Regular Representation of G

Let $g$ be the order of $G$ , and let $V$ be a vector space of dimension $g$ , with a basis $(e_t)_{t\in G}$ indexed by the elements $t$ of $G$ . For $s\in G$ , let $\rho_s$ be the linear map of $V$ into $V$ which sends $e_t$ to $e_{st}$ ; this defines a linear representation, which is called the regular representation of $G$ .