Thank you.
I don't understand what you mean. But I will tell you this.
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.