ATLAS: Alternating group A_{12}
Order = 239500800 = 2^{9}.3^{5}.5^{2}.7.11.
Mult = 2.
Out = 2.
Standard generators of A_{12} 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.A_{12} are preimages
A and B where A has order 3 and B has order 11.
Standard generators of S_{12} = A_{12}: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.S_{12} are preimages C and D where
D has order 11.
In the natural representations given here, we have a = cd^{1}cd = [c, d] and b = d.
An outer automorphism of A_{12} 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.
The representations of A_{12} 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.

Dimension 10 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 16 over GF(4):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 16 over GF(4):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 44 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 100 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
 Some representations in characteristic 3.

Dimension 10 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 45 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 54 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
 Some representations in characteristic 5.

Dimension 11 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 43 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 55 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 89 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of 2.A_{12} available are:

Dimension 16 over GF(3):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 16 over GF(3):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 32 over GF(5):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 32 over GF(7):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).

Dimension 32 over GF(11):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
The representations of S_{12} = A_{12}:2 available are:
 Faithful permutation representations, including all but one of the faithful primitive ones.

Permutations on 12 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 66 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 220 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 462 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 495 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 792 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 5040 points  imprimitive:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 5775 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 10395 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 15400 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
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.