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Let $X$ be a path-connected, locally path-connected and semilocally simply-connected space. Can we find a correspondence between degree $n$ covering spaces of $X$ and group homomorphism $\pi_1(X)\rightarrow S_n$? ($S_n$ is the permutation group)

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    Connected $n$ covering spaces are in correspondence with the orbits of all index $n$ subgroup acted by conjugation. I cannot find an easy way to identify these orbits.2012-08-21

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