ATLAS: Symplectic group S4(11)
Order = 12860654400 = 18.104.22.168.61.
Mult = 2.
Out = 2.
Standard generators of S4(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.S4(11) are preimages A and B
where B has order 3 and AB has order 61.
Standard generators of S4(11):2 are not yet defined.
Standard generators of 2.S4(11):2 are not yet defined.
To find standard generators for S4(11):
- Find an element of even order and power it up to give an involution
- 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=s30, c=s20.
- Check the order of [t, y] for a few random
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 S4(11) available are:
The representations of 2.S4(11) = Sp4(11) available are:
Permutations on 1464[a] points - action on points (Sp4(11)):
Permutations on 1464[b] points - action on isotropic lines (Sp4(11)):
Permutations on 2928 points (imprimitive):
- Some faithful irreducibles in characteristic 0
- Dimension 122 over Z (reducible over Q(b11)):
a and b (GAP).
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Version 2.0 created on 21st June 2004.
Last updated 21.06.04 by SJN.