The orbits of the group on ordered k-tuples of distinct points (g·(t₁,…,t_k) = (g[t₁],…,g[t_k])).
k = 1 is the point-orbits (orbits); k = 2 (on distinct pairs) refines orbitals; in general
the group is k-transitive iff this is a single orbit — the rungs of the transitivity ladder.