Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
dihedral group
|
| gptkbp:automorphismGroup |
gptkb:dihedral_group_of_order_18
|
| gptkbp:centralTo |
cyclic group of order 1
|
| gptkbp:cycle |
false
|
| gptkbp:hasNormalSubgroup |
gptkb:cyclic_group_of_order_9
cyclic group of order 2 |
| gptkbp:hasSubgroup |
gptkb:dihedral_group_of_order_6
gptkb:cyclic_group_of_order_9 cyclic group of order 2 cyclic group of order 3 |
| https://www.w3.org/2000/01/rdf-schema#label |
dihedral group of order 18
|
| gptkbp:isGroupOfSymmetriesOf |
regular nonagon
|
| gptkbp:isNilpotent |
false
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
semidirect product of C_9 and C_2
|
| gptkbp:isSimple |
false
|
| gptkbp:isSolvable |
true
|
| gptkbp:notation |
D_9
Dih_9 |
| gptkbp:numberOfElementsOfOrder1 |
1
|
| gptkbp:numberOfElementsOfOrder2 |
9
|
| gptkbp:numberOfElementsOfOrder9 |
2
|
| gptkbp:order |
18
|
| gptkbp:presentedBy |
⟨r, s | r^9 = s^2 = 1, s r s^{-1} = r^{-1}⟩
|
| gptkbp:bfsParent |
gptkb:symmetric_group_S_9
|
| gptkbp:bfsLayer |
8
|