represents the group generated by multiplication of the permutations perm1,…,permn.
- The generating permutations permi must be given in disjoint cyclic form, with head Cycles.
- Properties of a permutation group are typically computed by constructing a strong generating set representation of the group using the Schreier–Sims algorithm.
Examplesopen allclose all
This is the group of all rotations and reflections of a regular -sided polygon, the dihedral group, for . It can be generated by a rotation of an angle and a reflection along an axis through a vertex:
The group of automorphisms of a graph is represented using PermutationGroup:
Properties & Relations (3)
Neat Examples (1)
Wolfram Research (2010), PermutationGroup, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationGroup.html.
Wolfram Language. 2010. "PermutationGroup." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PermutationGroup.html.
Wolfram Language. (2010). PermutationGroup. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PermutationGroup.html