  In this paper we determine all finite groups G that can act on some compact
Riemann surface M with the property that if H is any non-trivial subgroup of G,
then the orbit surface M/H is the Riemann sphere. The idea is to look at the
induced action on the vector space of holomorphic differentials on M (in the
positive genus case) and then use the old-known (Wolf) classification of groups
admitting fixed point-free linear actions. A description of the corresponding
group actions is given in terms of Fuchsian representations.
