Is a given set of group elements a set of coset representatives?

I am afraid the question is a bit technical, but I hope someone might have stumbled into a similar subject, or give me a pointer of some kind.

If G is a group (in the sense of algebraic structure), and if g₁, ..., g_n are elements of G, is there an algorithm (or a function in some dedicated program, like GAP) to determine whether there is a subgroup of G such that those elements form a set of representatives for the cosets of the subgroup? (We may assume that G is a permutation group, and probably even the full symmetric group.)

(There are of course several algorithms to find the cosets of a given subgroups, like Todd-Coxeter algorithm; this is a kind of inverse question.)

Thanks, Daniele