Two-closure of supersolvable permutation group in polynomial time

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 $OmegatimesOmega$ 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.