Permutation Groups
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
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