ConjugacyClasses

The conjugacy classes of a finite group — the orbits of . Their number is the dimension of the centre of .

WikipediaConjugacy classMathWorldConjugacyClassWikidataQ1353233nLabconjugacy class

ConjugacyClasses(group)the classes, as a list of lists

GroupCentreDimension(group)how many there are

Domain: Group algebras

Details

An abelian group has one class per element, so
has classes for odd and for even
has three: the identity, the transpositions, and the 3-cycles
The classes partition the group, and the identity is always alone in its own

Examples

See also: ClassSum, GroupBasis