ATLAS: Alternating group A_{9}
Order = 181440 = 2^{6}.3^{4}.5.7
Mult = 2.
Out = 2.
Standard generators
Standard generators of A_{9} are a
and b where
a is in class 3A, b has order 7
and ab has order 9.
In the natural representation we may take
a = (1, 2, 3) and
b = (3, 4, 5, 6, 7, 8, 9).
Standard generators of the double cover 2.A_{9} are preimages A
and B where
A has order 3, and B has order 7.
Representations
The representations of A_{9} available are
- All primitive permutation representations.
- a and
b as
the above permutations on 9 points - the natural representation.
- a and
b as
permutations on 36 points.
- a and
b as
permutations on 84 points.
- a and
b as
permutations on 120 points.
- a and
b as
permutations on 120 points.
- a and
b as
permutations on 126 points.
- a and
b as
permutations on 280 points.
- a and
b as
permutations on 840 points.
- Faithful irreducibles in characteristic 2.
- a and
b as
8 × 8 matrices over GF(2) - the deleted permutation representation.
- a and
b as
8 × 8 matrices over GF(2).
- a and
b as
8 × 8 matrices over GF(2).
- a and
b as
7 × 7 matrices over GF(3).
- a and
b as
8 × 8 matrices over GF(5).
- a and
b as
8 × 8 matrices over GF(7).
- a and
b as
8 × 8 matrices over Z.
The representations of 2.A_{9} available are
- Permutation representations.
- A and
B as
permutations on 240 points.
- All faithful irreducibles in characteristic 3.
- A and
B as
8 × 8 matrices over GF(3).
- A and
B as
48 × 48 matrices over GF(3).
- A and
B as
104 × 104 matrices over GF(3).
- Faithful irreducibles in characteristic 5.
- A and
B as
8 × 8 matrices over GF(5).
- A and
B as
8 × 8 matrices over GF(5).
- Faithful irreducibles in characteristic 7.
- A and
B as
8 × 8 matrices over GF(7).
- A and
B as
8 × 8 matrices over GF(7).
- Faithful irreducibles in characteristic 0.
The representations of S_{9} = A_{9}:2 available are
- c and
d as
permutations on 9 points - the natural representation.
Return to main ATLAS page.
Last updated 13.06.00
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk