  A Beauville surface (of unmixed type) is a complex algebraic surface which is
the quotient of the product of two curves of genus at least 2 by a finite group
G acting freely on the product, where G preserves the two curves and their
quotients by G are isomorphic to the projective line, ramified over three
points. Such a group G is called a Beauville group. We show that if a
characteristically simple group G is a cartesian power of a finite simple
alternating group, then G is a Beauville group if and only if it has two
generators and is not isomorphic to A_5.
