ATLAS: Alternating group A11
Order = 19958400 = 27.34.52.7.11.
Mult = 2.
Out = 2.
Standard generators
Standard generators of A11 are a
and b where
a is in class 3A, b has order 9
and ab has order 11.
In the natural representation we may take
a = (1, 2, 3) and
b = (3, 4, 5, 6, 7, 8, 9, 10, 11).
Standard generators of the double cover 2.A11 are preimages
A
and B where
A has order 3 and B has order 9.
Standard generators of S11 = A11.2 are c
and d where
c is in class 2C,
d is in class 10D
and cd has order 11.
In the natural representation we may take
c = (1, 2)
and
d = (2, 3, 4, 5, 6, 7, 8, 9, 10, 11).
Standard generators of either of the double covers 2.S11 are preimages
C and D where
CD has order 11.
Representations
The representations of A11 available are
- All primitive permutation representations.
-
Permutations on 11 points - the natural representation above:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 55 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 165 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Permutations on 330 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 2520 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).
- All faithful irreducibles in characteristic 2 (up to Frobenius automorphisms).
-
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 32 over GF(2) -reducible 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).
-
Dimension 144 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 164 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 186 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 198 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 416 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 584 over GF(4):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 848 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
- Faithful irreducibles in characteristic 3.
-
Dimension 10 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 34 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 109 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 120 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 126 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 126 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 131 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
- Faithful irreducibles in characteristic 5.
-
Dimension 10 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 45 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).
-
Dimension 110 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 120 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
- Faithful irreducibles in characteristic 7.
-
Dimension 10 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 44 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 45 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 66 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
- Faithful irreducibles in characteristic 11.
-
Dimension 9 over GF(11):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 36 over GF(11):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 44 over GF(11):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 84 over GF(11):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of 2.A11 available are
-
Permutations on 5040 points:
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
- Faithful irreducibles in characteristic 3.
-
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 144 over GF(3):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
- Faithful irreducibles in characteristic 5.
-
Dimension 16 over GF(5):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
-
Dimension 16 over GF(5):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
-
Dimension 56 over GF(5):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
-
Dimension 56 over GF(5):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
- Faithful irreducibles over fields of characteristic 7.
-
Dimension 16 over GF(49):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
-
Dimension 16 over GF(49):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
-
Dimension 32 over GF(7) - reducible over GF(49):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
-
Dimension 144 over GF(7):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
- Faithful irreducibles in characteristic 11.
-
Dimension 16 over GF(11):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
-
Dimension 128 over GF(11):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
The representations of S11 = A11:2 available are
-
Permutations on 11 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
- There is a primitive permutation representation of S11
of degree 362880 on the cosets of the novelty 11:10.
However, we decided that this was just a bit too large to keep on file,
so if you want this representation, you can
make it yourself.
-
Dimension 32 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
The representations of 2.S11 (plus type) available are
-
Dimension 32 over GF(3):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
-
Dimension 32 over GF(5):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
-
Dimension 32 over GF(7):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
-
Dimension 16 over GF(11):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
The representations of 2.S11 (minus type) available are
Maximal subgroups
The maximal subgroups of A11 are:
Conjugacy classes
For definiteness, we choose ab to be in the class 11A,
and aababb to be in the class 21A.
Go to main ATLAS (version 2.0) page.
Go to alternating groups page.
Go to old A11 page - ATLAS version 1.
Anonymous ftp access is also available on
sylow.mat.bham.ac.uk.
Version 2.0 file created on 18th April 2000, from
Version 1 file last modified on 25.08.98.
Last updated 14.01.02 by RAW.
Information checked to
Level 0 on 18.04.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.