Playing games with groups

Doing mathematics is a pleasurable activity. It can be very much like playing a game. With the help of GAP as a juror, teacher there are zillions of games you can do by yourself. Some ideas:
- finding all groups ( of a specific order );
- finding the presentation formulas;
- finding the automorphism group;
- finding the character table;
- drawing the Cayley graph;
Once you start on this you get a sort of natural need for the use of either the Mathematica Abstract Algebra package, or even GAP ( or similar ), that is a mindset which makes learning the language rather easy.