Order of symmetric group irreps
This is a key detail for me, but I can't find any information about it in the Sage or GAP documentation: if I use
I get a 7x7 matrix, with rows indexed by conjugacy classes and columns indexed by irreps. Both of these things can be indexed, for instance, by Young diagrams of size 5.
How are the rows and columns ordered? Is it safe to assume that they will be ordered in reverse-lexicographic order on the Young diagrams, i.e.
5 ; 4,1 ; 3,2 ; 3,1,1 ; 2,2,1 ; 2,1,1,1 ; 1,1,1,1,1
This seems to be the case in the examples I've checked but I want to be sure that this is guaranteed by the code and not a coincidence in small examples.