|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
set of 6 elements
|
|
gptkbp:alternating_subgroup
|
gptkb:Alt(6)
|
|
gptkbp:automorphismGroup
|
gptkb:Z/2Z
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:conjugacy_classes
|
11
|
|
gptkbp:contains_subgroup_isomorphic_to
|
gptkb:A_2
gptkb:D_4
gptkb:D_5
gptkb:D_6
gptkb:S_3
gptkb:S_4
gptkb:Z/5Z
gptkb:Z/2Z
gptkb:A_4
gptkb:A_3
gptkb:A_5
gptkb:D_3
gptkb:Z/3Z
gptkb:Z/4Z
gptkb:S_5
gptkb:S_2
gptkb:D_2
gptkb:Z/6Z
|
|
gptkbp:degree
|
6
|
|
gptkbp:generation
|
transpositions
|
|
gptkbp:has_exceptional_outer_automorphism
|
true
|
|
gptkbp:hasElementOrder
|
2
1
15
3
4
5
6
|
|
gptkbp:hasSubgroup
|
gptkb:Alt(6)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Sym(6)
|
|
gptkbp:is_maximal_among_symmetric_groups_with_exceptional_outer_automorphism
|
true
|
|
gptkbp:is_not_a_direct_product_of_nontrivial_groups
|
true
|
|
gptkbp:is_not_a_direct_product_of_smaller_symmetric_groups
|
true
|
|
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
|
automorphism group of Alt(6)
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:notation
|
gptkb:S_6
|
|
gptkbp:number_of_elements_of_order_1
|
1
|
|
gptkbp:number_of_elements_of_order_15
|
48
|
|
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:bfsParent
|
gptkb:S_6
|
|
gptkbp:bfsLayer
|
7
|