Number of projective equivalence classes of irreducible linear representations

Definition

Suppose $G$ is a finite group and $K$ 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 $G$ over $K$ 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).