  We investigate the motion of a massless body interacting with the Maxwell
relative equilibrium, which consists of n bodies of equal mass at the vertices
of a regular polygon that rotates around a central mass. The massless body has
three equilibrium Zn-orbits from which families of Lyapunov orbits emerge.
Numerical continuation of these families using a boundary value formulation is
used to construct the bifurcation diagram for the case n=7, also including some
secondary and tertiary bifurcating families. We observe symmetry-breaking
bifurcations in this system, as well as certain period-doubling bifurcations.
