# ATLAS: Symplectic group S4(5)

Order = 4680000 = 26.32.54.13.
Mult = 2.
Out = 2.

### Standard generators

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.

### Representations

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:
• none

### Maximal subgroups

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.