|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:permutation_group
|
|
gptkbp:actsOn
|
set of 6 elements
|
|
gptkbp:automorphismGroup
|
order 2
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:conjugacy_classes
|
11
|
|
gptkbp:contains
|
gptkb:alternating_group_A_6
|
|
gptkbp:degree
|
6
|
|
gptkbp:generation
|
transpositions
5-cycles and transpositions
|
|
gptkbp:has_exceptional_outer_automorphism
|
true
|
|
gptkbp:has_unique_property
|
exceptional outer automorphism
|
|
gptkbp:hasSubgroup
|
gptkb:S_3
gptkb:S_4
gptkb:alternating_group_A_6
gptkb:S_5
gptkb:S_2
|
|
gptkbp:is_automorphism_group_of
|
gptkb:Mathieu_group_M_12
gptkb:projective_plane_of_order_4
gptkb:A_6
|
|
gptkbp:is_maximal_subgroup_of
|
gptkb:S_7
|
|
gptkbp:is_not_abelian
|
true
|
|
gptkbp:is_not_commutative
|
true
|
|
gptkbp:is_not_cyclic
|
true
|
|
gptkbp:is_not_nilpotent
|
true
|
|
gptkbp:is_not_simple
|
true
|
|
gptkbp:is_not_solvable
|
true
|
|
gptkbp:isomorphicTo
|
gptkb:automorphism_group_of_A_6
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSolvable
|
false
|
|
gptkbp:notation
|
gptkb:S_6
|
|
gptkbp:number_of_elements_of_order_1
|
1
|
|
gptkbp:number_of_elements_of_order_2
|
105
|
|
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:relatedTo
|
gptkb:Mathieu_group_M_12
gptkb:outer_automorphism_of_S_6
gptkb:projective_special_linear_group_PSL(2,9)
exceptional isomorphism
|
|
gptkbp:bfsParent
|
gptkb:dihedral_group_of_order_12
gptkb:Aut(A_6)
|
|
gptkbp:bfsLayer
|
8
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S 6
|