Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:dihedral_group |
| gptkbp:automorphismGroup |
gptkb:GL(2,2)
|
| gptkbp:centralTo |
{1, r^2}
|
| gptkbp:hasCharacterTable |
known
|
| gptkbp:hasConjugacyClasses |
5
|
| gptkbp:hasElementOrder |
2
1 4 |
| gptkbp:hasIrreducibleRepresentations |
5
|
| gptkbp:hasNormalSubgroup |
gptkb:Klein_four-group
cyclic group of order 4 |
| gptkbp:hasSubgroup |
gptkb:Klein_four-group
cyclic group of order 4 |
| gptkbp:isGroupOfSymmetriesOf |
regular quadrilateral
|
| gptkbp:isNilpotent |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
gptkb:symmetry_group_of_square
C_4 ⋊ C_2 |
| gptkbp:isSimple |
false
|
| gptkbp:isSolvable |
true
|
| gptkbp:isSymmetryGroupOf |
gptkb:public_square
|
| gptkbp:notation |
gptkb:D_4
gptkb:D8 Dihedral(4) |
| gptkbp:numberOfElementsOfOrder2 |
5
|
| gptkbp:numberOfElementsOfOrder4 |
2
|
| gptkbp:order |
8
|
| gptkbp:presentedBy |
⟨r, s | r^4 = s^2 = 1, s r s^{-1} = r^{-1}⟩
|
| gptkbp:bfsParent |
gptkb:symmetric_group_S_4
|
| gptkbp:bfsLayer |
8
|
| https://www.w3.org/2000/01/rdf-schema#label |
dihedral group D 4
|