Let $G$ be the finitely presented group $G=\left\langle a, b \mid a^{2} b^{3} a^{3} b^{2}=1\right\rangle$. Construct a path connected space $X$ with $\pi_{1}(X, x) \cong G$. Show that $X$ has a unique connected double cover $\pi: Y \rightarrow X$, and give a presentation for $\pi_{1}(Y, y)$.