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We compute the group homology, the topological K-theory of the reducedC^*-algebra, the algebraic K-theory and the algebraic L-theory of the groupring of the semi-direct product of the three-dimensional discrete Heisenberggroup by Z/4. These computations will follow from the more general treatment ofa certain class of groups G which occur as extensions 1-->K-->G-->Q-->1 of atorsionfree group K by a group Q which satisfies certain assumptions. The keyingredients are the Baum-Connes and Farrell-Jones Conjectures and methods fromequivariant algebraic topology.

K– andL–theory of the semi-direct product of the discrete 3–dimensional Heisenberg group by ℤ∕4