Index-two character restriction dichotomy
= Index-two character restriction dichotomy
Let $H\triangleleft G$ have index two, and let $\lambda$ be the nontrivial linear character of $G/H$ inflated to $G$. For an irreducible character $\chi$ of $G$, either $\operatorname{Res}_H^G\chi$ is irreducible and $\chi\ne\chi\lambda$, or the restriction is a sum of two distinct irreducible characters and $\chi=\chi\lambda$.