Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
finite symplectic group |
| gptkbp:actsOn |
2n-dimensional vector space over F_q
|
| gptkbp:centralTo |
cyclic group of order gcd(2,q-1)
|
| gptkbp:connectedTo |
gptkb:projective_symplectic_group_PSp(2n,q)
symplectic geometry classical groups Lie type groups |
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:dimensions |
2n
|
| gptkbp:hasSubgroup |
gptkb:GL(2n,q)
|
| gptkbp:hasType |
gptkb:C_n
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sp(2n,q)
|
| gptkbp:isChevalleyGroup |
yes
|
| gptkbp:isNotSimpleFor |
n = 1 or q = 2
|
| gptkbp:isSimple |
n > 1 and q > 2
|
| gptkbp:notation |
gptkb:Sp_{2n}(q)
|
| gptkbp:order |
q^{n^2} \\prod_{i=1}^n (q^{2i}-1)
|
| gptkbp:preserves |
non-degenerate alternating bilinear form
|
| gptkbp:bfsParent |
gptkb:PSp(2n,q)
|
| gptkbp:bfsLayer |
6
|