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We determine the numerical invariants of blocks with defect group      D 2 n ∗  C 2 m ≅  Q 2 n ∗  C 2 m D_{2^n}\ast C_{2^m}\cong Q_{2^n}\ast C_{2^m}       (central product), where      n ≥  3 n\ge 3       and      m ≥  2 m\ge 2      . As a consequence, we prove Brauer’s      k ( B ) 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. This paper continues B. Sambale,  Blocks with defect group      D 2 n ×  C 2 m D_{2^n}\times C_{2^m}       , J. Pure Appl. Algebra  216  (2012), 119–125.

Blocks with central product defect group 𝐷_{2ⁿ}∗𝐶_{2^{𝑚}}