Computing matrix representations

Let G be a …nite group and be a faithful irreducible character for G. Earlier papers by the …rst author describe techniques for computing a matrix representation for G which a¤ords whenever the degree (1) is less than 32. In the present paper we introduce a new, fast method which can be applied in the important case where G is perfect and the socle soc(G=Z(G)) of G over its centre is abelian. In particular, this enables us to extend the general construction of representations to all cases where (1) 100. The improved algorithms have been implemented in the new version 3.0.1 of the GAP package REPSN by the …rst author.