  We disprove a conjecture stating that the integral cohomology of any
crystallographic group Z^n \rtimes Z_m is given by the cohomology of Z_m with
coefficients in the cohomology of the group Z^n, by providing a complete list
of counterexamples up to dimension 5. We also find a counterexample with odd
order holonomy, m=9, in dimension 8 and finish the computations of the
cohomology of 6-dimensional crystallographic groups arising as orbifold
fundamental groups of certain Calabi-Yau toroidal orbifolds.
