Diverging sequence of symplectic matrices.

Question

I wanted to find examples of manifold that are compact and examples that are not compact. I think the orthogonal manifold $O(n)=\{X\in \mathbb{R}^{m\times n}:X^TX = I\}$ is compact since it is closed (because the preimage $F^{-1}(I)$ where $F : X\to X^TX)$. And it is bounded since for the orthogonal matrices, the norm of the colums are $1$ so the frobenius norm is $\sqrt{n}$. But what about the symplectic group $Sp(2n) = \{X\in \mathbb{R}^{2n\times 2n}:X^JX = J\}$ where $J = \begin{bmatrix}0 & I\\ -I & 0\end{bmatrix}$. Is there an easy example of symplectic matrices for witch the norm goes to infinity?