There is an equivalent description of double cosets in terms of single cosets. Let and both act by right multiplication on . Then acts by left multiplication on the product of coset spaces . The orbits of this action are in one-to-one correspondence with . This correspondence identifies with the double coset . Briefly, this is because every -orbit admits representatives of the form , and the representative is determined only up to left multiplication by an element of . Similarly, acts by right multiplication on , and the orbits of this action are in one-to-one correspondence with the double cosets . Conceptually, this identifies the double coset space with the space of relative configurations of an -coset and a -coset. Additionally, this construction generalizes to the case of any number of subgroups. Given subgroups , the space of -multicosets is the set of -orbits of .