"Source: Text/Group/GrpFPInt.text";
"Line: 1184";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFPInt.text, line: 1184
// Example: H79E15 ()
print "Example: H79E15";
ei := GetEchoInput();
SetEchoInput(true);
F<a,b,c,d,y,x,w> := FreeGroup(7);
z := y*c*a^2*b;
u := x*d;
t := w*c*a*d*b^2*c;
G<a,b,c,d,y,x,w>, psi :=
           quo< F | a^4, b^4, c^2, d^2, (a,b), (a*c)^2, (b*c)^2,
                       (c*d)^2, d*a*d*b^-1, y^3, (a^-1*b)^y*d*a^-1*b^-1,
                       (c*d*a^-1*b)^y*b^-1*a*d*c, a*d*y*d*a^-1*y, x^3,
                       a^x*b^-1, b^x*a*b, c^x*c, (x*d)^2, (u*z)^6, w^3,
                       (w,y), (a*b)^w*b^-1*a*d*c, (c*d*a^-1*b)^w*d*c*b^2,
                       (b^2*c*d)^w*a^-1*b^-1, (c*a^2*b*w)^2,
                      (a^-1*b)^w*d*a^-1*b^-1, (t*u)^3 >;
z1 := psi(z);
u1 := psi(u);
t1 := psi(t);
H := sub< G | z1*a^2*b^2, u1*c, t1*a^2*b^2 >;
phi, G1, K := CosetAction(G, H);
Degree(G1);
assert $1 eq 351;
print Order(G1), FactoredOrder(G1);
CompositionFactors(G1);
S := sub< G1 | phi(a), phi(b), phi(c), phi(d) >;
BSGS(S);
S;
SetEchoInput(ei);
