Exercise is essential for mastering mathematics, but it faces two major hurdles. First, students are often not motivated to do their homework. Second, checking traditional homework is a manual and labor-intensive process that becomes harder to support as the number of students increases. We argue that computer games could alleviate both problems. In contrast to homework, students are willing to spend many hours playing video games. And because video games keep track of the gamers' performance, they offer a scalable solution to the problem of checking the homework. We describe an experiment to augment traditional homework with a computer game that we have developed for exercising the topics of symmetry groups in an undergraduate college course. We describe the mathematical background of the subject matter, how we have embedded the mathematics into the game, the empirical results of playing the game, and the insights we have gained from this experiment.