Dihedral group of the hexagon
GPTKB entity
Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
dihedral group
|
| gptkbp:actsOn |
regular hexagon
|
| gptkbp:centralTo |
{identity, r^3}
|
| gptkbp:hasConjugacyClasses |
6
|
| gptkbp:hasIrreducibleRepresentations |
6
|
| gptkbp:hasNormalSubgroup |
gptkb:cyclic_group_of_order_6
|
| gptkbp:hasSubgroup |
gptkb:symmetric_group_S6
gptkb:cyclic_group_of_order_6 gptkb:dihedral_group_of_order_6 cyclic group of order 2 cyclic group of order 3 |
| gptkbp:hasType |
reflection
rotation |
| https://www.w3.org/2000/01/rdf-schema#label |
Dihedral group of the hexagon
|
| gptkbp:isFiniteGroup |
true
|
| gptkbp:isGroupOfSymmetriesOf |
regular hexagon
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
gptkb:D_6
gptkb:D_{12} |
| gptkbp:isSymmetryGroupOf |
regular hexagon
|
| gptkbp:notation |
gptkb:D_6
gptkb:D6 gptkb:D12 gptkb:D_{12} |
| gptkbp:numberOfReflections |
6
|
| gptkbp:numberOfRotations |
6
|
| gptkbp:order |
12
|
| gptkbp:presentedBy |
⟨r, s | r^6 = s^2 = 1, s r s = r^{-1}⟩
|
| gptkbp:bfsParent |
gptkb:D_6
|
| gptkbp:bfsLayer |
8
|