dihedral group of order 2^{n+1}
GPTKB entity
Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
dihedral group |
| gptkbp:centralTo |
\\langle r^{2^{n-1}} \\rangle
|
| gptkbp:hasNormalSubgroup |
\\langle r \\rangle
|
| gptkbp:hasOrderDivisibleBy |
4
|
| gptkbp:hasSubgroup |
gptkb:cyclic_group_of_order_2^n
elementary abelian group of order 4 |
| https://www.w3.org/2000/01/rdf-schema#label |
dihedral group of order 2^{n+1}
|
| gptkbp:isDiscrete |
true
|
| gptkbp:isFinite |
true
|
| gptkbp:isGeneratedBy |
two elements
|
| gptkbp:isGroupOfSymmetriesOf |
regular 2^n-gon
|
| gptkbp:isMetacyclic |
true
|
| gptkbp:isNilpotent |
false
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isNonAbelianForNGeq2 |
true
|
| gptkbp:isNonCyclic |
true
|
| gptkbp:isNonSimple |
true
|
| gptkbp:isSemidirectProduct |
cyclic group of order 2^n and cyclic group of order 2
|
| gptkbp:isSolvable |
true
|
| gptkbp:notation |
D_{2^{n+1}}
|
| gptkbp:numberOfElementsOfOrder2 |
2^{n+1} - 2^n
|
| gptkbp:order |
2^{n+1}
|
| gptkbp:presentedBy |
\\langle r, s \\mid r^{2^n} = s^2 = 1, srs = r^{-1} \\rangle
|
| gptkbp:bfsParent |
gptkb:symmetric_group_S_{2^n}
|
| gptkbp:bfsLayer |
8
|