  Let $\Gamma$ be a crystallographic group of dimension $n,$ i.e. a discrete,
cocompact subgroup of $\operatorname{Isom}(\mathbb{R}^n)$ =
$O(n)\ltimes\mathbb{R}^n.$ For any $n\geq 2,$ we construct a crystallographic
group with a trivial center and a trivial outer automorphism group.

Group Theory