(a) List the numbers that occur as the orders of elements of \(S_{4}\), and calculate how many elements there are in \(S_{4}\) of each of these orders.

(b) List all the possible cycle-shapes of even permutations in \(S_{6}\).

(c) Calculate the largest possible order of any permutation in \(S_{10}\).

(d) Calculate the largest possible order of any even permutation in \(S_{10}\).

(e) Find a value of \(n\) such that \(S_{n}\) has an element of order greater than \(n^{2}\).