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Let $H$ be an extension of a finite group $Q$ by a finite group $G$. Inspiredby the results of duality theorems for \'etale gerbes on orbifolds, we describethe number of conjugacy classes of $H$ that maps to the same conjugacy class of$Q$. Furthermore, we prove a generalization of the orthogonality relationbetween characters of $G$.

Conjugacy classes and characters for extensions of finite groups