## 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 $G$.