Some codes for permutation groups in sagemath. This is mainly intended for the purpose of computing the intersection density of a transitive group.
sage: G = permutation_group(SymmetricGroup(5))
sage: M = G.conjugacy_classes_subgroups()
sage: for x in M:
....: if x.is_isomorphic(DihedralGroup(6)):
....: H = x
....: break
sage: K = G.group_action(H)
sage: S = K.stabilizer(1)
sage: S.structure_description()
'D6'
sage: K.degree(),K.rank_of_group()