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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
cyclic group of order 2
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gptkbp:centralTo
|
trivial group
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gptkbp:hasCharacterTable
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known
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gptkbp:hasExponent
|
84
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gptkbp:hasMaximalSubgroup
|
gptkb:M_21
M_168
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gptkbp:hasOrderFactorization
|
2^3 × 3 × 7
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gptkbp:hasSubgroup
|
gptkb:S_4
gptkb:A_4
gptkb:D_14
gptkb:Z_2
gptkb:Z_3
gptkb:Z_7
gptkb:A_7
gptkb:S_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:is2TransitiveOn
|
7 points
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gptkbp:is3TransitiveOn
|
no set
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gptkbp:isFirstNonAbelianSimpleGroupOfOrder
|
168
|
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gptkbp:isNonAbelian
|
true
|
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gptkbp:isomorphicTo
|
gptkb:projective_linear_group_of_order_168
gptkb:PSL(2,_7)
GL(3, 2)
PGL(3, 2)
PSigmaL(2, 7)
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|
gptkbp:isPerfect
|
true
|
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gptkbp:isSimple
|
true
|
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gptkbp:isTransitiveOn
|
lines of the Fano plane
points of the Fano plane
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gptkbp:minimalDegreeOfFaithfulPermutationRepresentation
|
7
|
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gptkbp:order
|
168
|
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gptkbp:presentedBy
|
⟨a, b | a^7 = b^3 = (ab)^2 = 1⟩
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gptkbp:SchurMultiplier
|
cyclic group of order 3
|
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gptkbp:bfsParent
|
gptkb:PSL(n,_F)
|
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gptkbp:bfsLayer
|
7
|