The permutation is question is Solution Basically, there is more then one way of writing down the elements as products of transpositions... So (1,3,7) = (1,7) o (1,3) = (4,7) o (1,7) o (1,4) o (1,3) You can see this by following what happens to the elements in the product:... (4,7) o (1,7) o (1,4) o (1,3) 1 -> 3 3 -> 1 -> 4 -> 7 4 -> 1 -> 7 -> 4 7 -> 1 (remember apply transformations from the back) So you can see in this product: 1 -> 3 -> 7 -> 1 and 4-> 4 which is the group element (1,3,7).