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

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


///the quotient group NGC/C
//

Q:=quo<NGC|C>;

///the group S_4xC_2
//

Y:=PermutationGroup<6|(2,4),(1,2),(1,3),(5,6),Sym(6)!1>;



f:=hom<Q->Y|Y.1,Y.2,Y.3,Y.4,Y.5>;




///check that f is bijective
//

if Order(Kernel(f)) eq 1 then
 if Order(Image(f)) eq Order(Y) then
  print("");
  print("f is a group isomorphism Q--->Y");
 end if;
end if;