A representation of a group \(G\) is a homomorphism \(\phi:G \to GL(V)\) (\(GL\) is the general linear group) for some (finite-dimensional) vector space \(V\). The dimension of \(V\) is called the degree of \(\phi\). Note: The trivial representation sends all elements to \(1\).

Two representations \(\phi:G \to GL(V), \psi:G \to GL(W)\) are equivalent if there exists an isomorphism such that \(\psi_{g} = T\phi T^{-1}\) for all \(g \in G\). Where \(T:V \to W\).