Fundamental group determines homology groups for compact connected orientable 3-manifold

Statement

For a compact connected orientable manifold of dimension 3, knowledge of the isomorphism class of the Fundamental group (?) is sufficient to determine the isomorphism classes of all the homology groups.

Facts used

1. Hurewicz theorem: Used to get $H_{1}$ from $\pi _{1}$ as the abelianization.
2. Dual universal coefficients theorem: Used to get $H^{1}$ from $H_{1}$ as the torsion-free part.
3. Poincare duality theorem: Used to get $H_{2}$ from $H_{1}$. Also, confirms that $H_{0}$ and $H_{3}$ are isomorphic to $\mathbb {Z}$.