Q:=PermutationGroup<24|(2, 15, 21)(3, 17, 19)(4, 10, 7)(5, 23, 18)(8, 14, 13)(9, 11, 12),(1, 16, 6)(3, 17, 19)(4, 7, 10)(5, 9, 8)(11, 14, 23)(12, 13, 18)>;




NQ:=PermutationGroup<24|(3, 7)(4, 19)(10, 17)(11, 12)(13, 14)(15, 21)(18, 23)(20, 22),(1, 3)(6, 19)(11, 13)(12, 23)(14, 18)(15, 21)(16, 17)(22, 24),(1, 16)(3, 17)(5, 8)(7, 10)(11, 12)(13, 23)(14, 18)(15, 21), (1, 15, 6, 21)(2, 16)(3, 7, 19, 4)(8, 23, 9, 18)(10, 17)(11, 12, 13, 14),(1, 3, 6, 19)(2, 10)(4, 21, 7, 15)(8, 11, 9, 13)(12, 23, 14, 18)(16, 17)>;



///the quotient group NQ/Q
//

QQ:=quo<NQ|Q>;



///the gerneral linear group GL(2,3)
//

gens:=[Matrix(GF(3),2,2,[1,0,0,2]),
      Matrix(GF(3),2,2,[1,0,2,2]),
      Matrix(GF(3),2,2,[2,0,0,2]),
      Matrix(GF(3),2,2,[0,1,2,0]),
      Matrix(GF(3),2,2,[2,1,1,1])];


GL:=sub<GeneralLinearGroup(2,3)|gens>;

if GL eq GeneralLinearGroup(2,3) then
 print("the general linear group GL(2,3)");
end if;


f:=hom<QQ->GL|gens>;





if Order(Kernel(f)) eq 1 then
 if Order(Image(f)) eq Order(GL) then
  print("");
  print("f is a group isomorphism QQ--->GL(2,3)");
 end if;
end if;