Thompson group Th

E656680
finite simple group group (mathematics) sporadic simple group

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.

Jump to: Surface forms Statements Referenced by

Observed surface forms (1)

Surface form Occurrences
Thompson sporadic group 1

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 ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Monster group → hasSubgroup → Thompson group Th ⓘ
John G. Thompson → knownFor → Thompson group Th ⓘ
this entity surface form: Thompson sporadic group