PSL(2,7)
E262442
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.
All labels observed (6)
| Label | Occurrences |
|---|---|
| PSL(2,7) canonical | 16 |
| GL(3,2) | 1 |
| PGL(3,2) | 1 |
| PSL(2,7) by C2 | 1 |
| PSL_2(7) | 1 |
| projective linear group of 2×2 matrices over F_7 with determinant 1 modulo scalars | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2408391 — 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: PSL(2,7) Context triple: [Klein quartic, automorphismGroup, PSL(2,7)]
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A.
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.
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B.
SL(2,C)
SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
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C.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
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D.
Conway groups
Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
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E.
Kleinian group
A Kleinian group is a discrete subgroup of Möbius transformations acting on hyperbolic 3-space, central to the study of Riemann surfaces, complex dynamics, and low-dimensional topology.
- 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: PSL(2,7) Target entity description: 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.
-
A.
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.
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B.
SL(2,C)
SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
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C.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
-
D.
Conway groups
Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
-
E.
Kleinian group
A Kleinian group is a discrete subgroup of Möbius transformations acting on hyperbolic 3-space, central to the study of Riemann surfaces, complex dynamics, and low-dimensional topology.
- 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: PSL(2,7) Description of subject: 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.
Referenced by (21)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: PSL(2,7)
linked to: PSL(2,7)
PSL(2,7)
→
isomorphicTo
→
projective linear group of 2×2 matrices over F_7 with determinant 1 modulo scalars
ⓘ
linked to: PSL(2,7)
linked to: PSL(2,7)
linked to: PSL(2,7)
subject linked to:
Hurwitz surfaces