|
gptkbp:instanceOf
|
gptkb:group_of_people
permutation group
|
|
gptkbp:actsOn
|
set of 4 elements
|
|
gptkbp:automorphismGroup
|
gptkb:S_4
gptkb:C_2
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:containsElement
|
transpositions
3-cycles
identity permutation
4-cycles
products of disjoint transpositions
|
|
gptkbp:degree
|
4
|
|
gptkbp:generation
|
(1 2)
(1 2 3 4)
|
|
gptkbp:hasFaithfulPermutationRepresentation
|
degree 12
degree 4
degree 6
|
|
gptkbp:hasMaximalSubgroup
|
gptkb:S_5
|
|
gptkbp:hasNormalSubgroup
|
gptkb:alternating_group_A_4
|
|
gptkbp:hasQuotientGroup
|
gptkb:S_3
gptkb:C_2
|
|
gptkbp:hasSubgroup
|
gptkb:Klein_four-group
gptkb:alternating_group_A_4
gptkb:dihedral_group_D_4
2
1
12
3
4
6
8
cyclic group of order 4
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S 4
|
|
gptkbp:isImprimitive
|
false
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
automorphism group of Klein four-group
|
|
gptkbp:isPrimitive
|
true
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSolvable
|
true
|
|
gptkbp:isTransitiveOn
|
true
|
|
gptkbp:notation
|
gptkb:S_4
|
|
gptkbp:numberOfConjugacyClasses
|
5
|
|
gptkbp:numberOfElementsOfOrder1
|
1
|
|
gptkbp:numberOfElementsOfOrder2
|
9
|
|
gptkbp:numberOfElementsOfOrder3
|
8
|
|
gptkbp:numberOfElementsOfOrder4
|
6
|
|
gptkbp:order
|
24
|
|
gptkbp:usedIn
|
gptkb:algebra
gptkb:Galois_theory
group theory
|
|
gptkbp:bfsParent
|
gptkb:symmetric_group_S_5
gptkb:K_4_(complete_graph_on_4_vertices)
gptkb:dihedral_group_of_order_8
|
|
gptkbp:bfsLayer
|
7
|