A matrix is said to be monomial if every row and column has only one nonzero entry. Let G be a group. A representation ρ: G → GL n (ℂ) is said to be a monomial representation of G if there exists a basis with respect to which ρ(g) is a monomial matrix for every g ∈ G. We use elementary methods to classify the irreducible monomial representations of the groups L 2(q), L 3(q) and their natural decorations.