({{, (RefLink[GroupGenerators, paclet:ref/GroupGenerators])[group] 
returns a list of generators of group. }})

OpenersNotesSection(Spacer1)Details

The type of generators will depend on the representation type of the group.

For an explicit permutation representation, (RefLink[GroupGenerators, paclet:ref/GroupGenerators])[(RefLink[PermutationGroup, paclet:ref/PermutationGroup])[{(Subscript[g, 1]),…,(Subscript[g, n])}]] returns the list {(Subscript[g, 1]),…,(Subscript[g, n])}.

For a named abstract group, the generators of a default representation are returned.

OpenersPrimaryExamplesSection(Spacer1)Examples  (5)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Generators of a permutation group:

PermutationGroup[{Cycles[{{1,2}}],Cycles[{{1,3},{2,4}}]}]//GroupGenerators

A symmetric group is generated by default with two permutations, a transposition, and a shift:

GroupGenerators[SymmetricGroup[8]]

OpenersExampleSection1(Spacer1)Scope  (3)

Generators for a group defined by generators:

GroupGenerators[PermutationGroup[{Cycles[{{1,2},{3,4}}],Cycles[{{1,3},{2,4}}]}]]

Generators for a named group, using a default representation:

GroupGenerators[DihedralGroup[4]]

Support lengths of the default permutation generators of a sporadic simple group:

PermutationLength/@GroupGenerators[FischerGroupFi23[]]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[PermutationGroup, paclet:ref/PermutationGroup])  ▪  (RefLink[Cycles, paclet:ref/Cycles])}})}})

({{DocumentationFooterIconsRelatedTutorial.png, ({{Tutorials}, {▪(RefLinkPlain[Permutations, paclet:tutorial/Permutations])}, {▪(RefLinkPlain[Permutation Groups, paclet:tutorial/PermutationGroups])}, {▪(RefLinkPlain[Named Groups, paclet:tutorial/NamedGroups])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Group Theory, paclet:guide/GroupTheory])}})}})