|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
set of 2^n elements
|
|
gptkbp:automorphismGroup
|
trivial (for n > 2)
|
|
gptkbp:centralTo
|
trivial (identity only) for n > 1
|
|
gptkbp:contains
|
gptkb:alternating_group_A_{2^n}
|
|
gptkbp:generation
|
transpositions
|
|
gptkbp:hasElementOrder
|
any integer dividing (2^n)!
|
|
gptkbp:hasNormalSubgroup
|
gptkb:alternating_group_A_{2^n}
|
|
gptkbp:hasSubgroup
|
gptkb:alternating_group_A_{2^n}
gptkb:cyclic_group_of_order_2^n
gptkb:dihedral_group_of_order_2^{n+1}
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S {2^n}
|
|
gptkbp:innerAutomorphismGroup
|
isomorphic to S_{2^n}
|
|
gptkbp:isFinite
|
true
|
|
gptkbp:isMaximal
|
no
|
|
gptkbp:isMonolithic
|
true
|
|
gptkbp:isNilpotent
|
false
|
|
gptkbp:isNonAbelian
|
true (for n > 1)
|
|
gptkbp:isomorphicTo
|
automorphism group of a set of 2^n elements
|
|
gptkbp:isPerfect
|
false (for n > 1)
|
|
gptkbp:isPermutationGroup
|
true
|
|
gptkbp:isPrimitive
|
true
|
|
gptkbp:isSimple
|
false (for n > 1)
|
|
gptkbp:isSolvable
|
false (for n > 2)
|
|
gptkbp:isSupersolvable
|
false
|
|
gptkbp:isTransitiveOn
|
true
|
|
gptkbp:notation
|
gptkb:S_{2^n}
|
|
gptkbp:numberOfIssues
|
true (for n > 1)
|
|
gptkbp:order
|
(2^n)!
|
|
gptkbp:bfsParent
|
gptkb:complete_graph_K_{2^n}
|
|
gptkbp:bfsLayer
|
7
|