In learning a little about group theory I came across computational group theory which lead to this:
https://groupprops.subwiki.org/wiki/Category:Groups_of_a_particular_order
I also saw this:
Turing suggested using his “automatic computing engine” to enumerate the groups of order 720
I'm wondering how one familiarizes oneself with these different groups if there are so many, and more importantly what the practical use cases are in enumerating all these different groups (besides the pure mathematics of it). Most of the computational group theory seems to be about group theory itself, i.e. learning more about group structure and stuff like that. But I'm wondering if there are many applications of knowing about these structures outside of pure group theory, such as with software compilation (like type theory) or anything like that.