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Brauer’s theorem on induced characters is an invitation to an algorithm for computing the character table of a finite group. We describe an implementation of such an algorithm and report on its performance. The main ingredients of the algorithm are Brauer’s theorem, and lattice reduction by LLL. We report on the performance of the algorithm in computing character tables of various groups, including...
Algorithms for computing the soluble radical and p-cores of a permutation group are described. The algorithms are based on homomorphic reductions, and avoid the computation of Sylow subgroups and the use of backtrack searches. Their implementation in Magma demonstrates a significant improvement over previous methods.
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