Irreducible character degree

The degree of an irreducible character $\chi$ is $\chi (1)$, the dimension of the corresponding irreducible representation.

For a finite group $G$ and prime number $p$, the notationdenotes the irreducible characters whose irreducible character degree is coprime to $p$.

A linear character is the character of a one-dimensional representation and therefore has degree one.

A nonlinear irreducible character has degree greater than one.