Lcm of Schur indices of irreducible representations

Definition

For a group over a field

Suppose $G$ is a group and $K$ is a field whose characteristic does not divide the order of $G$. The lcm of Schur indices of irreducible representations of $G$ over $K$ is defined as the least common multiple of all the Schur index values of all the irreducible linear representations of $G$ over $K$.

Typical context: finite group and splitting field

The typical context is where $G$ is a finite group and $K$ is a splitting field for $G$. In particular, the characteristic of $K$ is either zero or is a prime not dividing the order of $G$, and every irreducible representation of $G$ over any extension field of $K$ can be realized over $K$.