Frobenius-Schur indicator of a representation (reviewed)

If $G$ is a finite group and $\chi$ is the character of an irreducible complex representation of $G$, then its Frobenius-Schur indicator is given by \[ \frac{1}{|G|}\sum_{g\in G} \chi(g^2).\] It is $0$, $1$, or $-1$ depending on whether the type of the representation is complex type, real, or quaternionic respectively.