3.
- Look for a conjugate b of c such that ab has
order 85 and ababb has order 14. 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 S4(13) available are:
-
Permutations on 2380[a] points - action on points (Sp4(13)):
a and
b (GAP).
-
Permutations on 2380[b] points - action on isotropic lines (Sp4(13)):
a and
b (GAP).
-
Permutations on 4760 points (imprimitive):
a and
b (GAP).
- Some faithful irreducibles in characteristic 0
- Dimension 170 over Z (reducible over Z(b13)):
a and b (GAP).
The representations of 2.S4(13) = Sp4(13) 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 17th June 2004.
Last updated 17.06.04 by SJN.