The GF(2) General Linear Group for Dimensions 2, 3, 4, and 5

This report contains some data about the General Linear Groups of GF(2) for dimensions 2, 3, 4, and 5. These groups are groups of matrices over GF(2), the integers modulo 2. The General Linear Group of order is the set of all non-singular matrices over some field, in this case, GF(2). We give the conjugacy classes of all matrices and all isomorphs of the symmetric group. The analysis for dimension 5 is incomplete. The observations we make here will be supported using short programs that use the GF2Matrices package, which is available as a Baylor Computer Science Technical report. (See http://beardocs.baylor.edu).