The "order of the equivalence classes" is just the number of elements in each equivalence class. And it is easy to prove that all equivalence classes, for a given equivalence relation, have the same number of elements so your answer will be a single number. Since you are dealing with groups, it might be simplest to find how many pairs (r, k) are equivalent to [itex](e_H, e_K)[/itex], the identity elements of each group.