Mathematica 8 adds new functions and algorithms to work with permutations and permutation groups. This provides, for the first time in Mathematica, systematic access to the vast variety of groups that can be efficiently constructed by multiplication of a set of permutations.

• Support for permutations in disjoint cyclic notation.
• Support for groups generated by sets of permutations. Pre-stored generators for infinite families of groups and sporadic groups.
• Visualization of groups as multiplication tables or Cayley graphs.
• Computation of orbits, stabilizers, centralizers, coset representatives, etc.

Compute the Multiplication Table of a Group »	Cayley Graph Representation of a Group »	Points moved by increasing permutations in a group »
Orders of Groups with Random Generators »	Compute the Conjugacy Class of an Element of a Permutation Group »	Stabilizer Chain for the 3x3x3 Rubik Group »

RELATED FUNCTIONS

Cycles  PermutationCycles  PermutationCyclesQ  PermutationList  PermutationListQ  RandomPermutation  Permute  FindPermutation  PermutationReplace  PermutationSupport  PermutationMax  PermutationMin  PermutationLength  PermutationProduct  InversePermutation  PermutationPower  PermutationOrder  PermutationGroup  GroupGenerators  GroupOrder  GroupElements  GroupElementQ  GroupElementPosition  GroupMultiplicationTable  CayleyGraph  GroupOrbits  GroupStabilizer  GroupSetwiseStabilizer  GroupActionBase  GroupStabilizerChain  GroupCentralizer  RightCosetRepresentative  SymmetricGroup  AlternatingGroup  DihedralGroup  CyclicGroup  AbelianGroup  MathieuGroupM11  MathieuGroupM12  MathieuGroupM22  MathieuGroupM23  MathieuGroupM24  JankoGroupJ1  JankoGroupJ2  JankoGroupJ3  JankoGroupJ4  ConwayGroupCo1  ConwayGroupCo2  ConwayGroupCo3  FischerGroupFi22  FischerGroupFi23  FischerGroupFi24Prime  HigmanSimsGroupHS  McLaughlinGroupMcL  SuzukiGroupSuz  HeldGroupHe  HaradaNortonGroupHN  ThompsonGroupTh  BabyMonsterGroupB  MonsterGroupM  ONanGroupON  RudvalisGroupRu  LyonsGroupLy  TitsGroupT