# Computing size of permutation group from generators

You're given $k$ permutations $a_1,\dots,a_k$. Consider closure of this set under the composition operation. What are most efficient and simple algorithms to calculate the size of this closure?

• Don't think there are efficient algorithms for doing this in a classical setting – Samuel Schlesinger Nov 6 '17 at 14:32
• I doubt that since there at least one such algorithm in Polynomial-time algorithms for permutation groups. What is asked here is maybe some general overview of existing algorithms and their key ideas. – Oleksandr Kulkov Nov 6 '17 at 18:26
• If you already know of some algorithms for this problem, please edit your question to provide a summary of the algorithms/references you already know of. As our help center says, "Try to make your question interesting for others by providing some background knowledge. Remember, questions should be based on knowledge sharing". – D.W. Nov 7 '17 at 23:55