symmetric group on 5 elements

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people non-abelian group permutation group
gptkbp:automorphismGroup	trivial group
gptkbp:centralTo	trivial group
gptkbp:degree	5
gptkbp:generation	(1 2) (1 2 3 4 5)
gptkbp:has_minimal_normal_subgroup	alternating group on 5 elements
gptkbp:has_quotient_group	trivial group alternating group on 5 elements
gptkbp:has_trivial_center	true
gptkbp:hasNormalSubgroup	alternating group on 5 elements
gptkbp:hasSubgroup	alternating group on 5 elements
https://www.w3.org/2000/01/rdf-schema#label	symmetric group on 5 elements
gptkbp:is_complete_group	true
gptkbp:is_maximal_among_permutation_groups_on_5_elements	true
gptkbp:is_not_simple	true
gptkbp:is_not_solvable	true
gptkbp:is_primitive	true
gptkbp:is_transitive	true
gptkbp:isomorphicTo	group of all permutations of 5 elements
gptkbp:isSimple	false
gptkbp:name	gptkb:S5
gptkbp:number_of_conjugacy_classes	7
gptkbp:number_of_elements_of_order_2	25
gptkbp:number_of_elements_of_order_3	20
gptkbp:number_of_elements_of_order_4	30
gptkbp:number_of_elements_of_order_5	24
gptkbp:number_of_elements_of_order_6	20
gptkbp:order	120
gptkbp:bfsParent	gptkb:S_5
gptkbp:bfsLayer	7