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.

All labels observed (1)

Label Occurrences
Janko group J4 canonical 1

How this entity was disambiguated

Statements (47)

Predicate Object
instanceOf finite simple group ⓘ
group in abstract algebra ⓘ
sporadic simple group ⓘ
belongsTo sporadic groups ⓘ
discoveredBy Zvonimir Janko ⓘ
discoveryYear 1975 ⓘ
documentedIn Atlas of Finite Groups ⓘ
hasAtlasName J4 ⓘ
hasLargeMinimalPermutationRepresentation true ⓘ
hasMaximalSubgroup 11^{1+2}.(5×2S4) ⓘ
29:28 ⓘ
2^{1+12}.3.M22.2 ⓘ
2^{4+12}.(3×A6).2 ⓘ
31:15 ⓘ
37:18 ⓘ
43:14 ⓘ
hasOuterAutomorphismGroupOrder 1 ⓘ
hasSchurMultiplierOrder 1 ⓘ
hasSporadicLabel J4 ⓘ
hasTrivialCenter true ⓘ
hasTrivialOuterAutomorphismGroup true ⓘ
hasTrivialSchurMultiplier true ⓘ
isExampleIn finite group theory ⓘ
sporadic group theory ⓘ
isLargestOf Janko groups ⓘ
isLargestSporadicDiscoveredBy Zvonimir Janko ⓘ
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 ⓘ
notation J4 ⓘ
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 ⓘ

How these facts were elicited

Referenced by (1)

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

Monster group → hasSubgroup → Janko group J4 ⓘ