General Linear Group of 2x2 invertible matrices over the field with 3 elements
GPTKB entity
Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
Finite group |
| gptkbp:actsOn |
2-dimensional vector space over F_3
|
| gptkbp:alsoKnownAs |
gptkb:GL(2,3)
|
| gptkbp:centerOrder |
2
|
| gptkbp:centralTo |
Scalar matrices with nonzero entries in F_3
|
| gptkbp:containsIdentityElement |
true
|
| gptkbp:containsNormalSubgroup |
gptkb:SL(2,3)
|
| gptkbp:determinant |
onto F_3^×
|
| gptkbp:field |
Finite field with 3 elements
|
| gptkbp:hasElementOrder |
2
3 4 6 8 |
| gptkbp:hasSubgroup |
Special Linear Group SL(2,3)
General Linear Group of 2x2 invertible matrices over the complex numbers |
| https://www.w3.org/2000/01/rdf-schema#label |
General Linear Group of 2x2 invertible matrices over the field with 3 elements
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
Symmetric group S_4 × C_2
|
| gptkbp:isQuotientOf |
Projective General Linear Group PGL(2,3)
|
| gptkbp:isSimple |
false
|
| gptkbp:numberOfConjugacyClasses |
8
|
| gptkbp:order |
48
|
| gptkbp:orderOfSL(2,3) |
24
|
| gptkbp:bfsParent |
gptkb:GL(2,3)
|
| gptkbp:bfsLayer |
8
|