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Let $C_2$ be the cyclic group of order $2$ and $D_{2n}$ be the dihedral groupof order $2n$, where $n$ is even. In this paper, we provide the exact values ofsome zero-sum constants over $D_{2n} \times C_2$, namely small Davenportconstant, Gao constant, $\eta$-constant and Erd\H os-Ginzburg-Ziv constant. Asa consequence, we prove the Gao's and Zhuang-Gao's Conjectures for this group.These are the first concrete results on zero-sum problems for a family ofnon-abelian groups of rank greater than $2$.

The main zero-sum constants over $D_{2n} \times C_2$