  Compact manifolds of G_2 holonomy may be constructed by dividing a
seven-torus by some discrete symmetry group and then blowing up the
singularities of the resulting orbifold. We classify possible group elements
that may be used in this construction and use this classification to find a set
of possible orbifold groups. We then derive the moduli Kahler potential for
M-theory on the resulting class of G_2 manifolds with blown up co-dimension
four singularities.
