|
gptkbp:instanceOf
|
gptkb:group_of_people
simple group
|
|
gptkbp:automorphismGroup
|
gptkb:symmetric_group_S6
cyclic group of order 4
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:hasElementOrder
|
2
10
3
4
5
6
|
|
gptkbp:hasNormalSubgroup
|
gptkb:symmetric_group_S6
|
|
gptkbp:hasSubgroup
|
gptkb:symmetric_group_S6
gptkb:Mathieu_group_M24
gptkb:Mathieu_group_M12
gptkb:projective_special_linear_group_PSL(2,9)
automorphism group of A6
outer automorphism group of A6
projective general linear group PGL(2,9)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
alternating group A6
|
|
gptkbp:is_a_doubly_transitive_group
|
true
|
|
gptkbp:is_a_Galois_group
|
true
|
|
gptkbp:is_a_Mathieu_group_subgroup
|
true
|
|
gptkbp:is_a_primitive_group
|
true
|
|
gptkbp:is_a_transitive_subgroup_of
|
gptkb:symmetric_group_S6
|
|
gptkbp:is_not_a_normal_subgroup_of
|
symmetric group S7
|
|
gptkbp:is_not_abelian
|
true
|
|
gptkbp:is_not_solvable
|
true
|
|
gptkbp:is_the_only_alternating_group_isomorphic_to_a_projective_special_linear_group
|
true
|
|
gptkbp:is_the_only_alternating_group_with_exceptional_isomorphisms
|
true
|
|
gptkbp:is_the_only_alternating_group_with_exceptional_Schur_multiplier
|
true
|
|
gptkbp:is_the_only_alternating_group_with_nontrivial_outer_automorphism_group
|
true
|
|
gptkbp:is_the_smallest_non-abelian_simple_group_with_nontrivial_outer_automorphism_group
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
gptkb:PSL(2,9)
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:minimal_degree_of_faithful_permutation_representation
|
6
|
|
gptkbp:number_of_conjugacy_classes
|
7
|
|
gptkbp:number_of_elements_of_order_10
|
72
|
|
gptkbp:number_of_elements_of_order_2
|
45
|
|
gptkbp:number_of_elements_of_order_3
|
80
|
|
gptkbp:number_of_elements_of_order_4
|
90
|
|
gptkbp:number_of_elements_of_order_5
|
72
|
|
gptkbp:number_of_elements_of_order_6
|
40
|
|
gptkbp:order
|
360
|
|
gptkbp:Schur_multiplier
|
gptkb:cyclic_group_of_order_6
|
|
gptkbp:bfsParent
|
gptkb:alternating_group_A5
|
|
gptkbp:bfsLayer
|
6
|