Inertia group of a character
= Inertia group of a character
{title2=$I_G(\theta)=\{g\in G:\theta^g=\theta\}$}
For $N\triangleleft G$ and $\theta\in\operatorname{Irr}(N)$, set $\theta^g(n)=\theta(g^{-1}ng)$. Its inertia group is its stabilizer under this conjugation action and contains $N$. Write $\operatorname{Irr}(G\mid\theta)$ for the <irreducible characters> of $G$ whose restriction to $N$ contains $\theta$.