Given $n,m,p,q$ natural numbers, such that $m,p,q < n.$ Find all natural numbers $r,s,t,a,b,c$ such that $p<r<n, q<a<n, s<m, b<m, t<a, c<r$ and the abelian group with presentation
$$G=\langle x,y,z\mid x^m=y^pz^q, y^r=x^sz^t, z^a=x^by^c\rangle$$
is isomorphic to the cyclic group $\Bbb Z_n$.
I tried for values $r =3, c=1, s=1, t=1, a=4, b=1$ but I don't know how to add all given conditions on GAP and to get final answer
gap> F:=FreeGroup("x","y","z");
<free group on the generators [ x, y, z ]>
gap> x:=F.1; y:=F.2; z:=F.3;
x
y
z
gap> G:=F/[x*y*(y*x)^-1,x*z*(z*x)^-1,y*z*(z*y)^-1,x^23*z^-3*y^-2, y^3*x^-1*z^-1,z^4*y^-1*x^-1];
<fp group on the generators [ x, y, z ]>
gap> Size(G);
231