In this paper, we consider the problem of linear modulation classification in the presence of unknown time offset, phase offset and received signal amplitude. We develop a novel hybrid maximum likelihood (HML) approach based on a Generalized Expectation Maximization (GEM) algorithm . Our approach is applicable to all QAM and PSK modulations, and it does not require any assumptions on the received signal-to-noise ratio (SNR). The GEM algorithm provides a tractable procedure to obtain maximum likelihood (ML) estimates which are extremely hard to obtain otherwise. Moreover, our approach employs only a small number of samples (in the order of hundreds) to perform both time and phase synchronization, signal power estimation, followed by modulation classification. The proposed approach also enables maximum a posteriori (MAP) decoding of the unknown constellation symbol sequence as a by-product of the GEM algorithm. We provide simulation results that show that the proposed approach provides excellent classification performance.