Janko group J4
E656681
Janko group J4 is one of the sporadic simple groups in finite group theory, notable as the largest of the Janko groups and a significant example among the 26 sporadic groups.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
finite simple group
ⓘ
group in abstract algebra ⓘ sporadic simple group ⓘ |
| belongsTo | sporadic groups ⓘ |
| discoveredBy | Zvonimir Janko NERFINISHED ⓘ |
| discoveryYear | 1975 ⓘ |
| documentedIn | Atlas of Finite Groups NERFINISHED ⓘ |
| hasAtlasName | J4 NERFINISHED ⓘ |
| hasLargeMinimalPermutationRepresentation | true ⓘ |
| hasMaximalSubgroup |
11^{1+2}.(5×2S4)
ⓘ
29:28 ⓘ 2^{1+12}.3.M22.2 ⓘ 2^{4+12}.(3×A6).2 NERFINISHED ⓘ 31:15 ⓘ 37:18 ⓘ 43:14 ⓘ |
| hasOuterAutomorphismGroupOrder | 1 ⓘ |
| hasSchurMultiplierOrder | 1 ⓘ |
| hasSporadicLabel | J4 NERFINISHED ⓘ |
| hasTrivialCenter | true ⓘ |
| hasTrivialOuterAutomorphismGroup | true ⓘ |
| hasTrivialSchurMultiplier | true ⓘ |
| isExampleIn |
finite group theory
ⓘ
sporadic group theory ⓘ |
| isLargestOf | Janko groups NERFINISHED ⓘ |
| isLargestSporadicDiscoveredBy | Zvonimir Janko NERFINISHED ⓘ |
| isNonAbelian | true ⓘ |
| isOneOf | 26 sporadic simple groups ⓘ |
| isPerfect | true ⓘ |
| isSimple | true ⓘ |
| isUsedIn | classification of finite simple groups ⓘ |
| minimalFaithfulPermutationDegree | 173067389 ⓘ |
| minimalFaithfulPermutationDegreeApprox | 1.7×10^8 ⓘ |
| namedAfter | Zvonimir Janko NERFINISHED ⓘ |
| notation | J4 NERFINISHED ⓘ |
| order | 86775571046077562880 ⓘ |
| orderFactorization | 2^21 × 3^3 × 5 × 7 × 11^3 × 23 × 29 × 31 × 37 × 43 ⓘ |
| orderPowerOf11 | 11^3 ⓘ |
| orderPowerOf2 | 2^21 ⓘ |
| orderPowerOf3 | 3^3 ⓘ |
| orderPowerOf5 | 5 ⓘ |
| orderPowerOf7 | 7 ⓘ |
| orderPrimeFactor |
23
ⓘ
29 ⓘ 31 ⓘ 37 ⓘ 43 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.