# ATLAS: Non­split extension 24.A8 = 24.L4(2)

Order = 322560 = 210.32.5.7.
Mult = 2.
Out = 1.
The page for the image A8 = L4(2) is available here.

The following information is available for 24.A8:

### Standard generators

Standard generators of 24.A8 are a and b where a is in class 3A, b has order 7, ab has order 6, [a, b] has order 2 and abab2ab5 has order 6. An equivalent condition to [a, b] having order 2 is that abbb has order 12. These generators map onto standard generators of A8.
Standard generators of the double cover 24.2A8 are preimages A and B where A has order 3 and B has order 7. These generators map onto standard generators of 2A8.

NB: Class 3A is the class of elements of order 3 with centraliser 3 × A5, and maps onto Class 3A of A8.

### Presentation

A presentation of 24.A8 on its standard generators is given below.

< a, b | a3 = b7 = (ab)6 = [a, b]2 = abab2a-1bab-2ab3ab-3ab-3 = 1 >.

This presentation is available in Magma format as follows: 24A8 on a and b.

### Representations

The representations of 24.A8 available are:
• Permutations on 30 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 128 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 11 over GF(2) - uniserial module 4.6.1: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 11 over GF(2) - uniserial module 1.6.4: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 15 over GF(3): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 15 over GF(5): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 15 over GF(7): a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Dimension 15 over Z - monomial: a and b (Meataxe), a and b (GAP), a and b (Magma). Go to main ATLAS (version 2.0) page. Go to miscellaneous groups page. There is no old 24A8 page (not even on the A8 page) in the ATLAS version 1. Anonymous ftp access is also available on sylow.mat.bham.ac.uk.

Version 2.0 created on 24th July 1999.
Last updated 24.07.99 by JNB.
Information checked to Level 0 on 24.07.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.