  The inner structure of neutron stars is still an open question. To make
progress and understand the qualitative impact of gauge interactions on the
neutron star structure we study neutron stars in a modified version of QCD. In
this modification the gauge group of QCD is replaced by the exceptional Lie
group G$_2$, which has neutrons and is accessible at finite density in lattice
calculations. Using an equation of state constructed from lattice calculations
we determine the mass-radius-relation for a neutron star in this theory using
the Tolman-Oppenheimer-Volkoff equation. The results exhibit an influence of
the non-trivial interactions on the mass-radius relation. However, the masses
of the quarks are found to have little influence. We also give density profiles
and the phase structure inside the neutron star. If the results carry over to
full QCD, much of the internal structure of neutron stars could already be
inferred from a precise measurement of the mass-radius relation.
