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.