Character orthogonality: (1/|G|)Σ χ_i(g) χ_j(g)* = δ_{ij}

First orthogonality relation for irreducible characters of a finite group (Schur 1905, Burnside 1911). For any finite group G with irreducible representations {ρ_i : G → GL(V_i)} and characters χ_i(g) = tr ρ_i(g), the characters are…