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How do I generate direct product of symmetric group $S_n$ and additive group of integers modulo $\mathbb Z/n\mathbb Z$ or $\mathbb Z_n$.

How do I generate cayley table for direct product of symmetric group $S_n$ and additive group of integers modulo $\mathbb Z/n\mathbb Z/m\mathbb Z$or$\mathbb Z_n$.Z_m$.

How do I generate cayley table for direct product of symmetric group $S_n$ and additive group of integers modulo $\mathbb Z/m\mathbb Z$ or $\mathbb Z_m$.