1. The problem statement, all variables and given/known data How many elements of order 2 does the symmetric group [itex]S_4[/itex] contain? 2. Relevant equations 3. The attempt at a solution I know that transpositions have order two. Moreover, any k-cycle has order k. Thus there are six elements with order two contained in [itex]S_4[/itex]? Is this all? Seems too simple.