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Let $G$ be a finite group, and suppose that a set of proper subgroups $H_1,\dotsc,H_n$ satisfy $G=\bigcup_{g\in G}\bigcup_{i=1}^nH_i^g$, where $H_i^g$ is the conjugate of $H_i$ by $g$. In this case, ...

Given an (irreducible complex) character of a finite group the following three construction all yield another irreducible character of the same degree: multiplying by a degree 1 character applying an ...