Conjugacy-class sum
= Conjugacy-class sum
{title2=$z_C$}
= Class sum
{synonym}
For a <conjugacy class> $C$ of a finite <group>, $z_C=\sum_{g\in C}g$ is central in its <group algebra>. In a complex <irreducible representation> of degree $d$ and <character of a representation> $\chi$, it acts by $|C|\chi(g)/d$; its trace gives this formula and <Schur lemma> gives scalarity.