[GAP Forum] Presentation and computations

[lopo apelo kosho]

Dear friends; 
I was wondering if you could advice with the following:
I have called the group F= [36,6] throuw presention by generators and relations. 
Now I am forming groups (say, H...) generated by some generators of F.  
The problem is that: 
GAP did not recognize H as subgroup of G.

I do not know how to handle this situation. 

I am attaching a sample part of the GAP session: 

gap> f:=FreeGroup(3);
<free group on the generators [ f1, f2, f3 ]>
gap> a:=f.1;b:=f.2;c:=f.3;
f1
f2
f3
gap> F:=f/[a^3,b^4,c^3,a^b*a,c^a*c^2,c^b*c^2];
<fp group on the generators [ f1, f2, f3 ]>
gap> h:=Group(a*c);
Group([ f1*f3 ])
gap> IsSubgroup(F,h);
false
gap> Order(h);
infinity
gap>


I WOULD BE MOOR THAN GRATEFUL FOR ANY HELP.
Thank you