  For a central perfect extension of groups $A \rightarrowtail
G\twoheadrightarrow Q$, first we study the natural image of $H_3(A,\mathbb{Z})$
in $H_3(G, \mathbb{Z})$. As a particular case, we show that if the extension is
universal this image is 2-torsion. Moreover when the plus-construction of the
classifying space of $Q$ is an $H$-space, we also study the kernel of the
surjective homomorphism $H_3(G,\mathbb{Z}) \to H_3(Q, \mathbb{Z})$.
