Is there software to help with group presentation

Question

I wrote a computer program that generates group presentations.

I would like to know the sizes of the resulting groups. I know that this is undecidable.

Are there good heuristic programs that can try to compute the size of a group given by generators and relations?

I am not interested in apporximating the size. Only in determining the exact size, when the software can do it, hopefully often in my cases.

Answer 1

You can use Magma Online Calculator. For instance, the following code:

 F<a, b> := FreeGroup(2);  

 G<x, y>, phi := quo< F | a^2, b^3, (a*b)^4 >;  

 #G

Answer 2

You can use GAP as well. Regarding to what O.L gave you I am posting an example accordingly:

 gap> f:=FreeGroup("a","b");;
 gap> a:=f.1;;    b:=f.2;;
 gap> g:=f/[a^2,b^3,(a*b)^4];
 gap> Elements(g);;
 gap> Size(g)

If you be familiar to use this software, then you'll wish to use it in sleep even!! It is indeed a wonderful and of course a powerful tool.