Author Description

This memoir contains a complete classification of the finite irreducible 2-subgroups of $GL(4, {\mathbb C})$. Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by a generating set of monomial matrices. The problem is treated by a variety of techniques, including elementary character theory, a method for describing Hasse diagrams of submodule lattices, and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups, and Schur indices of their defining characters, are also considered.It's features include: a complete classification of a class of $p$-groups; a first step towards extending presently available databases for use in proposed 'soluble quotient algorithms'; and, groups presented explicitly; may be used to test conjectures or to serve generally as a resource in group-theoretic computations.