TITLE: Software or tool for investigating groups
QUESTION [6 upvotes]: I'm interested in software that has the ability to investigate finite groups. In particular, I'd like to be able to ask it questions like "What are the solutions to $x^3 = 1$?" (i.e. find cube roots of unity) for a permutation group.
I've had a look at Maxima but don't see a way to ask it do that.

REPLY [3 votes]: There is also Magma, but unlike GAP it is not (in general) free.