symplectic group over finite field

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:algebraic_geometry gptkb:group_of_people
gptkbp:actsOn	2n-dimensional vector space over finite field
gptkbp:centralTo	order 2 (if q is odd)
gptkbp:definedIn	finite field
gptkbp:hasConnection	true (as algebraic group)
gptkbp:hasDerivedSubgroup	itself (for n \\geq 2, q > 2)
gptkbp:hasSubgroup	general linear group over finite field
gptkbp:hasType	C_n (in Lie type classification)
https://www.w3.org/2000/01/rdf-schema#label	symplectic group over finite field
gptkbp:isChevalleyGroup	true
gptkbp:isClassicalGroup	true
gptkbp:isFiniteSimpleGroup	for n \\geq 2, q > 2
gptkbp:isPerfect	true (for n \\geq 2, q > 2)
gptkbp:isReductive	true
gptkbp:isSimple	n \\geq 2, q > 2
gptkbp:isSplitGroup	true
gptkbp:notation	Sp(2n, F_q)
gptkbp:order	q^{n^2} \\prod_{i=1}^n (q^{2i}-1)
gptkbp:preserves	non-degenerate alternating bilinear form
gptkbp:relatedTo	gptkb:general_linear_group orthogonal group
gptkbp:usedIn	gptkb:algebraic_geometry coding theory representation theory finite group theory
gptkbp:Weyl_group	hyperoctahedral group
gptkbp:bfsParent	gptkb:symplectic_groups
gptkbp:bfsLayer	7