The Groups of Order 512

Recent progress in computational representation theory is surveyed. As an application of some methods for constructing ordinary character tables Brauer pairs among 2-groups of order up to 28 are determined. Furthermore the present status of the library of the tables of marks for simple groups which is available in GAPis described. Finally the state of the art of computational modular representation theory is summarized, by listing not only results on Brauer character tables of finite simple groups, which have been computed since the appearance of the first part of this paper, but also recent advances in the algorithms for dealing with representations over finite fields as well as Brauer characters. Also results concerning the structure of the module category of the group algebra of a finite simple group are reviewed.