Thompson group Th
E656680
Thompson group Th is a sporadic simple group in finite group theory, notable as one of the 26 sporadic groups and a large subgroup of the Monster group.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Thompson group Th canonical | 1 |
| Thompson sporadic group | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338410 — 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: Thompson group Th Context triple: [Monster group, hasSubgroup, Thompson group Th]
-
A.
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.
-
B.
Frattini
Frattini is an Italian surname associated with various notable figures in fields such as mathematics, politics, and the arts.
-
C.
Alexander–Briggs notation
Alexander–Briggs notation is a classical system for naming and classifying knots in knot theory, assigning each distinct knot a unique label based on its crossing number and order in knot tables.
-
D.
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.
-
E.
Weil group
The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
- 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: Thompson group Th Target entity description: Thompson group Th is a sporadic simple group in finite group theory, notable as one of the 26 sporadic groups and a large subgroup of the Monster group.
-
A.
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.
-
B.
Frattini
Frattini is an Italian surname associated with various notable figures in fields such as mathematics, politics, and the arts.
-
C.
Alexander–Briggs notation
Alexander–Briggs notation is a classical system for naming and classifying knots in knot theory, assigning each distinct knot a unique label based on its crossing number and order in knot tables.
-
D.
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.
-
E.
Weil group
The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
finite simple group
ⓘ
group (mathematics) ⓘ sporadic simple group ⓘ |
| alsoKnownAs |
Th
NERFINISHED
ⓘ
Thompson sporadic group NERFINISHED ⓘ |
| hasAtlasNotation | Th NERFINISHED ⓘ |
| hasAutomorphismGroup | Thompson group Th NERFINISHED ⓘ |
| hasElementOrder |
1
ⓘ
10 ⓘ 12 ⓘ 13 ⓘ 15 ⓘ 19 ⓘ 2 ⓘ 21 ⓘ 3 ⓘ 30 ⓘ 31 ⓘ 39 ⓘ 4 ⓘ 5 ⓘ 6 ⓘ 7 ⓘ |
| hasLargestElementOrder | 31 ⓘ |
| hasMinimalFaithfulComplexRepresentationDegree | 248 ⓘ |
| hasMinimalFaithfulPermutationDegree | 248 ⓘ |
| hasOuterAutomorphisms | false ⓘ |
| hasPermutationRepresentationDegree |
248
ⓘ
27000 ⓘ |
| hasPrimeDivisor |
13
ⓘ
19 ⓘ 2 ⓘ 3 ⓘ 31 ⓘ 5 ⓘ 7 ⓘ |
| hasRank3PermutationRepresentationDegree | 248 ⓘ |
| hasTrivialAbelianization | true ⓘ |
| hasTrivialSchurMultiplier | true ⓘ |
| isCenterTrivial | true ⓘ |
| isInAtlasOfFiniteGroups | true ⓘ |
| isNonAbelian | true ⓘ |
| isOneOf | 26 sporadic groups ⓘ |
| isPerfect | true ⓘ |
| isSimple | true ⓘ |
| isSporadicGroupNumber | 22 ⓘ |
| isSubgroupOf |
Fischer–Griess Monster
NERFINISHED
ⓘ
Monster group NERFINISHED ⓘ |
| namedAfter | John G. Thompson NERFINISHED ⓘ |
| order | 90745943887872000 ⓘ |
| orderFactorization | 2^15 · 3^10 · 5^3 · 7^2 · 13 · 19 · 31 ⓘ |
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: Thompson group Th Description of subject: Thompson group Th is a sporadic simple group in finite group theory, notable as one of the 26 sporadic groups and a large subgroup of the Monster group.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Thompson sporadic group