To facilitate HRI's transition from dyadic to group interaction, new methods are needed for robots to sense and understand team behavior. We introduce the Robot-Centric Group Detection and Tracking System (REGROUP), a new method that enables robots to detect and track groups of people from an ego-centric perspective using a crowd-aware, tracking-by-detection approach. Our system employs a novel technique that leverages person re-identification deep learning features to address the group data association problem. REGROUP is robust to real-world vision challenges such as occlusion, camera egomotion, shadow, and varying lighting illuminations. Also, it runs in real-time on real-world data. We show that REGROUP outperformed three group detection methods by up to 40% in terms of precision and up to 18% in terms of recall. Also, we show that REGROUP's group tracking method outperformed three state-of-the-art methods by up to 66% in terms of tracking accuracy and 20% in terms of tracking precision. We plan to publicly release our system to support HRI teaming research and development. We hope this work will enable the development of robots that can more effectively locate and perceive their teammates, particularly in uncertain, unstructured environments.