# Applications of computation on very large groups

I have been studying computational group theory and I am reading and trying to implement these algorithms. But what that is actually bothering me is, what is the practical advantage of computing all properties of extremely large groups, moreover it is a hard problem?

It might give birth to new algorithms but does it solve any problem specific to group theory or other branches affected by it?

• I recently proved a theorem for which the smallest example of one of the cases had order $37,646,400$. We had to computationally verify its existence. – Alexander Gruber Jun 1 '13 at 16:00