ATLAS: Alternating group A12
Order = 239500800 = 29.35.52.7.11.
Mult = 2.
Out = 2.
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.
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.
-
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.A12 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 S12 = A12:2 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.