GAP:IrrepDegreeGroupingFull

Function type
This is a coded (not in-built) function in GAP to group together all groups of a given order based on their degrees of irreducible representations.

Behavior
The function is invoked as:

IrrepDegreeGroupingFull(n)

where $$n$$ is a natural number. The output is a list of pairs of lists, where each pair is as follows:


 * The first member of the pair is itself a list of pairs describing a collection of degrees of irreducible representations over $$\mathbb{C}$$: the first member of each pair is a degree and the second member is the number of irreducible representations of that degree.
 * The second member of the pair is the list of second parts of GAP IDs of groups of order $$n$$ having those degrees of irreducible representations.

Code
IrrepDegreeGroupingFull := function(n) local L,M,m,N; L := List(AllSmallGroups(n),CharacterDegrees); M := SortedList(Set(L)); m := Length(L); N := List(M,i -> [i,Filtered([1..m],j->L[j]=i)]); return(SortedList(N)); end;;