  In this article we study Kummer's $\mathcal D$-groupoid, which is the
groupoid of symmetries of a meromorphic projective structure. We give necessary
and sufficient conditions for its minimality, in the sense of not having
infinite sub-$\mathcal D$-groupoids. The condition that we find turns out to be
equivalent to the strong minimality of the non-linear Schwarzian equation and
the non-integrability by means of Liouvillian functions of the linear
Schwarzian equation.
