  Does a space enjoying good finiteness properties admit an algebraic model
with commensurable finiteness properties? In this note, we provide a rational
homotopy obstruction for this to happen. As an application, we show that the
maximal metabelian quotient of a very large, finitely generated group is not
finitely presented. Using the theory of 1-minimal models, we also show that a
finitely generated group $\pi$ admits a connected 1-model with
finite-dimensional degree 1 piece if and only if the Malcev Lie algebra
$\mathfrak{m}(\pi)$ is the lower central series completion of a finitely
presented Lie algebra.
