# Tag Info

The answer to the first part of your question is yes. Given a permutation group $G = \langle S \rangle$, there is a polynomial time algorithm (clearly more efficient than the brute force approach which has factorial complexity), the Schreier-Sims algorithm (https://en.wikipedia.org/wiki/Schreier%E2%80%93Sims_algorithm) which computes a base and strong ...