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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

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