We provide a systematic and thorough exploration of the A(48) family symmetry and the consistent generalised CP symmetry. A model-independent analysis of the achievable lepton flavor mixing is performed by considering all the possible remnant symmetries in the neutrino and the charged lepton sectors. We find a new interesting mixing pattern in which both lepton mixing angles and CP phases are nontrivial functions of a single parameter theta. The value of theta can be fixed by the measured reactor mixing angle theta(13), and the excellent agreement with the present data can be achieved. A supersymmetric model based on Delta(48) family symmetry and generalised CP symmetry is constructed, and this new mixing pattern is exactly reproduced.