Let $H\vartriangleleft G$, and $\theta$ be an irreducible $\mathbb{C}$-character of $H$. Suppose $\theta$ is invariant in $G$ and $\theta(1)=9$.
Question: Is $\theta$ extendible to $G$?
Is a $G$-invariant character $\theta$ of $H$ extendible to $G$?
C. Simon
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