PermutationGroupQ — test if a list of permutations forms a permutation group

MultiplicationTable  ▪  SamenessRelation

CyclicGroup — group of circular shift permutations

DihedralGroup — dihedral group

SymmetricGroup  ▪  AlternatingGroup  ▪  KSubsetGroup  ▪  KSubsetGroupIndex

MultiplicationTable — obtain a table of group multiplications

Orbits — find orbits induced by the action of the group

ReflexiveQ  ▪  TransitiveQ

OrbitRepresentatives  ▪  OrbitInventory

CycleStructure — compute cycle structure of a permutation

CycleIndex — cycle index of a group of permutations

SymmetricGroupIndex — cycle index of a symmetric group

CyclicGroupIndex  ▪  DihedralGroupIndex  ▪  AlternatingGroupIndex

SymmetricGroupIndex  ▪  PairGroup  ▪  PairGroupIndex