  Let $G$ be an elementary abelian $p$-group. We calculate
$K_2(\mathbb{Z}[G]/I)$ for certain ideals $I \subseteq \mathbb{Z}[G]$ of the
finite $p$-power index through computations of Dennis-Stein symbols. As an
application, for $p$ an odd prime, we give a complete description of the
relative group $SK_1(\mathbb{Z}[G],p^k\mathbb{Z}[G])$ and obtain more precise
lower bounds of the prank of $K_2(\mathbb{Z}[G])$ and $Wh_2(G)$.
