"Source: Text/Group/GrpFP.text";
"Line: 719";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 719
// Example: H80E8 ()
print "Example: H80E8";
ei := GetEchoInput();
SetEchoInput(true);
G<x,y,z,h,k,a> := FPGroup< x, y, z, h, k, a | 
   x^2, y^2, z^2, (x,y), (y,z), (x,z), h^3, k^3, (h,k), 
   (x,k), (y,k), (z,k), x^h*y, y^h*z, z^h*x, a^2, a*x*a*y,
   a*y*a*x, (a,z), (a,k), (a*h)^2 >;
for i := 0 to 1 do
    for j := 0 to 1 do
        for k := 0 to 1 do
             for l := 0 to 2 do
                rel := G.1^i*G.2^j*G.3^k*G.5^l*(G.6*G.4)^2 = Id(G);
                K := ReplaceRelation(G, 21, rel);
                print Order(K), Index(K, sub< K | K.6, K.4>);
            end for;
        end for;
    end for;
end for;
SetEchoInput(ei);
