character of a finite group

Definition.

Let $G$ be a finite group, and let $K$ be a field. A character from $G$ to $K$ is a group homomorphism $\chi \mathrm{:}G\mathrm{\to }{K}^{\mathrm{\times }}$, where $K^{\mathrm{\times }}$ is the multiplicative group $K\mathrm{\setminus }\mathrm{\{}{\mathrm{0}}_K\mathrm{\}}$.

Example:The Dirichlet characters are characters from $\mathbb{Z}/m\mathbb{Z}$ to $ℂ$.