  Combinatorial Hantzsche-Wendt groups were introduced by W. Craig and P.A.
Linnell. Every such a group $G_n$, where $n$ is a natural number, encodes the
holonomy action of any $n+1$-dimensional Hantzsche-Wendt manifold. $G_2$ is the
fundamental group of the classical Hantzsche-Wendt manifold -- the only one
$3$-dimensional oriented flat manifold with non-cyclic holonomy group. In this
article, we describe the structure of the automorphism and of the outer
automorphism groups of combinatorial Hantzsche-Wendt groups.
