  Combinatorial Hantzsche-Wendt groups G(n) were defined by W. Craig and P. A.
Linnell. For n = 2 it is a fundamental group of 3-dimensional oriented flat
manifold with no cyclic holonomy group. We calculate the Hilbert-Poincare
series of G(n), n > 0 with Q and F2 coefficients. Moreover, we prove that a
cohomological dimension of G(n) is equal to n + 1. Some other properties of
this group are also considered.
