[GAP Forum] Problem with computing

[Яков Кононов]

 Hello!

I want to compute the abelianization
of the kernel of the map F->G,
where F is finitely presented group
with generators  a_1, ..., a_10 and relations
a_1^2=...=a_10^2=e, a_1*a_2*a_3*a_4*a_5=a_6*a_7*a_8*a_9*a_10=e,
G is abelian group (Z/2)^4 with basis e_1,...,e_4.
The map is given by images
a_1->e_1,
a_2->e_2,
a_3->e_3,
a_4->e_4,
a_5->e_1*e_2*e*3*e_4,
a_6->e_2*e_3*e_4,
a_7->e_1*e_3*e_4,
a_8->e_1*e_3,
a_9->e_2*e_4,
a_10->e_3*e_4.

 I realize it by the following code:

f:=FreeGroup(10);
F:=f/[f.1^2,f.2^2,f.3^2,f.4^2,f.5^2,f.6^2,f.7^2,f.8^2,f.9^f,f.10^2,f.1*f.2*f.3*f.4*f.5,f.6*f.8*f.8*f.9*f.10];
G:=Group((1,2),(3,4),(5,6),(7,8));
hom:=GroupHomomorphismByImages(F,G,[F.1,F.2,F.3,F.4,F.5,F.6,F.7,F.8,F.9,F.10],[(1,2),(3,4),(5,6),(7,8),(1,2)(3,4)(5,6)(7,8),(3,4)(5,6)(7,8),(1,2)(5,6)(7,8),(1,2)(5,6),(3,4)(7,8),(5,6)(7,8)]);
iso:=IsomorphismFpGroup(Kernel(hom));
h:=Range(iso);
comm:=CommutatorFactorGroup(h);
Order(comm);
 

But it says, that the order is infinity, but it is
obviously impossible, because it is finitely
generated subgroup by elements of order
2.

Thank you,
Yakov Kononov.