Let G be a group of order 60 and suppose G has exactly one Sylow 5 -subgroup and exactly one Sylow 3 -subgroup.
Which of the following statements must be true?
1
G is a cyclic group.
2
G is isomorphic to \( \mathbb{Z}_{60} \) .
3
G is isomorphic to \( \mathbb{Z}_5 \times \mathbb{Z}_3 \times \mathbb{Z}_4 \) .
4
G is not necessarily abelian, but the Sylow 5 - and 3 -subgroups are normal.