I have searched a lot about applications of finite groups in computer science. Most of the results include:
- Finite fields or groups of numbers coprime to $n$ which are widely used in cryptography and coding theory
- Permutations (symmetric group)
- Ring of matrices over an arbitrary field
But group theory is much more enormous and broader than these groups and includes many exotic enormous groups. I wonder if there are some applications of other groups in computer science. Specifically, I would appreciate if you mention some other finite (or at least finitely generated) groups (not semigroups or monoids) with their applications.
Example) for instance, optimal solving of a Rubik's cube is a computationally-intensive problem (which is called God's algorithm). Another example I want to see is something like monster group or some other finite simple groups.