What is so special about Klein 4-group? This is my first course in abstract algebra and so far I am only learning about groups. So is there anyone who can explain to me why Klein 4-group is so special that it warrants a category of its own. Please explain as clearly as possible as I am still new to algebra. Thanks

The smallest anything is often of interest.  One reason is that it lets us think about why it works when nothing smaller does.  In this case, it hints that prime groups are always cyclic, and might provide a motivation to prove Lagrange's theorem, which is extremely useful.  
