Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:projective_symplectic_group |
| gptkbp:abbreviation |
gptkb:Projective_Symplectic_Group_of_degree_2n_over_field_of_order_q
|
| gptkbp:actsOn |
gptkb:geometry
|
| gptkbp:centerOfSp(2n,q) |
order gcd(2,q-1)
|
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:hasSubgroup |
gptkb:PGL(2n,q)
|
| https://www.w3.org/2000/01/rdf-schema#label |
PSp(2n,q)
|
| gptkbp:isChevalleyGroup |
true
|
| gptkbp:isClassicalGroup |
true
|
| gptkbp:isFiniteSimpleGroup |
true (for n>1 or n=1 and q>3)
|
| gptkbp:isGroupOfLieType |
true
|
| gptkbp:isNonAbelian |
true (for n>1)
|
| gptkbp:isPerfect |
true (for n>1 or n=1 and q>3)
|
| gptkbp:isQuotientOf |
gptkb:Sp(2n,q)
center of Sp(2n,q) |
| gptkbp:isSimple |
false (for n=1 and q=2 or 3)
true (for n>1 or n=1 and q>3) |
| gptkbp:notation |
gptkb:PSp_{2n}(q)
|
| gptkbp:order |
q^{n^2} \\prod_{i=1}^n (q^{2i}-1)/gcd(2,q-1)
|
| gptkbp:preserves |
symplectic form
|
| gptkbp:relatedTo |
orthogonal group
finite simple group classification |
| gptkbp:bfsParent |
gptkb:Weyl_group
|
| gptkbp:bfsLayer |
5
|