Regular character
= Regular character
{title2=$\chi_{\mathrm{reg}}(g)=|G|\,\delta_{g,e}$}
The <character> of the <regular representation> of a finite <group> is $|G|$ at the identity and zero elsewhere. Left multiplication permutes its group-indexed <basis>, and a nonidentity element fixes none of those <basis vectors>. Thus each complex <irreducible representation> occurs with <representation multiplicity> equal to its <dimension>, by the <character inner product>.