Fischer group Fi24′
E656677
The Fischer group Fi24′ is one of the 26 sporadic simple groups, notable as a large and highly structured finite simple group discovered by Bernd Fischer and closely related to the Monster group.
Statements (52)
| Predicate | Object |
|---|---|
| instanceOf |
Fischer group
ⓘ
finite simple group ⓘ sporadic simple group ⓘ |
| appearsIn | Atlas of Finite Groups NERFINISHED ⓘ |
| discoverer | Bernd Fischer NERFINISHED ⓘ |
| hasAbbreviation | Fi24′ NERFINISHED ⓘ |
| hasAlternativeName | Fischer group Fi24 prime NERFINISHED ⓘ |
| hasAssociated3TranspositionGroup | Fi24 NERFINISHED ⓘ |
| hasAtlasName | Fi24′ NERFINISHED ⓘ |
| hasCentralizerOf3TranspositionStructure | 2×Fi23 ⓘ |
| hasCentralizerOfInvolutionStructure | 2·Fi22 NERFINISHED ⓘ |
| hasElementOrder |
10
ⓘ
11 ⓘ 12 ⓘ 13 ⓘ 14 ⓘ 15 ⓘ 17 ⓘ 2 ⓘ 23 ⓘ 29 ⓘ 3 ⓘ 31 ⓘ 4 ⓘ 47 ⓘ 5 ⓘ 6 ⓘ 7 ⓘ 8 ⓘ |
| hasMinimalFaithfulComplexRepresentationDegree | 783 ⓘ |
| hasMinimalFaithfulPermutationRepresentationDegree |
306,936
ⓘ
306936 ⓘ |
| hasOrder | 1255205709190661721292800 ⓘ |
| hasOrderFactorization |
11
ⓘ
13 ⓘ 17 ⓘ 23 ⓘ 29 ⓘ 2^21 ⓘ 31 ⓘ 3^16 ⓘ 47 ⓘ 5^2 ⓘ 7^3 ⓘ |
| hasOuterAutomorphismGroupOrder | 2 ⓘ |
| hasRank | 3-transposition group ⓘ |
| hasSchurMultiplierOrder | 3 ⓘ |
| isDerivedFrom | 3-transposition construction of Bernd Fischer ⓘ |
| isGeneratedBy | 3-transpositions ⓘ |
| isOneOf | 26 sporadic simple groups ⓘ |
| isRelatedTo | Monster group NERFINISHED ⓘ |
| isSubquotientOf | Monster group NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.