The conjugacy classes of S n correspond to the cycle types of permutations; that is, two elements of S n are conjugate in S n if and only if they consist of the same number of disjoint cycles of the same lengths. For instance, in S 5, (1 2 3)(4 5) and (1 4 3)(2 5) are conjugate; (1 2 3)(4 5) and (1 2)(4 5) are not. A conjugating element of S n can be constructed in "two line notation" by placing the "cycle notations" of the two conjugate permutations on top of one another. Continuing the previous example, k = ( 1 2 3 4 5 1 4 3 2 5 ) , which can be written as the product of cycles as (2 4). This permutation then relates (1 2 3)(4 5) and (1 4 3)(2 5) via conjugation, that is, ( 2 4 ) ∘ ∘ ( 1 2 3 ) ( 4 5 ) ∘ ∘ ( 2 4 ) = ( 1 4 3 ) ( 2 5 ) . It is clear that such a permutation is not unique.