Can anyone help here?
Do I make a Cayley table? If so, Im confused how to traverse the permutation. If I start at (15)(24), it goes 1 to 5, 5 to 4, 4 to 1 ... is this correct for first step?
First, you should have known about cycle notation before even tackling this problem.
You also should how to show that a subset of a group is a subgroup of the group.
In order to show that a subset H of G is a subgroup you must show that the identity is in H and that H is closed with respect to the group operation and group inverse.
Constructing a group table is one possible way to proceed.