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gptkbp:instanceOf
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gptkb:group_of_people
gptkb:projective_symplectic_group
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gptkbp:abbreviation
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gptkb:Projective_Symplectic_Group_of_degree_2n_over_field_of_order_q
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gptkbp:actsOn
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gptkb:geometry
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gptkbp:centerOfSp(2n,q)
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order gcd(2,q-1)
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gptkbp:definedIn
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finite field of order q
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gptkbp:hasSubgroup
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gptkb:PGL(2n,q)
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gptkbp:isChevalleyGroup
|
true
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gptkbp:isClassicalGroup
|
true
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gptkbp:isFiniteSimpleGroup
|
true (for n>1 or n=1 and q>3)
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gptkbp:isGroupOfLieType
|
true
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gptkbp:isNonAbelian
|
true (for n>1)
|
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gptkbp:isPerfect
|
true (for n>1 or n=1 and q>3)
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gptkbp:isQuotientOf
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gptkb:Sp(2n,q)
center of Sp(2n,q)
|
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gptkbp:isSimple
|
false (for n=1 and q=2 or 3)
true (for n>1 or n=1 and q>3)
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gptkbp:notation
|
gptkb:PSp_{2n}(q)
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gptkbp:order
|
q^{n^2} \prod_{i=1}^n (q^{2i}-1)/gcd(2,q-1)
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gptkbp:preserves
|
symplectic form
|
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gptkbp:relatedTo
|
gptkb:orthogonal_group
finite simple group classification
|
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gptkbp:bfsParent
|
gptkb:finite_Chevalley_group
gptkb:groups_of_Lie_type
gptkb:untwisted_group_of_Lie_type
gptkb:finite_group_of_Lie_type
|
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gptkbp:bfsLayer
|
9
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|
https://www.w3.org/2000/01/rdf-schema#label
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PSp(2n,q)
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