Computing the character table of a finite group

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 local subgroups of 3Fi24 and maximal subgroups of the Monster. We find that for many interesting groups it performs far better than using the current standard method (Burnside–Dixon–Schneider).