Is there a relation between narcissism and poor character?

No :) Unhealthy narcissism is not an indication of "poor character" so much as an indication that the person, as a child, was probably not given enough positive reinforcement and stroking. As a result, the person has a craving to be stroked and validated and complimented and often the center of attention. But this does not make the person a bad person, just a vulnerable person.
Narcissism. The hallmark of a narcissist is an immense ego, grandiosity, and self-importance, as well as being entitled, and a tendency to use and objectify others as well as thinking of people in all-good or all-bad terms instead of shades of gray. The core of a narcissist is profound insecurity and poor self-esteem.