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.
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
NERFINISHED
ⓘ
involution centralizer ⓘ |
| hasConjugacyClasses | finitely many ⓘ |
| hasDoubleCover | 2.HN NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| isSimple | true ⓘ |
| isSubquotientOf | Monster group NERFINISHED ⓘ |
| namedAfter |
Koichiro Harada
NERFINISHED
ⓘ
Simon P. Norton NERFINISHED ⓘ |
| order | 273030912000000 ⓘ |
| orderFactorization |
11
ⓘ
19 ⓘ 2^14 ⓘ 31 ⓘ 3^6 ⓘ 5^6 ⓘ 7 ⓘ |
| studiedIn | finite group theory ⓘ |
| symbol | HN NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.