|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:automorphismGroupIsomorphicTo
|
gptkb:S_3
|
|
gptkbp:centerIsTrivial
|
true
|
|
gptkbp:has1CyclicSubgroupOfOrder3
|
true
|
|
gptkbp:has3CyclicSubgroupsOfOrder2
|
true
|
|
gptkbp:hasElementOrder
|
2
1
3
|
|
gptkbp:hasNormalSubgroup
|
gptkb:S_3
gptkb:C_3
trivial group
|
|
gptkbp:hasSubgroup
|
S_n for n ≥ 3
|
|
gptkbp:hasSubgroupIsomorphicTo
|
gptkb:C_2
gptkb:C_3
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
S 3
|
|
gptkbp:isGroupOfPermutationsOn
|
3 elements
|
|
gptkbp:isGroupOfSymmetriesOf
|
gptkb:equilateral_triangle
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
gptkb:dihedral_group_of_order_6
|
|
gptkbp:isQuotientOf
|
free group on 2 generators by relations a^3 = b^2 = (ab)^2 = e
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:isSmallestNonAbelianGroup
|
true
|
|
gptkbp:isSolvable
|
true
|
|
gptkbp:isTransitivePermutationGroup
|
true
|
|
gptkbp:numberOfConjugacyClasses
|
3
|
|
gptkbp:numberOfIrreducibleRepresentations
|
3
|
|
gptkbp:order
|
6
|
|
gptkbp:outerAutomorphismGroupIsomorphicTo
|
gptkb:C_2
|
|
gptkbp:presentedBy
|
⟨a,b | a^3 = b^2 = e, bab = a^{-1}⟩
|
|
gptkbp:bfsParent
|
gptkb:Klein_four-group
gptkb:A_3
|
|
gptkbp:bfsLayer
|
5
|