For a permutation group $G$, and a stable set $X$ of positive integers, the RestrictedPermGroup( G, X ) command returns a permutation group obtained by restricting the action of $G$ to the set $X$.

The set $X$ must be stable under the action of $G$; that is, for any element $x$ in $X$, we must have $x^g$ in $X$, for all $g$ in $G$. For example, $X$ might be an orbit of $G$, or a union of orbits of $G$.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{CyclicGroup}\left(72\,'\mathrm{mindegree}'\right)$

$G≔C_{17}$

$H≔\mathrm{RestrictedPermGroup}\left(G\,\left\{1\,2\,3\,4\,5\,6\,7\,8\right\}\right)$

$H≔⟨\left(1\,2\,3\,4\,5\,6\,7\,8\right)⟩$

$\mathrm{RestrictedPermGroup}\left(G\,\left\{10\,11\,12\,13\,14\,15\right\}\right)$

Error, (in Perm:-extPermRestrict) new domain is not fixed set-wise