Abstract.  

In this GAP (www.gap-system.org) demonstration I will focus on computing with (mostly finite) groups on a computer. There are several ways to represent a group: by a finite presentation, by generating permutations, by generating matrices, ...
I will show what can be computed with these groups, this depends on the representation. Some questions are for example: What is the order of the group? What can we say about the structure of the group? Can we compute subgroups? Can we decide if a given permutation or matrix is contained in our group?