  We compute the group homology, the topological K-theory of the reduced
C^*-algebra, the algebraic K-theory and the algebraic L-theory of the group
ring of the semi-direct product of the three-dimensional discrete Heisenberg
group by Z/4. These computations will follow from the more general treatment of
a certain class of groups G which occur as extensions 1-->K-->G-->Q-->1 of a
torsionfree group K by a group Q which satisfies certain assumptions. The key
ingredients are the Baum-Connes and Farrell-Jones Conjectures and methods from
equivariant algebraic topology.
