  We are interested in the question of the existence of flat manifolds for
which all $\mathbb R$-irreducible components of the holonomy representation are
either absolutely irreducible, of complex or of quaternionic type. In the first
two cases such examples are well known. But the existence of the third type of
flat manifolds was unknown to the authors. In this article we construct such an
example. Moreover, we present a list of finite groups for which a construction
of manifolds of quaternionic type is impossible.
