I have a question. The automorphism group of the linear groups $GL(n,q)$, the group of linear transformations of $V = \mathbb{F}_q^n$, and $SL(n,q)$, the subgroup of $GL(n,q)$ consisting of elements of determinant $1$, are well understood. Here $q$ is a prime power $p^r$ and $n$ is any positive integer.

My question is: what is known about the automorphism group of $AGL(n,q)$ and $ASL(n,q)$? Here $AGL(n,q)$ is the affine linear group $V \rtimes GL(n,q)$, semidirect product of $V = \mathbb{F}_q^n$ and $GL(n,q)$ with the natural action of $GL(n,q)$ on $V$. These groups have matrix representations, as you can see here https://en.wikipedia.org/wiki/Affine_group

What I know for sure is that there are the inner automorphisms, and the Frobenius automorphism (raise the coefficients to the power $r$) that comes from the matrix representation described in the link. But is there something else?

Is there a nice complete description of the automorphism groups of $AGL(n,q)$ and $ASL(n,q)$?

Thanks

I have a question. The automorphism group of the linear groups $GL(n,q)$, the group of linear transformations of $V = \mathbb{F}_q^n$, and $SL(n,q)$, the subgroup of $GL(n,q)$ consisting of elements of determinant $1$, are well understood. Here $q$ is a prime power $p^r$ and $n$ is any positive integer.

My question is: what is known about the automorphism group of $AGL(n,q)$ and $ASL(n,q)$? Here $AGL(n,q)$ is the affine linear group $V \rtimes GL(n,q)$, semidirect product of $V = \mathbb{F}_q^n$ and $GL(n,q)$ with the natural action of $GL(n,q)$ on $V$. These groups have matrix representations, as you can see here https://en.wikipedia.org/wiki/Affine_group

What I know for sure is that there are the inner automorphisms, and the Frobenius automorphism (raise the coefficients to the power $p$) that comes from the matrix representation described in the link. But is there something else?

Is there a nice complete description of the automorphism groups of $AGL(n,q)$ and $ASL(n,q)$?

Thanks