This paper explores the viability and development of the first edition of the researcher's mathematical card game, Groups, as a learning tool for elementary group theory, a topic in abstract algebra. "Groups" was play-tested by six undergraduate students in late 2016 who provided feedback on "Groups" from both utility-centric and design-centric perspectives. This paper addresses how well undergraduates with no prior group theory experience understand the fundamentals of group theory after playing several games of "Groups," and how well undergraduates with prior knowledge of group theory related the "Groups" game play and mechanics to the fundamentals of group theory. Based on interview and questionnaire data, players found "Groups" to be an engaging and effective learning tool with both strengths and weaknesses in the tested iteration.