With the increasing availability and affordability of personal robots, they will no longer be confined to large corporate warehouses or factories but will instead be expected to operate in less controlled environments alongside larger groups of people. In addition to ensuring safety and efficiency, it is crucial to minimize any negative psychological impact robots may have on humans and follow unwritten social norms in these situations. Our research aims to develop a model that can predict the movements of pedestrians and perceptuallysocial groups in crowded environments. We introduce a new Social Group Long Short-term Memory (SG-LSTM) model that models human groups and interactions in dense environments using a socially-aware LSTM to produce more accurate trajectory predictions. Our approach enables navigation algorithms to calculate collision-free paths faster and more accurately in crowded environments. Additionally, we also release a large video dataset with labeled pedestrian groups for the broader social navigation community. We show comparisons with different metrics on different datasets (ETH, Hotel, MOT15) and different prediction approaches (LIN, LSTM, O-LSTM, S-LSTM) as well as runtime performance.