  We construct a maximal discrete extension of the paramodular group with a
full level-2 structure. The corresponding Siegel variety parametrizes
(birationally) the space of Kummer surfaces associated to (1,p)-polarized
abelian surfaces with a level-2 structure. In the case p=3 this is related to
the Barth-Nieto quintic and in this case we also determine the space of cusp
forms of weight 3.
