The $2$-closure $\overline{ G}$ of a permutation group $G$ on $\Omega$ is defined to be the largest permutation group on $\Omega$, having the same orbits on $\Omega\times\Omega$ as $G$. It is proved that if $G$ is supersolvable, then $\overline{ G}$ can be found in polynomial time in $|\Omega|$. As a byproduct of our technique, it is shown that the composition factors of $\overline{ G}$ are cyclic or alternating of prime degree.
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