# ATLAS: Linear group L3(11)

Order = 212427600 = 24.3.52.7.113.19.
Mult = 1.
Out = 2.

### Standard generators

Standard generators of L3(11) are a and b where a has order 3, b is in class 11A, ab has order 120, abb has order 10 and ababb has order 40. The last two conditions can be replaced by ab5 has order 55.

Standard generators of L3(11):2 are not defined.

NB: Class 11A is the class of transvections in the natural representation of L3(11).

### Presentations

Presentations for L3(11) and L3(11):2 on their standard generators are given below.

< a, b | a3 = b11 = aba-1bab-2a-1baba-1b-2 = (abab-1)3a-1b-2a-1b-1 = 1 >.

These presentations are available in Magma format as follows: L3(11) on a and b and L3(11):2 on c and d.

### Representations

The representations of L3(11) available are
• Permutations on 133 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 132 over GF(2): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 132 over GF(3): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 132 over GF(5): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 131 over GF(7): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 3 over GF(11): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP). - the natural representation.
• Dimension 131 over GF(19): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 132 over Z: a and b (GAP).
The representations of L3(11):2 available are
• none.

Go to main ATLAS (version 2.0) page.
Go to linear groups page.
Go to old L3(11) page - ATLAS version 1.
Anonymous ftp access is also available on sylow.mat.bham.ac.uk.9

Version 2.0 created on 30th July 1999.
Last updated 04.13.04 by SJN.
Information checked to Level 0 on 30.07.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.