I will describe a new algorithm for computing the character table of a finite group. The main ingredients of the algorithm are Brauer's theorem on induced characters and lattice reduction by LLL. We find that for many interesting groups it performs far better than using the current standard method (Burnside–Dixon–Schneider). I will report on the performance of the algorithm in computing character tables of various groups, including local subgroups of 3Fi₂₄ and some maximal subgroups of the Monster.