# 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.
• a and b as the above permutations on 11 points - the natural representation.
• a and b as permutations on 55 points.
• a and b as permutations on 165 points.
• a and b as permutations on 330 points.
• a and b as permutations on 462 points.
• a and b as permutations on 2520 points.
• a and b as permutations on 2520 points.
• Faithful irreducibles over fields of characteristic 2.
• a and b as 10 × 10 matrices over GF(2).
• a and b as 16 × 16 matrices over GF(4).
• a and b as 16 × 16 matrices over GF(4) - the dual of the above.
• a and b as 32 × 32 matrices over GF(2) - reducible over GF(4).
• a and b as 44 × 44 matrices over GF(2).
• a and b as 100 × 100 matrices over GF(2).
• a and b as 144 × 144 matrices over GF(2).
• a and b as 164 × 164 matrices over GF(2).
• a and b as 186 × 186 matrices over GF(2).
• a and b as 198 × 198 matrices over GF(2).
• Faithful irreducibles in characteristic 3.
• a and b as 10 × 10 matrices over GF(3).
• a and b as 34 × 34 matrices over GF(3).
• a and b as 45 × 45 matrices over GF(3).
• a and b as 109 × 109 matrices over GF(3).
• a and b as 120 × 120 matrices over GF(3).
• a and b as 126 × 126 matrices over GF(3).
• a and b as 126 × 126 matrices over GF(3) - the dual of the above.
• a and b as 131 × 131 matrices over GF(3).
• Faithful irreducibles in characteristic 5.
• a and b as 10 × 10 matrices over GF(5).
• a and b as 43 × 43 matrices over GF(5).
• a and b as 45 × 45 matrices over GF(5).
• a and b as 55 × 55 matrices over GF(5).
• a and b as 89 × 89 matrices over GF(5).
• a and b as 110 × 110 matrices over GF(5).
• a and b as 120 × 120 matrices over GF(5).
• Faithful irreducibles in characteristic 7.
• a and b as 10 × 10 matrices over GF(7).
• a and b as 44 × 44 matrices over GF(7).
• a and b as 45 × 45 matrices over GF(7).
• a and b as 66 × 66 matrices over GF(7).
• Faithful irreducibles in characteristic 11.
• a and b as 9 × 9 matrices over GF(11).
• a and b as 36 × 36 matrices over GF(11).
• a and b as 44 × 44 matrices over GF(11).
• a and b as 84 × 84 matrices over GF(11).
The representations of 2.A11 available are
• A and B as permutations on 5040 points.
• Faithful irreducibles in characteristic 3.
• A and B as 16 × 16 matrices over GF(3).
• A and B as 16 × 16 matrices over GF(3) - the dual of the above.
• A and B as 144 × 144 matrices over GF(3).
• Faithful irreducibles in characteristic 5.
• A and B as 16 × 16 matrices over GF(5).
• A and B as 16 × 16 matrices over GF(5) - the dual of the above.
• A and B as 56 × 56 matrices over GF(5).
• Faithful irreducibles over fields of characteristic 7.
• A and B as 16 × 16 matrices over GF(49).
• A and B as 16 × 16 matrices over GF(49) - the dual of the above.
• A and B as 32 × 32 matrices over GF(7) - reducible over GF(49).
• A and B as 144 × 144 matrices over GF(7).
• Faithful irreducibles in characteristic 11.
• A and B as 16 × 16 matrices over GF(11).
• A and B as 128 × 128 matrices over GF(11).
The representations of S11 = A11:2 available are
• c and d as permutations on 11 points - the natural representation.
• 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.
• c and d as 32 × 32 matrices over GF(2).
The representations of 2.S11 (plus type) available are
• C and D as 32 × 32 matrices over GF(3).
• C and D as 32 × 32 matrices over GF(5).
• C and D as 32 × 32 matrices over GF(7).
• C and D as 16 × 16 matrices over GF(11).
The representations of 2.S11 (minus type) available are
• none.

### Maximal subgroups

The maximal subgroups of A11 are: