"Source: Text/Group/GrpFP.text";
"Line: 7360";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 7360
// Example: H80E55 ()
print "Example: H80E55";
ei := GetEchoInput();
SetEchoInput(true);
B := BraidFPGroup(4);
G := PSL(2,16);
P := HomomorphismsProcess(B, G : Surjective := false,
                                 TimeLimit := 10);
while not IsEmpty(P) do
   if DefinesHomomorphism(P) then
      f := Homomorphism(P);
      img := Image(f);
      if IsMaximal(G,img) then
         print "found image which is maximal subgroup";
         break;
      end if;
   end if;
   if IsValid(P) then
      NextElement(~P);
    else
      print "Limit has been reached";
      break;
   end if;
end while;

f;
SetEchoInput(ei);
