Let X be a nonorientable Klein surface (KS in short), that is a
compact nonorientable surface with a dianalytic structure defined
on it. A Klein surface X is said to be q-hyperelliptic if and only if there exists an involution Φ on X (a dianalytic homeomorphism of order
two) such that the quotient X/〈Φ〉 has algebraic genus q. q-hyperelliptic nonorientable KSs without boundary
(nonorientable Riemann surfaces) were characterized by means of
non-Euclidean crystallographic groups. In this paper, using that
characterization, we determine bounds for the order of the
automorphism group of a nonorientable q-hyperelliptic Klein surface X such that X/〈Φ〉 has no boundary and
prove that the bounds are attained. Besides, we obtain the
dimension of the Teichmüller space associated to this type of surfaces.
