From Nathan Carter:
Group Explorer is mathematical visualization software for the abstract algebra classroom. It helps the user visualize group theory, builds students' intuition, and enables experimentation with groups. Each picture of a group is very interactive. Study properties of the group by reorganizing or highlighting a diagram. Save views to use in a report or web page.
Group Explorer comes with a vast library of groups, very handy for learning by example, for testing conjectures, and getting one's hands dirty in the real subject matter of group theory. Each group in the library, when double-clicked opens a group info window, full of useful information about the group.