# ATLAS: Dempwolff group 25.L5(2) (non­split extension)

Order = 319979520 = 215.32.5.7.31.
Mult = 1.
Out = 1.
The page for the image L5(2) is available here.

The following information is available for 25.L5(2):

### Standard generators

Standard generators of the Dempwolff group 25.L5(2) are a and b where a has order 2, b has order 5, ab has order 21, ababb has order 10, abababbbb has order 28 and abababbbabb has order 5. These generators map onto standard generators of L5(2).
NB: There is just one class of involutions of 25.L5(2) not in the normal 25 and it maps onto class 2A of L5(2).

### Presentation

A presentation of 25.L5(2) on its standard generators is given below.

< a, b | a2 = b5 = (ab)21 = [a, b2]4 = [a, b-2ab-2][a, b]3 = (ababab-2)2(abab-1ab)2(ab-1)2 = 1 >.

This presentation is available in Magma format as follows: 25L5(2) on a and b.

### Representations

The representations of 25.L5(2) available are:
• Permutations on 7440 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
- On the cosets of C(a) = 24.24.L3(2) - CFs of rep are 1+30+30+124+217+280+868+930+1240+3720.
• Permutations on 7440 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 7440 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 69 over GF(2): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 248 over GF(3): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 248 over GF(5): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 248 over GF(7): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 248 over GF(31): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 248 over Z: a and b (Meataxe), a and b (Magma). Go to main ATLAS (version 2.0) page. Go to miscellaneous groups page. Go to old 25L5(2) page (on the L5(2) page) - ATLAS version 1. Anonymous ftp access is also available on sylow.mat.bham.ac.uk.

Version 2.0 created on 5th May 1999.
Last updated 27.05.99 by JNB.
Information checked to Level 1 on 27.05.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.