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gptkbp:instanceOf
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gptkb:group_of_people
projective special linear group
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gptkbp:actsOn
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gptkb:projective_plane_of_order_2
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gptkbp:automorphismGroup
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gptkb:Fano_plane
trivial
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gptkbp:centralTo
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trivial
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gptkbp:foundIn
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classification of finite simple groups
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gptkbp:hasSubgroup
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gptkb:S_4
gptkb:A_4
gptkb:D_14
gptkb:Z_2
gptkb:Z_3
gptkb:Z_7
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https://www.w3.org/2000/01/rdf-schema#label
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PSL(3,2)
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gptkbp:isNonAbelian
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true
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gptkbp:isomorphicTo
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gptkb:PSL(2,7)
gptkb:GL(3,2)
gptkb:PGL(3,2)
gptkb:PSigmaL(2,7)
gptkb:group_of_automorphisms_of_the_Fano_plane
gptkb:projective_linear_group_of_order_168
group of orientation-preserving symmetries of the Klein quartic
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gptkbp:isPerfect
|
true
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gptkbp:isSimple
|
true
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gptkbp:isTransitiveOn
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7 lines of the Fano plane
7 points of the Fano plane
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gptkbp:minimalDegreePermutationRepresentation
|
7
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gptkbp:order
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168
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gptkbp:presentedBy
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⟨a,b|a^7=b^3=(ab)^2=1⟩
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gptkbp:SchurMultiplier
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trivial
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gptkbp:bfsParent
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gptkb:PSL(2,7)
gptkb:projective_special_linear_group
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gptkbp:bfsLayer
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6
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