Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
projective special linear group |
| gptkbp:automorphismGroup |
order 2gcd(2, q-1)
|
| gptkbp:centerOfSL2q |
order gcd(2, q-1)
|
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:fullName |
Projective Special Linear Group of 2x2 matrices over finite field of order q
|
| gptkbp:generation |
2x2 matrices with determinant 1 over F_q, modulo scalar matrices
|
| https://www.w3.org/2000/01/rdf-schema#label |
PSL(2, q)
|
| gptkbp:isomorphicTo |
A_4 for q=3
A_5 for q=5 S_4 for q=4 |
| gptkbp:isQuotientOf |
SL(2, q) by its center
|
| gptkbp:isSimple |
true
|
| gptkbp:isSimpleException |
not simple for q=2 or q=3
|
| gptkbp:LieType |
gptkb:A_1
|
| gptkbp:minimalDegreeOfFaithfulPermutationRepresentation |
q(q^2-1)/gcd(2, q-1)
|
| gptkbp:notation |
gptkb:PSL(2,_q)
|
| gptkbp:order |
q(q^2-1)/gcd(2, q-1)
|
| gptkbp:rank |
1
|
| gptkbp:type |
gptkb:Weyl_group
|
| gptkbp:usedIn |
classification of finite simple groups
|
| gptkbp:bfsParent |
gptkb:PSL2
|
| gptkbp:bfsLayer |
7
|