I am very new to the theory of groups and am writing a program that generates all subgroups of the symmetric group $S_n$; the idea is to find the generators for each subgroup.
With this thread, I was hoping to get some ideas about the following questions:
- Does there exists a way to pick the generators beforehand to avoid
recomputing the same subgroups? - If so, what would be a could starting point for me?
Currently, I am picking the set of generators by some arbitrary set of permutations from $S_n$.