Conjugates(H, g) : GrpPC, GrpPCElt -> { GrpPCElt }

g ^ H : GrpPCElt, GrpPC -> { GrpPCElt }

Given a group H and an element g belonging to a group K such that H and K are subgroups of some covering group, this function returns the set of conjugates of g under the action of H. If H = K, the function returns the conjugacy class of g in H.

Classes(G) : GrpPC -> [ <RngIntElt, RngIntElt, GrpPCElt> ]

Construct a set of representatives for the conjugacy classes of G. The classes are returned as a sequence of tuples containing the class length, the order of the elements in the class and a representative element for the class.

The class map M: G -> {1, ..., n} for the group G, where n is the number of conjugacy classes of G.

The designated representative for the conjugacy class of G containing x (relative to existing conjugacy classes).

Given a group G and elements g and h belonging to G, return the value true if g and h are conjugate in G. The function also returns a second value in the event that the elements are conjugate: an element z which conjugates g into h.

IsConjugate(G, H, K) : GrpPC, GrpPC, GrpPC -> BoolElt, GrpPCElt

Given a group G and subgroups H and K belonging to G, return the value true if G and H are conjugate in G. The function returns a second value in the event that the subgroups are conjugate: an element z which conjugates H into K.

Nclasses(G) : GrpPC -> RngIntElt

The number of conjugacy classes of elements of the group G.

The power map M associated with the conjugacy classes of G. M describes where the elements of the conjugacy classes of G move under powers. That is, <c, n>@M returns the class number where class c moves under the power n. The value of c must be in the range [1 ... Nclasses(G)].

M: {1 ... n} x Z -> {1 ... n}