# ATLAS: Alternating group A10

Order = 1814400 = 27.34.52.7.
Mult = 2.
Out = 2.

### Standard generators

Standard generators of A10 are a and b where a is in class 3A, b has order 9, ab has order 8 and abb has order 12.
In the natural representation we may take a = (1, 2, 3) and b = (2, 3, 4, 5, 6, 7, 8, 9, 10).
Standard generators of the double cover 2.A10 are preimages A and B where A has order 3 and B has order 9.

Standard generators of S10 = A10.2 are c and d where c is in class 2C, d has order 9 and cd has order 10.
In the natural representation we may take c = (1, 2) and d = (2, 3, 4, 5, 6, 7, 8, 9, 10).
Standard generators of either of the double covers 2.S10 are preimages C and D where D has order 9.

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

### Automorphisms

An outer automorphism of A10 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 A10 available are:
• All primitive permutation representations.
• All faithful irreducibles in characteristic 2 (up to Frobenius automorphisms):
• All faithful irreducibles in characteristic 3:
• All faithful irreducibles in characteristic 5:
• Some faithful irreducibles in characteristic 7:
The representations of 2.A10 available are:
The representations of S10 = A10:2 available are:

### Maximal subgroups

The maximal subgroups of A10 are:
• A9
• S8
• (A7 x 3):2
• (A5 x A5):4
• (A6 x A4):2
• 24:S5
• M10

### Conjugacy classes

We define class 9A to be the class containing b, and class 21A to be the class containing abbb. This choice is compatible with the ABC.
Go to main ATLAS (version 2.0) page.
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Go to old A10 page - ATLAS version 1.
Anonymous ftp access is also available on for.mat.bham.ac.uk.

Version 2.0 file created on 18th April 2000, from Version 1 file last modified on 07.03.98.
Last updated 09.01.08 by JNB.
Information checked to Level 0 on 18.04.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.