  Let $\nabla$ be a meromorphic connection on a vector bundle over a compact
Riemann surface $\Gamma$. An automorphism $\sigma:\Gamma\to\Gamma$ is called a
symmetry of $\nabla$ if the pull-back bundle and the pull-back connection can
be identified with $\nabla$. We study the symmetries by means of what we call
the Fano Group; and, under the hypothesis that $\nabla$ has a unimodular
reductive Galois group, we relate the differential Galois group, the Fano group
and the symmetries by means of an exact sequence.
