Representations of the first degree of Abelian groups

A complete description of $\operatorname{Hom}(G,\operatorname{Aut}V)$, where $V$ is a vector space of dimension $1$ on a finite field $\mathbb{F}_{q}$, on the rational field $\mathbb{Q}$, on the field of real numbers $\mathbb{R}$, and on the field of complex numbers $\mathbb{C}$ is given. The description is given in each of these four cases for any Abelian group $G$.