Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
dihedral group |
| gptkbp:automorphismGroup |
gptkb:dihedral_group_of_order_12
|
| gptkbp:centralTo |
trivial group
|
| gptkbp:has_6_reflections |
true
|
| gptkbp:has_6_rotations |
true
|
| gptkbp:hasNormalSubgroup |
gptkb:cyclic_group_of_order_6
cyclic group of order 2 |
| gptkbp:hasSubgroup |
gptkb:symmetric_group_S_6
|
| https://www.w3.org/2000/01/rdf-schema#label |
dihedral group of order 12
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
gptkb:symmetry_group_of_regular_hexagon
|
| gptkbp:notation |
gptkb:D_6
gptkb:Dih_6 gptkb:D6 |
| gptkbp:number_of_elements_of_order_1 |
1
|
| gptkbp:number_of_elements_of_order_2 |
7
|
| gptkbp:number_of_elements_of_order_3 |
2
|
| gptkbp:number_of_elements_of_order_6 |
2
|
| gptkbp:order |
12
|
| gptkbp:presentedBy |
⟨r, s | r^6 = s^2 = 1, s r s^{-1} = r^{-1}⟩
|
| gptkbp:used_in |
gptkb:geometry
crystallography group theory |
| gptkbp:bfsParent |
gptkb:G_2
gptkb:exceptional_Lie_group_G2 |
| gptkbp:bfsLayer |
6
|