An algorithm for constructing representations of finite groups

We shall describe an algorithm for computing an irreducible matrix representation R which affords a given character χ of a given group G. The algorithm uses properties of the structure of G which can be computed efficiently by a program such as GAP, theoretical results from representation theory, theorems from group theory (including the classification of finite simple groups), and linear algebra. All results in this paper have been implemented in the GAP package REPSN.