|
gptkbp:instanceOf
|
gptkb:group_of_people
permutation group
|
|
gptkbp:actsOn
|
set of 9 elements
|
|
gptkbp:automorphismGroup
|
trivial group
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:characterTable
|
known
|
|
gptkbp:conjugacyClasses
|
30
|
|
gptkbp:degree
|
9
|
|
gptkbp:generation
|
cycles
transpositions
|
|
gptkbp:hasElementOrder
|
2
1
3
4
5
6
7
8
9
|
|
gptkbp:hasMaximalSubgroup
|
gptkb:S_5_×_S_4
gptkb:S_6_×_S_3
gptkb:alternating_group_A_9
S_7 × S_2
S_8 × S_1
|
|
gptkbp:hasNormalSubgroup
|
gptkb:alternating_group_A_9
|
|
gptkbp:hasSubgroup
|
gptkb:alternating_group_A_8
gptkb:symmetric_group_S_8
gptkb:alternating_group_A_9
gptkb:cyclic_group_of_order_9
gptkb:dihedral_group_of_order_18
2
18
3
4
5
6
72
8
9
5040
40320
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
symmetric group S 9
|
|
gptkbp:innerAutomorphismGroup
|
gptkb:symmetric_group_S_9
|
|
gptkbp:isNonAbelian
|
false
|
|
gptkbp:isomorphicTo
|
automorphism group of a set with 9 elements
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSolvable
|
false
|
|
gptkbp:notation
|
gptkb:S_9
|
|
gptkbp:order
|
362880
|
|
gptkbp:presentedBy
|
generated by (1 2) and (1 2 ... 9) with standard relations
|
|
gptkbp:primitive
|
true
|
|
gptkbp:representationTheory
|
30 irreducible representations
|
|
gptkbp:transitive
|
true
|
|
gptkbp:bfsParent
|
gptkb:A_8
|
|
gptkbp:bfsLayer
|
7
|