|
gptkbp:instanceOf
|
gptkb:group_of_people
permutation group
|
|
gptkbp:automorphismGroup
|
gptkb:Z2
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:degree
|
6
|
|
gptkbp:exceptional_property
|
has exceptional outer automorphism
|
|
gptkbp:generation
|
(1 2)
(1 2 3 4 5 6)
|
|
gptkbp:has_outer_automorphism
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:A5
gptkb:C21
gptkb:A4
gptkb:C9
gptkb:V4
gptkb:C8
gptkb:D6
gptkb:C18
gptkb:C60
gptkb:S5
gptkb:C12
gptkb:C240
gptkb:C5
gptkb:C7
gptkb:alternating_group_A6
C10
C3
C4
C35
S4
C14
C2
S3
C15
C20
C6
C42
C24
C28
C30
C36
C48
C72
C10 x C3
C10 x C3 x C2
C12 x C5
C12 x C5 x C2
C12 x C6
C120
C120 x C1
C15 x C2
C15 x C2 x C2
C18 x C4
C180
C180 x C1
C2 x C2
C24 x C3
C240 x C1
C3 x C2
C3 x C2 x C2
C3 x C3
C30 x C2
C30 x C2 x C2
C36 x C2
C360
C360 x C1
C4 x C3
C4 x C3 x C2
C5 x C2
C5 x C2 x C2
C6 x C2
C6 x C2 x C2
C6 x C3
C6 x C3 x C2
C6 x C5
C6 x C5 x C2
C6 x C6
C6 x C6 x C2
C60 x C2
C60 x C2 x C2
C72 x C1
C720
C720 x C1
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S6
|
|
gptkbp:isomorphicTo
|
automorphism group of A6
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSolvable
|
false
|
|
gptkbp:notation
|
gptkb:S6
|
|
gptkbp:number_of_conjugacy_classes
|
11
|
|
gptkbp:number_of_elements_of_order_1
|
1
|
|
gptkbp:number_of_elements_of_order_10
|
72
|
|
gptkbp:number_of_elements_of_order_15
|
48
|
|
gptkbp:number_of_elements_of_order_2
|
120
|
|
gptkbp:number_of_elements_of_order_3
|
80
|
|
gptkbp:number_of_elements_of_order_4
|
90
|
|
gptkbp:number_of_elements_of_order_5
|
144
|
|
gptkbp:number_of_elements_of_order_6
|
120
|
|
gptkbp:order
|
720
|
|
gptkbp:primitive
|
true
|
|
gptkbp:transitive
|
true
|
|
gptkbp:bfsParent
|
gptkb:Tutte–Coxeter_graph
|
|
gptkbp:bfsLayer
|
6
|