Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
orthogonal group |
| gptkbp:actsOn |
2n-dimensional vector space over F_q
|
| gptkbp:automorphismGroup |
Aut(Sp_{2n}(q))
|
| gptkbp:connectedTo |
representation theory
symplectic geometry |
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:dimensions |
2n
|
| gptkbp:hasSubgroup |
GL_{2n}(q)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sp {2n}(q)
|
| gptkbp:isCenter |
cyclic group of order gcd(2, q-1)
|
| gptkbp:isChevalleyGroup |
true
|
| gptkbp:isPerfect |
true (for n>1, q>2)
|
| gptkbp:isQuotientOf |
projective symplectic group PSp_{2n}(q)
|
| gptkbp:isSimple |
true (for n>1, q>2)
|
| gptkbp:notation |
C_n(q)
|
| gptkbp:order |
q^{n^2} \\prod_{i=1}^n (q^{2i}-1)
|
| gptkbp:preserves |
non-degenerate alternating bilinear form
|
| gptkbp:relatedTo |
classical group
Lie type group finite simple group (for n>1, q>2) |
| gptkbp:bfsParent |
gptkb:Sp(2n,q)
gptkb:PSp_{2n}(q) |
| gptkbp:bfsLayer |
7
|