Exceptional character

Definition
Let $$G$$ be a finite group, $$N$$ a normal subgroup, and $$(S,\tau)$$ a coherent pair for $$N$$ in $$G$$. Then, for any character $$\chi \in S$$, either $$\tau(\chi)$$ or $$-\tau(\chi)$$ is an irreducible character of $$G$$. An irreducible character arising in such a way is called an exceptional character (or more precisely, an exceptional character obtained by extending from $$N$$).