Brauer character inner product
= Brauer character inner product
{c}
For class functions on the p-regular elements of a finite group,
$$
\langle\phi,\psi\rangle_{p'}
=\frac1{|G|}\sum_{g\ p\text{-regular}}\overline{\phi(g)}\psi(g).
$$
Equivalently, summing over p-regular conjugacy-class representatives $x$ gives weights $1/|C_G(x)|$.