  We determine the numerical invariants of blocks with defect group D_{2^n} *
C_{2^m} = Q_{2^n} * C_{2^m} (central product), where n > 2 and m > 1. As a
consequence, we prove Brauer's k(B)-conjecture, Olsson's conjecture (and more
generally Eaton's conjecture), Brauer's height zero conjecture, the
Alperin-McKay conjecture, Alperin's weight conjecture and Robinson's ordinary
weight conjecture for these blocks. Moreover, we show that the gluing problem
has a unique solution in this case.
