FriCAS impements several algorithms for working with goups:

• "meat Axe", that is algorithm for splitting representations of groups (or assiciative algebras) over finite fields
• Schreier-Sims algorithm for finding base and strong generators of a permutation group
• Tod-Coxeter coset enumeration, to build permutation representation of group given by a presentation

One can also use more naive method, like ExampleCharacterTable