FriCAS implements several algorithms for working with groups:
- "meat Axe", that is algorithm for splitting representations of groups (or associative 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