= Frobenius-Schur indicator
{c}
{title2=$\nu(\chi)=|G|^{-1}\sum_{g\in G}\chi(g^2)$}
{wiki=Frobenius–Schur_indicator}
For an irreducible complex <character of a representation>, the indicator is $1$ for real type, $-1$ for quaternionic type and $0$ for complex type, the latter meaning $\chi\ne\overline\chi$. It detects the invariant bilinear form on an irreducible representation. For an odd-order group, squaring permutes its elements, so every nontrivial irreducible character has indicator zero by <character orthogonality>.
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