Solution
= Solution
For a <character> $\chi$ of a <representation> of $H\leq K$, the <induced character> is
$$
\boxed{\operatorname{Ind}_H^K\chi(g)=\frac1{|H|}\sum_{x\in K\,;\,x^{-1}gx\in H}\chi(x^{-1}gx).}
$$
The sum is zero when no conjugate of $g$ meets $H$.