 On the other hand, for |"G"| = 60 = 22 · 3 · 5, then "n"3 = 10 and "n"5 = 6 is perfectly possible.And in fact, the smallest simple non-cyclic group is "A"5, the alternating group over 5 elements.It has order 60, and has 24 cyclic permutations of order 5, and 20 of order 3.