Character formula for an induced representation
= Character formula for an induced representation
For $H\leq G$ and an $H$-character $\chi$,
$$
(\operatorname{Ind}_H^G\chi)(g)=\frac1{|H|}
\sum_{\substack{x\in G\\x^{-1}gx\in H}}\chi(x^{-1}gx).
$$
= Character formula for an induced representation
For $H\leq G$ and an $H$-character $\chi$,
$$
(\operatorname{Ind}_H^G\chi)(g)=\frac1{|H|}
\sum_{\substack{x\in G\\x^{-1}gx\in H}}\chi(x^{-1}gx).
$$