Given the ring R of class functions, return the number of conjugacy classes of the finite group underlying R.
Given the ring R of class functions, return a sequence of pairs, one pair <o,n> for each conjugacy class of the underlying group, where o is the order of the group elements in the class, and n is the length of (number of group elements in) the class.
Given the ring R of class functions on a finite group G, return G. This will cause an error if R does not have a group attached. If unsure whether or not R has a group attached, check the texttt{Group} attribute of R using texttt{assigned R`Group}.
Given a character ring R, return the associated class power map. This will cause an error unless R has a power map assigned, or has a group attached. The texttt{PowerMap} is an attribute of R, as is texttt{Group}, and its presence can be checked using texttt{assigned R`PowerMap}.If the power map of R is not already assigned, and there is an assigned group, this function will compute the power map using operations within the group.
The kernel of the character x of G, i.e. the normal subgroup of G consisting of those elements g for which x(g) = x(1).
The centre of the character x of G, i.e. the subgroup of G consisting of those classes C of G for which |x(g)|, g in C, is equal to the degree of x.
The minimal cyclotomic field containing all values of the class function x.
The subfield of the coefficient field of the class function x that is generated by the values of x.
The degree of the character field of the class function x as an extension of the rational numbers.