ATLAS: Symplectic group S_{4}(5)
Order = 4680000 = 2^{6}.3^{2}.5^{4}.13.
Mult = 2.
Out = 2.
Standard generators of S_{4}(5) are a and b where
a is in class 2B, b is in class 3B and ab is in class 13C.
The last condition is equivalent to: ab has order 13
and ababb has order 12.
Standard generators of 2.S_{4}(5) are preimages A and B
where B has order 3 and AB has order 13.
Standard generators of S_{4}(5):2 are c and d where
c is in class 2D, d is in class 3B and cd is in class 26A.
The last condition is equivalent to: cd has order 26
and cdcdd has order 10.
Standard generators of either group 2.S_{4}(5):2 are preimages
C and D where D has order 3.
The representations of S_{4}(5) available are:

Permutations on 156[a] points  on the cosets of 5^1+2:4A5:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 156[b] points  on the cosets of 5^3:A5.4:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 300 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 325 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 5 over GF(5)  the representation as O5(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 12 over GF(4):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 13 over GF(9):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of 2.S_{4}(5) available are:

Permutations on 624 points:
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 4 over GF(5)  the representation as Sp4(5):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
The representations of S_{4}(5):2 available are:

Dimension 5 over GF(5)  the representation as O5(5):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 24 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 40 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 64 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 104[a] over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 104[b] over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 26 over GF(3):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
The representations of 2.S_{4}(5):2 available are:
The maximal subgroups of S_{4}(5) are as follows. Words in preparation  mostly wrong at the moment!
Go to main ATLAS (version 2.0) page.
Go to classical groups page.
Go to old S4(5) page  ATLAS version 1.
Anonymous ftp access is also available.
See here for details.
Version 2.0 created on 13th June 2000.
Last updated 27.06.00 by JNB.
Information checked to
Level 0 on 13.06.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.