The classification of surfaces with p_g = q = 0 isogenous to a product of curves

We classify all the surfaces with p_g = q = 0 which admit an unramified covering which is isomorphic to a product of curves. Beyond the trivial case \PP^1 x \PP^1 we find 17 families which we explicitly describe. We reduce the problem to a combinatorial description of certain generating systems for finite groups which we solve using also MAGMA's library of groups of small order.