Fischer–Griess Monster
E656672
The Fischer–Griess Monster is the largest sporadic simple group in finite group theory, a vast and highly complex algebraic structure central to the classification of finite simple groups.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Fischer–Griess Monster canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338369 — 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: Fischer–Griess Monster Context triple: [Monster group, alsoKnownAs, Fischer–Griess Monster]
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A.
Conway–Norton collaboration
The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
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B.
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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C.
Chevalley
Chevalley is a French surname most prominently associated with Claude Chevalley, a influential 20th-century mathematician known for his work in algebra and group theory.
-
D.
Frattini
Frattini is an Italian surname associated with various notable figures in fields such as mathematics, politics, and the arts.
-
E.
Clebsch
Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
- 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: Fischer–Griess Monster Target entity description: The Fischer–Griess Monster is the largest sporadic simple group in finite group theory, a vast and highly complex algebraic structure central to the classification of finite simple groups.
-
A.
Conway–Norton collaboration
The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
-
B.
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.
-
C.
Chevalley
Chevalley is a French surname most prominently associated with Claude Chevalley, a influential 20th-century mathematician known for his work in algebra and group theory.
-
D.
Frattini
Frattini is an Italian surname associated with various notable figures in fields such as mathematics, politics, and the arts.
-
E.
Clebsch
Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
- F. None of above. chosen
Statements (65)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic structure
ⓘ
finite simple group ⓘ group (mathematics) ⓘ sporadic simple group ⓘ |
| actsOn | 196883-dimensional complex vector space ⓘ |
| alsoKnownAs |
Friendly Giant
ⓘ
Monster group ⓘ the Monster ⓘ |
| belongsTo |
sporadic groups
ⓘ
linked to:
sporadic simple groups
|
| centralTo | classification of finite simple groups ⓘ |
| constructedBy | Robert Griess ⓘ |
| constructionYear | 1980 ⓘ |
| hasAutomorphismGroup | itself ⓘ |
| hasElementOrder |
11
ⓘ
13 ⓘ 17 ⓘ 19 ⓘ 2 ⓘ 23 ⓘ 29 ⓘ 3 ⓘ 31 ⓘ 41 ⓘ 47 ⓘ 5 ⓘ 59 ⓘ 7 ⓘ 71 ⓘ |
| hasNontrivialSmallRepresentationDimension | 196883 ⓘ |
| hasOuterAutomorphisms | false ⓘ |
| hasPrimeDivisor |
11
ⓘ
13 ⓘ 17 ⓘ 19 ⓘ 2 ⓘ 23 ⓘ 29 ⓘ 3 ⓘ 31 ⓘ 41 ⓘ 47 ⓘ 5 ⓘ 59 ⓘ 7 ⓘ 71 ⓘ |
| hasTrivialCenter | true ⓘ |
| hasTrivialRepresentationDimension | 1 ⓘ |
| isFullAutomorphismGroupOf | Griess algebra ⓘ |
| isLargest |
sporadic group by order
ⓘ
sporadic simple group ⓘ |
| isNonAbelian | true ⓘ |
| isPerfectGroup | true ⓘ |
| isSimple | true ⓘ |
| isSubgroupOf | automorphism group of the Griess algebra ⓘ |
| minimalFaithfulComplexRepresentationDimension | 196883 ⓘ |
| numberOfConjugacyClasses | 194 ⓘ |
| order | 808017424794512875886459904961710757005754368000000000 ⓘ |
| orderFactorization | 2^46 · 3^20 · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 ⓘ |
| predictedBy |
Bernd Fischer
ⓘ
Robert Griess ⓘ |
| relatedTo |
Griess algebra
ⓘ
modular function j ⓘ monstrous moonshine ⓘ moonshine module ⓘ |
| symbol | M ⓘ |
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: Fischer–Griess Monster Description of subject: The Fischer–Griess Monster is the largest sporadic simple group in finite group theory, a vast and highly complex algebraic structure central to the classification of finite simple groups.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.