  We study finite-dimensional groups definable in models of the theory of real
closed fields with a generic derivation (also known as CODF). We prove that any
such group definably embeds in a semialgebraic group. We extend the results to
several more general contexts; strongly model complete theories of large
geometric fields with a generic derivation, model complete o-minimal expansions
of RCF with a generic derivation, open theories of topological fields with a
generic derivation. We also give a general theorem on recovering a definable
group from generic data in the context of geometric structures.
