Question: how many abelian groups are there of order 6?
Answer: Order 6 (2 groups: 1 abelian, 1 nonabelian) In cycle notation for permutations, its elements are (1), (1 2), (1 3), (2, 3), (1 2 3) and (1 3 2). There are four proper subgroups of S_3; they are all cyclic.