AllMultiplicityFreeSubgroups

AllMultiplicityFreeSubgroups(G) returns the set of representatives of all conjugacy classes of proper subgroups H such that the Schurian scheme defined by G and H is commutative. For example, for the symmetric group of degree 5, we have the following result :

gap> AllMultiplicityFreeSubgroups(SymmetricGroup(5));                
[ Group([ (1,2,3,4), (1,2) ]), Group([ (1,2,3), (1,2), (4,5) ]), 
  Group([ (3,4), (1,4)(2,3), (1,3)(2,4) ]), Group([ (4,5), (1,2,3) ]), 
  Alt( [ 1 .. 4 ] ), Alt( [ 1 .. 5 ] ), Group([ (1,2,3), (1,2)(4,5) ]), 
  Group([ (2,3,4,5), (2,4)(3,5), (1,2,3,5,4) ]), 
  Group([ (2,4)(3,5), (1,2,3,5,4) ]) ]