  Recently, Cardoso et al. constructed an exact solution of Einstein's
equations that describes a supermassive black hole immersed into a dark matter
halo. In this work use a solution-generating technique, which is a direct
generalization of some of the Ehlers-Harrison transformation in the Ehlers
formalism in order to construct in an exact analytical form the charged version
of the Cardoso et al. solution. We describe some of its physical properties
and, finally, we also present its magnetized version.
