In this paper, we construct Beauville surfaces with group for , and curves , such that the orbit of S under the action of the absolute Galois group contains non-homeomorphic conjugate surfaces. When the orbit consists exactly of two surfaces that have non-isomorphic fundamental groups, and the curves , have genera 8 and 49, which is shown to be the minimum for which there is a pair of non-homeomorphic Galois conjugate Beauville surfaces. As p grows the orbits contain an arbitrarily large number of non-homeomorphic surfaces.
Along the way we prove a metric rigidity theorem for Beauville surfaces which provides an elementary proof of the part of Catanese始s theory needed to prove our results.