We report on an exploratory study in which we investigate the factor structure of an in-development survey on student experiences during group exams and subsequently examine how these factors can be modelled using performance and self-reported performance measures, while focusing on the role of group familiarity because it is a measure that we could influence with interventions. We ran an Exploratory Factor Analysis on a suite of questions that sought to investigate aspects of their group-exam experience, such as participation equity, the prevalence of productive group-work behaviours, and their personal experiences within the group. After stepwise item removal that took us from an item pool of twenty-one down to fourteen, our Exploratory Factor Analysis saw a four-factor structure emerge as the preferred option, consistent with the dominant focus of our underlying question design. The four factors that emerged---"presence of under-contributors", "presence of dominators", "productive group-work behaviours" and "personal experience"---and the questions that were removed as part of the factor analysis process indicate directions for future question development. These results suggest that our survey could be sensitive to the impact of interventions designed to improve overall student experience in group exams by targeting improvements in sense of academic familiarity with their groupmates, participation equity or productive group-work behaviours.