GroupCentreDimension

A name from the enumeratio catalogue with no kernel of its own yet; this page carries its crosswalk only.

Mapped through to oscar for the oracle; not yet written up here.

GroupCentreDimension(...)Mapped through to oscar for the oracle; not yet written up here.

SageMathenumeratio_centre_dimension(...)Oscarnumber_of_conjugacy_classes((...).G)

Typed signatures

Type	Package	Applies
(expression<CyclicGroup> | expression<DihedralGroup> | expression<GroupDirectProduct>) -> integer	groupalgebra	always

Domain: Oracle

Examples

Basic #

The number of conjugacy classes of $D_4$

live ↗

In$\mathrm{GroupCentreDimension}(\mathrm{DihedralGroup}(4))$Out$5$

In an abelian group every element is its own class

live ↗

In$\mathrm{GroupCentreDimension}(\mathrm{CyclicGroup}(5))$Out$5$

About

Examples	2
Checked against	Wolfram Language 2 agreeSageMath 2 agree
Crosswalk	SageMathOscar

Implementation

mappedoscarpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

The number of conjugacy classes, which is the dimension of the centre of the group algebra.

mappedwolframpackages/oracle/src/mappings.ts

Wolfram has no conjugacy classes; the number of them is the average size of a centralizer (Burnside), from GroupCentralizer.