// generating by shuffles

SetLogFile("shufgen1.log":Overwrite:=true); 

// set up group and generating shuffles
G := SymmetricGroup(4);
 t1 := G!(1,2); t2 := G!(2,3); t3 := G!(3,4);  S := {t1,t2,t3};
//t := G!(1,2); c :=  G!(1,2,3,4); S := {t,c};
//d := G!(1,2)(3,4); c := G!(1,2,3); S := {d,c};

// set up counters
Nlist := [1];
Blist := [1];
oldnum := 1;
 
// build group
W := {Id(G)};
for j in [1..12] do
    W := W join {x*y:x in W, y in S};
    print W;
    newnum := #W; 
    Nlist := Append(Nlist,newnum);
    Blist := Append(Blist,newnum-oldnum);
    print [j,newnum,newnum-oldnum];
    oldnum := newnum; 
    end for; 

print Nlist;
print Blist;

UnsetLogFile();