Order of elements in a symmetric group

Let S7 denote the symmetric group.

  1. Give an example of two non-conjugate elements of S7 that have the same order.
  2. If gS7 has maximal order, what is the order of g?
  3. Does the element g that you found in part (2) lie in A7? Fully justify your answer.
  4. Determine whether the set {hS7|h|=|g|} is a single conjugacy class in S7, where g is the element you found in part (2).