Many models have been developed in recent years to describe pedestrian group behavior. Most prior research on group behavior focuses mainly on small groups and does not provide a general approach for grouping pedestrians with respect to different group sizes. They also analyze pedestrian group dynamics in normal circumstances. However, people's reactions who are aware of an emergency are not the same as how they respond to normal or usual situations. The central focus of this paper is to study pedestrian group behavior during evacuation. To accomplish these objectives, a new model is proposed with some extensions of a social force model in its emergency context. The new extensions are intended to simulate the single leader-centered and group-centered crowd behavior in emergencies. Besides small pedestrian groups, larger ones are also considered, and extensions are added in this direction. The model is calibrated using the results of an existing experimental study. Then, the model is verified by testing for the occurrence of certain emergent patterns. The results indicate that the proposed model can capture these trends. Additionally, the model is validated by comparing the simulation results with experimental results available in the literature. Also, several different evacuation scenarios are used to evaluate the proposed model. The simulation results show that leader-centered behavior performs better than group-centered behavior with respect to the evacuation time for small groups. The number of leaders also affects the evacuation time. Moreover, an increase in the number of leaders positively influences the effect of the width of the door on evacuation time, but the size of this effect depends on the number of leaders. Finally, group-centered behavior results in less evacuation time than leader-centered behavior in the presence of multiple exits, and leader-centered (also called single leader-centered in this study) behavior causes a more unbalanced use of the exits than group-centered behavior.