Cyclic group of prime-square order

Definition
Let $$p$$ be a prime number. The cyclic group of order $$p^2$$, denoted $$C_{p^2}, \mathbb{Z}_{p^2}, \mathbb{Z}/p^2\mathbb{Z}$$, is defined as the cyclic group with $$p^2$$ elements.

This is the cyclic group corresponding to the partition $$2$$ of $$2$$.