ATLAS: Symplectic group S4(5)
Order = 4680000 = 26.32.54.13.
Mult = 2.
Out = 2.
Standard generators of S4(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.S4(5) are preimages A and B
where B has order 3 and AB has order 13.
Standard generators of S4(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.S4(5):2 are preimages
C and D where D has order 3.
The representations of S4(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.S4(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 S4(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.S4(5):2 available are:
The maximal subgroups of S4(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.