|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:automorphismGroup
|
gptkb:symmetric_group_S4
cyclic group of order 2
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:derivedSubgroup
|
gptkb:Klein_four-group
|
|
gptkbp:hasCharacterTable
|
yes
|
|
gptkbp:hasConjugacyClassCount
|
4
|
|
gptkbp:hasElementOrder
|
2
1
3
|
|
gptkbp:hasIndexInS4
|
2
|
|
gptkbp:hasIrreducibleRepresentationsCount
|
4
|
|
gptkbp:hasNormalSubgroup
|
gptkb:Klein_four-group
gptkb:symmetric_group_S4
trivial group
itself
|
|
gptkbp:hasOrderFactorization
|
2^2 × 3
|
|
gptkbp:hasPermutationRepresentationDegree
|
4
|
|
gptkbp:hasSubgroup
|
gptkb:Klein_four-group
gptkb:symmetric_group_S4
|
|
gptkbp:hasSylow2SubgroupOrder
|
4
|
|
gptkbp:hasSylow3SubgroupOrder
|
3
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
alternating group A4
|
|
gptkbp:isGroupOfEvenPermutations
|
true
|
|
gptkbp:isNonAbelian
|
false
true
|
|
gptkbp:isNoncyclic
|
true
|
|
gptkbp:isomorphicTo
|
group of even permutations on 4 elements
|
|
gptkbp:isPerfect
|
false
|
|
gptkbp:isQuotientOfS4ByV4
|
true
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSmallestNonabelianAlternatingGroup
|
true
|
|
gptkbp:isSmallestNonabelianGroup
|
false
|
|
gptkbp:isSmallestNoncyclicSimpleGroup
|
false
|
|
gptkbp:isSolvable
|
true
|
|
gptkbp:isTransitiveOn
|
set of 4 elements
|
|
gptkbp:isTransitiveSubgroupOf
|
gptkb:symmetric_group_S4
|
|
gptkbp:numberOfElementsOfOrder1
|
1
|
|
gptkbp:numberOfElementsOfOrder2
|
3
|
|
gptkbp:numberOfElementsOfOrder3
|
8
|
|
gptkbp:numberOfSylow2Subgroups
|
3
|
|
gptkbp:numberOfSylow3Subgroups
|
4
|
|
gptkbp:order
|
12
|
|
gptkbp:presentedBy
|
⟨ x, y | x^3 = y^2 = (xy)^3 = 1 ⟩
|
|
gptkbp:bfsParent
|
gptkb:alternating_group_A5
|
|
gptkbp:bfsLayer
|
6
|