Our paper introduces a novel approach for collision avoidance (CA) among social groups that uses the collective gaze-movement angle (CGMA) between groups as the primary approach for collision prediction. Rules are used for handling the CA steering such that it mimics how real human groups travel together in wide-open walkable areas. We also show how to apply reciprocal velocity obstacle (RVO) based CA to groups as an alternative, and we use this alternative as a baseline for comparison in our approach for group-to-group CA. In an immersive evaluation using a head-mounted display, a group of people determined that our CA approach was much more believable than the RVO based CA approach for groups.