Combinatorial Hantzsche-Wendt group

Let n\in N. By a combinatorial Hantzsche-Wendt group we shall understand a finite presented group
G_n = {x_1, ..., x_n  |  x_i^{-1} x_j^2 x_i x_j^2  \forall i\neq j}.
During a talk I will present properties (topological, homological) of the above group.
Moreover, some relations with a classical Hantzsche-Wendt groups will be given,
where by a classical Hantzsche-Wendt group I understand a fundamental group of
a n-dimensional oriented flat Riemannian manifold with a holonomy group (Z_2)^{n-1}.