|
gptkbp:instanceOf
|
gptkb:group_of_people
simple group
|
|
gptkbp:automorphismGroup
|
gptkb:symmetric_group_S5
trivial group
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:commutator_subgroup
|
gptkb:alternating_group_A5
|
|
gptkbp:derived_length
|
1
|
|
gptkbp:generation
|
(1 2 3), (1 2 3 4 5)
|
|
gptkbp:hasElementOrder
|
2
3
5
|
|
gptkbp:hasSubgroup
|
gptkb:symmetric_group_S5
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
alternating group A5
|
|
gptkbp:is_not_a_subgroup_of
|
gptkb:alternating_group_A4
gptkb:alternating_group_A6
|
|
gptkbp:is_not_abelian
|
true
|
|
gptkbp:is_not_cyclic
|
true
|
|
gptkbp:is_not_nilpotent
|
true
|
|
gptkbp:is_not_solvable
|
true
|
|
gptkbp:is_simple_non-abelian_group
|
true
|
|
gptkbp:is_smallest_non-abelian_simple_group
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
gptkb:icosahedral_group
rotation group of dodecahedron
rotation group of icosahedron
|
|
gptkbp:isPerfect
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:minimal_degree_of_faithful_linear_representation_over_C
|
3
|
|
gptkbp:minimal_degree_of_faithful_permutation_representation
|
5
|
|
gptkbp:number_of_conjugacy_classes
|
5
|
|
gptkbp:number_of_elements_of_order_2
|
15
|
|
gptkbp:number_of_elements_of_order_3
|
20
|
|
gptkbp:number_of_elements_of_order_5
|
24
|
|
gptkbp:order
|
60
|
|
gptkbp:Schur_multiplier
|
cyclic group of order 2
|
|
gptkbp:used_in
|
gptkb:algebraic_geometry
gptkb:topology
gptkb:Galois_theory
group theory
representation theory
classification of finite simple groups
Galois group of some quintic polynomials
geometry of dodecahedron
geometry of icosahedron
solvability of quintic equations
|
|
gptkbp:bfsParent
|
gptkb:icosahedral_group
|
|
gptkbp:bfsLayer
|
5
|