FiniteGroup
Related Interpreter »Notable mathematical groups of finite order.
Entity["FiniteGroup",name] or 
represents an entity of type "FiniteGroup".
[prop]
gives the value of a specified property.
[{propi,…}]
gives the value of a list of properties.
EntityClass["FiniteGroup",{propispeci,…}]
represents a class of entities with values of propi defined by speci.
Sample Entities
-
…
Sample Entity Classes
-
…
Properties
-
Abelian Abelian AlternateNames alternate names Alternating alternating AssociatedPeople associated people AutomorphismGroup automorphism group BravaisLattices Bravais lattice CayleyGraph Cayley graph Center center CenterElements center elements CharacterTable character table Classes raw classes ClassNumber class number CommutatorSubgroup commutator subgroup CommutatorSubgroupElements commutator subgroup elements ConjugacyClasses conjugacy classes ConjugacyClassNames conjugacy class names ConjugacyClassSizes conjugacy class sizes CrystalFamily crystal family CrystalForm crystal form CrystalSystem crystal system CycleGraph cycle graph CycleIndex cycle index Cycles cycles Cyclic cyclic DefiningRelations defining relations Dihedral dihedral ElementNames element names Elements elements EntityClasses entity classes EntityTypeList entity type list Exponent exponent Generators indexed generators HermannMauguin Hermann‐Mauguin notation Information information InnerAutomorphismGroup inner automorphism group InverseGenerators inverse generators Inverses inverses IsomorphicGroups isomorphic groups LatticeSystems lattice system MatrixRepresentation matrix representation MultiplicationTable indexed multiplication table Name name Nonabelian nonabelian Nonalternating nonalternating Noncyclic noncyclic Nondihedral nondihedral Nonperfect nonperfect Nonsimple nonsimple Nonsolvable nonsolvable Nonsporadic nonsporadic Nonsymmetric nonsymmetric Nontransitive nontransitive NormalSubgroupElements normal subgroup elements NormalSubgroups normal subgroups Notation notation Orbifold orbifold notation Order order OuterAutomorphismGroup outer automorphism group ParameterRange parameter range Perfect perfect PermutationGroupRepresentation permutation group representation PermutationRepresentation permutation representation PointGroupType type QuotientGroups quotient groups RepresentationDimensions representation dimensions RepresentationNames representation names Schoenflies Schönflies notation SchurMultiplier Schur multiplier ShortName short name Shubnikov Shubnikov magnetic group Simple simple Solvable solvable SpaceRepresentation space representation Sporadic sporadic SubgroupElements subgroup elements Subgroups subgroups SylowSubgroupCounts Sylow subgroup counts SylowSubgroupElements Sylow subgroup elements SylowSubgroups Sylow subgroups Symmetric symmetric Transitive transitive Transitivity transitivity
Details
- "FiniteGroup" entities include particular named finite groups, as well as members of parametrized families.
- "FiniteGroup" entity classes include common mathematical types of groups such as "Abelian", "Cyclic" and "Sporadic", together with the negations of these.
- Mathematical properties are available for most "FiniteGroup" entities that are concisely representable and either well known or straightforward to compute. Properties for some parametrized family members are computed on the fly and may be specified using symbolic parameters.
- Some properties are available for the "FiniteGroup" entity type as a whole and can be given using the form EntityValue["FiniteGroup",property]. Such properties include:
-
"Properties" the list of available properties "PropertyCanonicalNames" the standard names of available properties "SampleEntities" a sample list of available entities (typically of length 10) "SampleEntityClasses" a sample list of available entity classes (typically of length 10) "EntityCount" number of entities available "Entities" the list of available entities "EntityCanonicalNames" the standard names of available entities "EntityClasses" the list of available entity classes "EntityClassCanonicalNames" the standard names of available entity classes "PropertyClasses" the list of available property classes "PropertyClassCanonicalNames" the standard names of available property classes "PropertyCount" number of properties available - The following annotations can be used in the third argument of EntityValue["FiniteGroup",property,annotation]:
-
"EntityAssociation" an association of entities and entity-property values "PropertyAssociation" an association of properties and entity-property values "EntityPropertyAssociation" an association in which the specified entities are keys, and values are a nested association of properties and entity-property values "PropertyEntityAssociation" an association in which the specified properties are keys, and values are a nested association of entities and entity-property values "Dataset" a dataset in which the specified entities are keys, and values are an association of property names and entity-property values - The following annotations can be used in the second argument of EntityValue[property,annotation]:
-
"Description" a brief textual description of the property
for entity discovery: