# Number of projective equivalence classes of irreducible linear representations

## Definition

Suppose is a finite group and is a field. The **number of projective equivalence classes of irreducible linear representations** is defined in the following equivalent ways:

- It is the number of equivalence classes of irreducible linear representations of over under the action of the multiplicative group of one-dimensional representations.
- It is the number of equivalence classes of irreducible linear representations under the equivalence relation of being projectively equivalent (see also projective representation).