Is there a command in GAP to obtain all transformations on $n$ symbols (so there should be $n^n$ of them). I can not find such a command in https://www.gap-system.org/Manuals/doc/ref/chap53.html#X7B51CE257B814B09 but I would think that there is such a command since one can even find all finite groups of a given (low) order using GAP. The output should be a list containing all transformation from [1..n] to [1..n]. So for example for n=2, the list looks like this:
[Transformation([1,2]),Transformation([1,1]),Transformation([2,2]),Transformation([2,1])];
Not "my" solution, from another GAP user:
gap> List(FullTransformationSemigroup(3));does the job, returning
[ Transformation( [ 1, 1, 1 ] ), Transformation( [ 1, 1, 2 ] ), Transformation( [ 1, 1 ] ), Transformation( [ 1, 2, 1 ] ), ...