We show that K3 surfaces with non-symplectic automorphisms of prime order can be used to construct new compact irreducible G(2)-manifolds. This technique was carried out in detail by Kovalev and Lee for non-symplectic involutions. We use the Chen-Ruan orbifold cohomology to determine the Hodge diamonds of certain complex threefolds, which are the building blocks for this approach. (C) 2012 Elsevier B.V. All rights reserved.