Schur index of irreducible character in characteristic zero divides exponent

This article states a result of the form that one natural number divides another. Specifically, the (Schur index) of a/an/the (irreducible linear representation) divides the (exponent of a group) of a/an/the (finite group).
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Statement

Suppose $G$ is a finite group, $\varphi$ is an Irreducible linear representation (?) of $G$ over $\mathbb {C}$, and $m(\chi )$ is the Schur index (?) of $\chi$. Then, $m(\chi )$ divides the exponent of $G$.

Here, $\mathbb {C}$ can be replaced by any splitting field for $G$ of characteristic zero.

Related facts

• Square of Schur index of irreducible character in characteristic zero divides order
• Schur index divides degree of irreducible representation