Automorphism group of alternating group:A6

Definition
This group is defined in the following equivalent ways:


 * 1) It is the defining ingredient::automorphism group of defining ingredient::alternating group:A6.
 * 2) It is the defining ingredient::automorphism group of defining ingredient::symmetric group:S6.
 * 3) It is the member of family::projective semilinear group of degree two over the field of nine elements, i.e., it is the group $$P\Gamma L(2,9)$$.

Note that for any $$n \ne 2,6$$, the automorphism group of the alternating group $$A_n$$ is precisely the symmetric group $$S_n$$, which is a complete group. The case $$n = 2$$ is uninteresting, and the case $$n = 6$$ is the only case where the automorphism group of the alternating group is strictly bigger than the symmetric group. Similarly, it is the only case where the automorphism group of the symmetric group is strictly bigger than the symmetric group.