|
gptkbp:instanceOf
|
gptkb:group_of_people
permutation group
|
|
gptkbp:actsOn
|
set of 3 elements
|
|
gptkbp:alternatingSubgroup
|
gptkb:alternating_group_A_3
|
|
gptkbp:alternatingSubgroupOrder
|
3
|
|
gptkbp:automorphismGroup
|
gptkb:symmetric_group_S_3
trivial group
|
|
gptkbp:CayleyTable
|
well-defined
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:commutatorSubgroup
|
gptkb:alternating_group_A_3
|
|
gptkbp:conjugacyClasses
|
3
|
|
gptkbp:containsElement
|
(1 2 3)
(1 2)
(1 3 2)
(1 3)
(2 3)
identity permutation
|
|
gptkbp:degree
|
3
|
|
gptkbp:generation
|
(1 2 3)
(1 2)
|
|
gptkbp:hasElementOrder
|
2
1
3
|
|
gptkbp:hasNormalSubgroup
|
trivial group
|
|
gptkbp:hasSubgroup
|
cyclic group of order 2
cyclic group of order 3
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S 3
|
|
gptkbp:irreducibleRepresentationDegrees
|
2
1
|
|
gptkbp:isNonAbelian
|
false
|
|
gptkbp:isomorphicTo
|
gptkb:dihedral_group_D_3
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSolvable
|
true
|
|
gptkbp:maximalNormalSubgroup
|
gptkb:alternating_group_A_3
|
|
gptkbp:numberOfElementsOfOrder1
|
1
|
|
gptkbp:numberOfElementsOfOrder2
|
3
|
|
gptkbp:numberOfElementsOfOrder3
|
2
|
|
gptkbp:numberOfIrreducibleRepresentations
|
3
|
|
gptkbp:order
|
6
|
|
gptkbp:permutationRepresentation
|
faithful
|
|
gptkbp:presentedBy
|
⟨a, b | a^3 = b^2 = e, bab = a^2⟩
|
|
gptkbp:usedIn
|
group theory
representation theory
symmetry analysis
permutation puzzles
|
|
gptkbp:bfsParent
|
gptkb:Lie_algebra_su(3)
|
|
gptkbp:bfsLayer
|
6
|