Blocks with defect group D₂ₙ * C₂ₘ

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We determine the numerical invariants of blocks with defect group D₂ₙ * C₂ₘ = Q₂ₙ * C₂ₘ (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.