Harada–Norton group
E659250
The Harada–Norton group is one of the 26 sporadic simple groups in finite group theory, notable for its large order and close relationship to the Monster group.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Harada–Norton group canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338407 — 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: Harada–Norton group Context triple: [Monster group, hasSubgroup, Harada–Norton group]
-
A.
Fischer–Griess Monster
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.
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B.
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.
-
C.
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.
-
D.
Fischer group Fi24′
The Fischer group Fi24′ is one of the 26 sporadic simple groups, notable as a large and highly structured finite simple group discovered by Bernd Fischer and closely related to the Monster group.
-
E.
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.
- 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: Harada–Norton group Target entity description: The Harada–Norton group is one of the 26 sporadic simple groups in finite group theory, notable for its large order and close relationship to the Monster group.
-
A.
Fischer–Griess Monster
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.
-
B.
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.
-
C.
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.
-
D.
Fischer group Fi24′
The Fischer group Fi24′ is one of the 26 sporadic simple groups, notable as a large and highly structured finite simple group discovered by Bernd Fischer and closely related to the Monster group.
-
E.
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.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
abstract algebraic structure
ⓘ
finite simple group ⓘ sporadic simple group ⓘ |
| appearsIn | classification of finite simple groups ⓘ |
| belongsTo | 26 sporadic simple groups ⓘ |
| definedOver | finite set ⓘ |
| hasAtlasLabel | HN ⓘ |
| hasCentralizerInMonster |
2.HN
ⓘ
involution centralizer ⓘ |
| hasConjugacyClasses | finitely many ⓘ |
| hasDoubleCover | 2.HN ⓘ |
| hasOuterAutomorphismGroupOrder | 2 ⓘ |
| hasPermutationRepresentationDegree | various large degrees ⓘ |
| hasPrimeDivisor |
11
ⓘ
19 ⓘ 2 ⓘ 3 ⓘ 31 ⓘ 5 ⓘ 7 ⓘ |
| hasRank | finite rank ⓘ |
| hasRepresentationTheory | complex representations ⓘ |
| hasSchurMultiplierOrder | 2 ⓘ |
| hasTrivialCenter | true ⓘ |
| hasType | sporadic simple group of pariah type (historical classification context) ⓘ |
| hasYearOfDiscovery | 1970s ⓘ |
| isA |
non-abelian simple group
ⓘ
perfect group ⓘ sporadic group ⓘ |
| isFinite | true ⓘ |
| isNonAbelian | true ⓘ |
| isRelatedTo | Monster group ⓘ |
| isSimple | true ⓘ |
| isSubquotientOf | Monster group ⓘ |
| namedAfter |
Koichiro Harada
ⓘ
Simon P. Norton ⓘ |
| order | 273030912000000 ⓘ |
| orderFactorization |
11
ⓘ
19 ⓘ 2^14 ⓘ 31 ⓘ 3^6 ⓘ 5^6 ⓘ 7 ⓘ |
| studiedIn | finite group theory ⓘ |
| symbol | HN ⓘ |
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: Harada–Norton group Description of subject: The Harada–Norton group is one of the 26 sporadic simple groups in finite group theory, notable for its large order and close relationship to the Monster group.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.