PGL(2,7)
E904567
PGL(2,7) is the projective general linear group of 2×2 invertible matrices over the finite field with 7 elements, a finite group of order 336 that acts as the full collineation group of the projective line over that field.
All labels observed (2)
| Label | Occurrences |
|---|---|
| PGL(2,7) canonical | 2 |
| GL(2,7)/Z(GL(2,7)) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11098604 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: PGL(2,7) Context triple: [PSL(2,7), automorphismGroup, PGL(2,7)]
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A.
PSL(2,7)
PSL(2,7) is a finite simple group of order 168, notable as the full automorphism group of the Klein quartic and as a key example in the theory of projective linear groups over finite fields.
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B.
PSL(2,ℤ/Nℤ)
PSL(2,ℤ/Nℤ) is the projective special linear group of 2×2 matrices with entries in the ring of integers modulo N, modulo scalar matrices, forming a fundamental example of a finite (or, for composite N, generally non-simple) group in algebra and number theory.
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C.
SL(2,ℤ)
SL(2,ℤ) is the group of 2×2 integer matrices with determinant 1, fundamental in number theory, geometry, and the theory of modular forms.
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D.
PSL(2,\mathbb{C})
PSL(2,ℂ) is the group of Möbius transformations acting as all biholomorphic automorphisms of the Riemann sphere.
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E.
modular group PSL(2,Z)
The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: PGL(2,7) Target entity description: PGL(2,7) is the projective general linear group of 2×2 invertible matrices over the finite field with 7 elements, a finite group of order 336 that acts as the full collineation group of the projective line over that field.
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A.
PSL(2,7)
PSL(2,7) is a finite simple group of order 168, notable as the full automorphism group of the Klein quartic and as a key example in the theory of projective linear groups over finite fields.
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B.
PSL(2,ℤ/Nℤ)
PSL(2,ℤ/Nℤ) is the projective special linear group of 2×2 matrices with entries in the ring of integers modulo N, modulo scalar matrices, forming a fundamental example of a finite (or, for composite N, generally non-simple) group in algebra and number theory.
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C.
SL(2,ℤ)
SL(2,ℤ) is the group of 2×2 integer matrices with determinant 1, fundamental in number theory, geometry, and the theory of modular forms.
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D.
PSL(2,\mathbb{C})
PSL(2,ℂ) is the group of Möbius transformations acting as all biholomorphic automorphisms of the Riemann sphere.
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E.
modular group PSL(2,Z)
The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
- F. None of above. chosen
Statements (50)
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: PGL(2,7) Description of subject: PGL(2,7) is the projective general linear group of 2×2 invertible matrices over the finite field with 7 elements, a finite group of order 336 that acts as the full collineation group of the projective line over that field.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: PGL(2,7)