g := PolycyclicGroup <s,c,x1,x2,x3,y1,y2,y3,w1,w2,z1,z2,z3|
     s^3,c^7,
     c^s=c^4,
     x1^2=y1,x2^2=y2,x3^2=y3,y1^2=z1,y2^2=z2,y3^2=z3,w1^2,w2^2,z1^2,z2^2,z3^2,
     x2^x1=x2*y2*y3*w1*w2*z1*z2*z3,x3^x1=x3*y1*y2*w1*z2,
     x3^x2=x3*y1*w1*w2*z1*z3,
     y2^x1=y2*w1,y3^x1=y3*w2,
     y2^y1=y2*z3,y3^y1=y3*z2*z3,y3^y2=y3*z1*z2,
     y1^x2=y1*w1*w2*z1*z2*z3,y3^x2=y3*w1*z1,
     y1^x3=y1*w1*z1*z2,y2^x3=y2*w1*w2*z2,
     w1^x1=w1*z3,w2^x1=w2*z2*z3,w1^x2=w1*z1*z2,w2^x2=w2*z1*z2*z3,
     w1^x3=w1*z2*z3,w2^x3=w2*z1*z3,
     x1^c=x1*x2*x3*w1*z1,x2^c=x1*x3*y1*y3*w1*z3,x3^c=x1,
     y1^c=y1*y2*z1*z2,y2^c=y2*y3*z2*z3,y3^c=y1,
     w1^c=w1*z2,w2^c=w2*z1*z2*z3,
     z1^c=z1*z2*z3,z2^c=z1*z3,z3^c=z1,
     x1^s=x1*z3,x2^s=x2*x3*y2*y3*w1*w2*z1*z3,x3^s=x2,
     y2^s=y1*y2*y3,y3^s=y2,w1^s=w1*w2,w2^s=w1,z2^s=z2*z3,z3^s=z2
     >;