# ATLAS: Alternating group A12

Order = 239500800 = 29.35.52.7.11.
Mult = 2.
Out = 2.

### Standard generators

Standard generators of A12 are a and b where a is in class 3A, b has order 11, ab has order 10 and abb has order 35.
In the natural representation we may take a = (1, 2, 3) and b = (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12).
Standard generators of the double cover 2.A12 are preimages A and B where A has order 3 and B has order 11.

Standard generators of S12 = A12:2 are c and d where c is in class 2D, d has order 11 and ab has order 12.
In the natural representation we may take c = (1, 2) and d = (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12).
Standard generators of either of the double covers 2.S12 are preimages C and D where D has order 11.

In the natural representations given here, we have a = cd-1cd = [c, d] and b = d.

### Automorphisms

An outer automorphism of A12 may be realised by mapping (a, b) to (a-1, ba-1). In the natural representations given here, this outer automorphism is conjugation by c.

### Representations

The representations of A12 available are:
• Some primitive permutation representations.
• Permutations on 12 points - the natural representation above: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 66 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 220 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 462 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 495 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 792 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Permutations on 2520 points: a and b (Meataxe), a and b (Meataxe binary), a and b (GAP).
• Some representations in characteristic 2.
• Some representations in characteristic 3.
• Some representations in characteristic 5.
The representations of 2.A12 available are:
The representations of S12 = A12:2 available are:
• Faithful permutation representations, including all but one of the faithful primitive ones. Go to main ATLAS (version 2.0) page. Go to alternating groups page. Go to old A12 page - ATLAS version 1. Anonymous ftp access is also available on for.mat.bham.ac.uk.

Version 2.0 file created on 17th April 2000.
Last updated 16.01.02 by JNB.
Information checked to Level 0 on 17.04.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.