Given a group $G < S_N$ is there an "efficient" way to identify (or construct) the "minimal" permutation groups $H_i \leq S_N$ such that $G < H_i$? $H_i$'s are minimal in the sense that there $\not \exists H' \quad s.t.\quad G<H'<H_i$.
closed as off-topic by Shaun, The Count, José Carlos Santos, Shailesh, 0XLR Aug 11 at 3:09
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