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Let $G$ be a finite group and $N\unlhd G$. In this note, we construct a classposet of $G$ for some cyclic subgroup $C$ of $G$. And we find a relationbetween $m_{G,N}$ and the Euler characteristic of some nerve spaces of theseposets(see Main Theorem).

A topological interpretation about $m_{G, N}$ for finite group $G$ with normal subgroup $N$