4947.sagews

F:=FreeGroup("a","s");

<free group on the generators [ a, s ]>

a:=F.1;s:=F.2;

a s

Rel:=[a^3,s^7,s^a*s^-4];

[ a^3, s^7, a^-1*s*a*s^-4 ]

G:=F/Rel;

<fp group on the generators [ a, s ]>

Size(G);

21

Ff:=FreeGroup(6);

<free group on the generators [ f1, f2, f3, f4, f5, f6 ]>

a1:=Ff.1;s1:=Ff.2;a2:=Ff.3;s2:=Ff.4;a3:=Ff.5;s3:=Ff.6;

f1 f2 f3 f4 f5 f6

Rele:=[a1^3,s1^7,s1^a1*s1^-4,a2^3,s2^7,s2^a2*s2^-4,a3^3,s3^7,s3^a3*s3^-4,a1*s1*a2,a2*s2*a3, a3*s3*a1^-1];

G:=Ff/Rele;

<fp group on the generators [ f1, f2, f3, f4, f5, f6 ]>

C:=DerivedSubgroup(G);

Group(<fp, no generators known>)

Size(G/C);

3

D:=DerivedSubgroup(C);

Group(<fp, no generators known>)

Size(C/D);

7

H:=DerivedSubgroup(D);

Group([ f4, f6^-1*f2^-1, f1*f4*f1^-1, f2*f6^-1*f2^-2, f2^-2*f3^-1*f1^-1 ])

hom:=IsomorphismFpGroup(H);

[ <[ [ 3, 1 ] ]|f1*f4*f1^-1>, <[ [ 4, -2, 4, -1, 4, -1 ] ]|f2^ 2*f6*f2*f6*f2*f6*f2*f6*f2^-1> ] -> [ F1, F2 ]

h:=Range(hom);

<fp group on the generators [ F1, F2 ]>

RelatorsOfFpGroup(h);

[ F1^7, F2^7, F1*F2*F1^-1*F2*F1*F2*F1^-1*F2*F1^2*F2^-3*F1, F2*F1^-1*F2*F1^-1*F2*F1^-1*F2*F1^-1*F2*F1^-1*F2*F1^-1*F2*F1^-1, F1^-1*F2^-3*F1*F2^-3*F1^-2*F2*F1^-3*F2*F1^-1, F1^-1*F2*F1^-1*F2^-2*F1*F2^-2*F1^-1*F2^-2*F1*F2^-2*F1^-1*F2*F1^-1, F1*F2^-1*F1*F2^-1*F1^2*F2^-1*F1*F2^-1*F1^2*F2^-3*F1*F2^-3*F1, F1^-1*F2*F1*F2*F1^-1*F2*F1^-1*F2^2*F1*F2^-1*F1*F2^-1*F1*F2^-1*F1*F2^2*F1^ -1*F2, F1^2*F2^-1*F1*F2^-3*F1*F2^-3*F1*F2^-1*F1*F2^-3*F1*F2^-3*F1*F2^-1*F1 , F2^-3*F1*F2^-3*F1*F2^-3*F1*F2^-3*F1*F2^-3*F1*F2^-3*F1*F2^-3*F1 ]