The group organization used for group learning in a knowledge intensive domain like software development affects educational achievement. This paper proposes a group organization system for software engineering education done through group learning. The organizational problem itself is defined and why a Genetic Algorithm (GA) is an appropriate means of solving this problem is explained. This system is a Web application developed with open source software and runs on an open source software platform. Based on the group organization data collected from actual classes, we generated various group organizations by using different strategy parameter values. We then gave a questionnaire to actual students asking them which solution produced the fairest group organization. The replies received revealed that the candidate solution that set greater weight on leadership capability and system analysis capability was the fairest.