Classifying finite monomial linear groups of prime degree in characteristic zero

Let [Formula: see text] be a prime and let the complex field. We explicitly classify finite solvable irreducible monomial subgroups of up to conjugacy. That is, we give complete irredundant list text]-conjugacy class representatives as generating sets matrices. Copious structural information about non-solvable is also proved, enabling classification all such groups bar one family. explain obstacles in that exceptional case. For text], text]. Our classifications are available publicly Magma.