Indicator character

Definition
The indicator character of a finite group is the virtual character whose value at an element is the number of square roots that element has. In other words, the indicator character of a group $$G$$ sends $$x$$ to the number of solutions of $$y^2 = x$$ in $$y$$.

Taking the inner product of a given character with the indicator character, gives the Frobenius-Schur indicator of the given character.