Conway groups
E29418
family of sporadic simple groups
finite group
finite simple group
lattice in 24-dimensional Euclidean space
mathematical concept
mathematician
sporadic simple group
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.
All labels observed (7)
| Label | Occurrences |
|---|---|
| Conway group Co1 | 4 |
| Conway groups canonical | 4 |
| automorphism group of the Leech lattice | 4 |
| Conway group Co3 | 3 |
| Conway group | 2 |
| Conway group Co0 | 2 |
| Conway group Co2 | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T231136 — 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: Conway groups Context triple: [John H. Conway, notableWork, Conway groups]
-
A.
Noether's isomorphism theorems
Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
-
B.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Group of Five
The Group of Five refers to the five NCAA Division I FBS football conferences outside the traditional power conferences, generally considered to have less financial resources, media exposure, and competitive depth.
-
E.
Matrix
Matrix is a professional haircare and hair color brand widely used in salons and owned by the cosmetics company L'Oréal.
- 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: Conway groups Target entity description: 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.
-
A.
Noether's isomorphism theorems
Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
-
B.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Group of Five
The Group of Five refers to the five NCAA Division I FBS football conferences outside the traditional power conferences, generally considered to have less financial resources, media exposure, and competitive depth.
-
E.
Matrix
Matrix is a professional haircare and hair color brand widely used in salons and owned by the cosmetics company L'Oréal.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
family of sporadic simple groups
ⓘ
finite group ⓘ finite simple group ⓘ finite simple group ⓘ finite simple group ⓘ lattice in 24-dimensional Euclidean space ⓘ mathematical concept ⓘ mathematician ⓘ sporadic simple group ⓘ sporadic simple group ⓘ sporadic simple group ⓘ |
| classification | part of the 26 sporadic simple groups ⓘ |
| consistOf |
Co1
ⓘ
Co2 ⓘ Co3 ⓘ |
| containsSubgroup |
Conway groups
self-linksurface differs
ⓘ
surface form:
Conway group Co1
Conway groups self-linksurface differs ⓘ
surface form:
Conway group Co2
Conway groups self-linksurface differs ⓘ
surface form:
Conway group Co3
|
| definedOver | finite sets ⓘ |
| dimension | 24 ⓘ |
| discoveredBy |
John H. Conway
ⓘ
surface form:
John Horton Conway
|
| discoveryContext | study of symmetries of the Leech lattice ⓘ |
| field |
group theory
ⓘ
group theory ⓘ |
| hasAutomorphismGroup |
Conway groups
self-linksurface differs
ⓘ
surface form:
automorphism group of the Leech lattice
|
| hasCardinality | 3 ⓘ |
| hasMember |
Conway groups
self-linksurface differs
ⓘ
surface form:
Conway group Co1
Conway groups self-linksurface differs ⓘ
surface form:
Conway group Co2
Conway groups self-linksurface differs ⓘ
surface form:
Conway group Co3
|
| hasProperty |
centerless
ⓘ
finite simple groups ⓘ non-abelian ⓘ non-abelian ⓘ non-abelian ⓘ non-abelian simple groups ⓘ |
| isSubgroupOf |
Conway groups
self-linksurface differs
ⓘ
surface form:
automorphism group of the Leech lattice
Conway groups self-linksurface differs ⓘ
surface form:
automorphism group of the Leech lattice
automorphism group of the Leech lattice ⓘ |
| isSubsetOf | sporadic simple groups ⓘ |
| knownFor | discovery of Conway groups ⓘ |
| namedAfter |
John H. Conway
ⓘ
surface form:
John Horton Conway
|
| order |
4157776806543360000
ⓘ
42305421312000 ⓘ 495766656000 ⓘ |
| relatedTo |
Leech lattice
ⓘ
Monster group ⓘ Conway groups self-linksurface differs ⓘ
surface form:
automorphism group of the Leech lattice
|
| yearDiscoveredApprox | 1960s ⓘ |
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: Conway groups Description of subject: 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.
Referenced by (21)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
John Horton Conway
this entity surface form:
Conway group
this entity surface form:
automorphism group of the Leech lattice
this entity surface form:
Conway group Co1
this entity surface form:
Conway group Co2
this entity surface form:
Conway group Co3
subject surface form:
Conway group Co1
this entity surface form:
automorphism group of the Leech lattice
subject surface form:
Conway group Co2
this entity surface form:
automorphism group of the Leech lattice
subject surface form:
automorphism group of the Leech lattice
this entity surface form:
Conway group Co1
subject surface form:
automorphism group of the Leech lattice
this entity surface form:
Conway group Co2
subject surface form:
automorphism group of the Leech lattice
this entity surface form:
Conway group Co3
subject surface form:
Leech lattice
this entity surface form:
automorphism group of the Leech lattice
subject surface form:
John H. Conway
subject surface form:
John H. Conway
this entity surface form:
Conway group
this entity surface form:
Conway group Co0
this entity surface form:
Conway group Co0
this entity surface form:
Conway group Co1
this entity surface form:
Conway group Co3
this entity surface form:
Conway group Co1