Finite Irreducible Imprimitive Nonmonomial Complex Linear Groups of Degree 4

The article contains a classification of the groups indicated in the title, consisting of a parametrised list of groups, each relevant group being conjugate in GL(4, ) to precisely one group on the list (and each group on the list being relevant). Each group on this list is given by a generating set of matrices, whose entries are explicit functions of finitely many integers satisfying certain relations. Also included is a similar classification of the finite primitive subgroups of GL(2, ).