alternating group A n (for n > 2)

URI: https://gptkb.org/entity/alternating_group_A_n_(for_n_>_2)
GPTKB entity
Statements (48)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkbp:automorphismGroup Z/2Z for n = 6
trivial for n ≠ 6
gptkbp:centralTo trivial for n > 2
gptkbp:consistsOf even permutations of n elements
gptkbp:generation 3-cycles
gptkbp:hasSubgroup gptkb:symmetric_group_S_n
https://www.w3.org/2000/01/rdf-schema#label alternating group A n (for n > 2)
gptkbp:is_a_building_block_in_the_classification_of_finite_simple_groups true
gptkbp:is_a_composition_factor_of_every_non-solvable_finite_group true
gptkbp:is_a_transitive_subgroup_of_S_n true
gptkbp:is_abelian false for n > 2
gptkbp:is_doubly_transitive true for n > 3
gptkbp:is_non-solvable true for n > 4
gptkbp:is_normal_subgroup_of gptkb:symmetric_group_S_n
gptkbp:is_not_simple false for n = 4
gptkbp:is_not_triply_transitive true for n > 5
gptkbp:is_the_only_non-abelian_simple_group_of_order_121645100408832000 true for n = 19
gptkbp:is_the_only_non-abelian_simple_group_of_order_1307674368000 true for n = 15
gptkbp:is_the_only_non-abelian_simple_group_of_order_168 true for n = 7
gptkbp:is_the_only_non-abelian_simple_group_of_order_181440 true for n = 9
gptkbp:is_the_only_non-abelian_simple_group_of_order_20160 true for n = 8
gptkbp:is_the_only_non-abelian_simple_group_of_order_20922789888000 true for n = 16
gptkbp:is_the_only_non-abelian_simple_group_of_order_2432902008176640000 true for n = 20
gptkbp:is_the_only_non-abelian_simple_group_of_order_2520 true for n = 7
gptkbp:is_the_only_non-abelian_simple_group_of_order_355687428096000 true for n = 17
gptkbp:is_the_only_non-abelian_simple_group_of_order_360 true for n = 6
gptkbp:is_the_only_non-abelian_simple_group_of_order_3628800 true for n = 10
gptkbp:is_the_only_non-abelian_simple_group_of_order_39916800 true for n = 11
gptkbp:is_the_only_non-abelian_simple_group_of_order_479001600 true for n = 12
gptkbp:is_the_only_non-abelian_simple_group_of_order_60 true for n = 5
gptkbp:is_the_only_non-abelian_simple_group_of_order_6227020800 true for n = 13
gptkbp:is_the_only_non-abelian_simple_group_of_order_6402373705728000 true for n = 18
gptkbp:is_the_only_non-abelian_simple_group_of_order_87178291200 true for n = 14
gptkbp:is_the_only_non-abelian_simple_group_of_order_<_60 false
gptkbp:is_the_smallest_non-abelian_simple_group true for n = 5
gptkbp:is_triply_transitive true for n = 4,5
gptkbp:isNonAbelian true for n > 4
gptkbp:isomorphicTo PSL(2,5) for n = 5
gptkbp:isPerfect true for n > 4
gptkbp:isSimple true
true for n = 5 or n > 4
true for n > 4
gptkbp:minimal_degree_of_faithful_linear_representation_over_C n-1
gptkbp:minimal_degree_of_faithful_permutation_representation n
gptkbp:order n!/2
gptkbp:bfsParent gptkb:symmetric_group_S_n
gptkbp:bfsLayer 6