Abstract
A complete procedure is described for constructing the irreducible KG-modules and their Brauer characters, where K is a finite field of characteristic p and G is a finite permutation or matrix group. The central idea is to construct a sequence {S1,…,Sn} of KG-modules, each having relatively small dimension, such that each Si has one or more irreducible constituents that are not constituents of S1,…,Si−1. The Meataxe, used in conjunction with condensation, is used to extract the new irreducibles from each Si. The algorithm has been implemented in Magma and is capable of constructing irreducibles of dimension over 200000.
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