|
gptkbp:instanceOf
|
gptkb:group_of_people
dihedral group
|
|
gptkbp:centralTo
|
{identity, rotation by 180 degrees}
|
|
gptkbp:containsElement
|
gptkb:identity
reflection over diagonal 1
reflection over diagonal 2
reflection over horizontal axis
reflection over vertical axis
rotation by 180 degrees
rotation by 270 degrees
rotation by 90 degrees
|
|
gptkbp:hasNormalSubgroup
|
gptkb:Klein_four-group
cyclic group of order 4
|
|
gptkbp:hasSubgroup
|
gptkb:Klein_four-group
cyclic group of order 4
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
D 4
|
|
gptkbp:isNonAbelian
|
false
|
|
gptkbp:isomorphicTo
|
gptkb:symmetry_group_of_square
|
|
gptkbp:notation
|
gptkb:D_4
gptkb:Dihedral_group_of_order_8
|
|
gptkbp:number_of_conjugacy_classes
|
5
|
|
gptkbp:number_of_subgroups
|
10
|
|
gptkbp:order
|
8
|
|
gptkbp:order_of_each_element
|
2
1
4
|
|
gptkbp:presentedBy
|
⟨r, s | r^4 = s^2 = 1, s r = r^{-1} s⟩
|
|
gptkbp:usedIn
|
gptkb:geometry
abstract algebra
group theory
|
|
gptkbp:bfsParent
|
gptkb:D_8
gptkb:figure-eight_knot_complement
gptkb:dihedral_group_of_order_8
|
|
gptkbp:bfsLayer
|
7
|