Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
permutation group |
| gptkbp:A3 |
cyclic group of order 3
isomorphicTo |
| gptkbp:centralTo |
trivial group
|
| gptkbp:containsElement |
gptkb:identity
(1 2 3) (1 2) (1 3 2) (1 3) (2 3) |
| gptkbp:generation |
(1 2 3)
(1 2) |
| gptkbp:hasNormalSubgroup |
gptkb:A3
|
| gptkbp:hasSubgroup |
gptkb:symmetric_group_S_n_(n_≥_3)
|
| https://www.w3.org/2000/01/rdf-schema#label |
symmetric group S3
|
| gptkbp:isNonAbelian |
false
|
| gptkbp:isomorphicTo |
gptkb:dihedral_group_D3
|
| gptkbp:isSimple |
false
|
| gptkbp:isSolvable |
true
|
| gptkbp:notation |
S3
|
| gptkbp:numberOfConjugacyClasses |
3
|
| gptkbp:numberOfIrreducibleRepresentations |
3
|
| gptkbp:numberOfRooms |
6
|
| gptkbp:order |
6
|
| gptkbp:presentedBy |
⟨a, b | a^3 = b^2 = e, bab = a^2⟩
|
| gptkbp:smallestNonAbelianGroup |
true
|
| gptkbp:usedIn |
gptkb:Galois_theory
group theory permutation puzzles |
| gptkbp:bfsParent |
gptkb:SU(3)
gptkb:dihedral_group_of_order_6 |
| gptkbp:bfsLayer |
6
|