Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
dihedral group |
| gptkbp:actsOn |
gptkb:public_square
|
| gptkbp:automorphismGroup |
gptkb:public_square
|
| gptkbp:centralTo |
cyclic group of order 2
|
| gptkbp:containsElement |
gptkb:identity
reflection over horizontal axis reflection over vertical axis rotation by 180 degrees rotation by 270 degrees rotation by 90 degrees reflection over anti-diagonal reflection over main diagonal |
| gptkbp:hasApplication |
gptkb:geometry
crystallography group theory |
| gptkbp:hasConjugacyClasses |
5
|
| gptkbp:hasIrreducibleRepresentations |
5
|
| gptkbp:hasSubgroup |
gptkb:Klein_four-group
gptkb:symmetric_group_S4 cyclic group of order 4 |
| https://www.w3.org/2000/01/rdf-schema#label |
symmetry group of square
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
gptkb:D4
|
| gptkbp:name |
gptkb:dihedral_group_of_order_8
|
| gptkbp:order |
8
|
| gptkbp:presentedBy |
<r, s | r^4 = s^2 = 1, s r = r^{-1} s>
|
| gptkbp:symbol |
gptkb:D4
|
| gptkbp:bfsParent |
gptkb:D_4
|
| gptkbp:bfsLayer |
8
|