| Abstract | Given an intransitive permutation group H with orbits O1, O2, ..., we can write H as a direct product of permutation groups G1 x G2 x ... Gk, with the groups having pairwise disjoint domains of action. We will present a polynomial time algorithm by C. Jefferson and M. Chang (2022), which computes the finest partition P of the orbits of H, such that H is the direct product of G1 x ... x Gk with the i-th group having the union of orbits in Pi as its domain of action. This algorithm is now available in Sage. |