If you want to talk shit about mai fieldu, you are free to do so, but be aware that representation theory is pretty much just group theory using different means.
Now group theory is pretty good in applications, because it captures the fundamental notion of symmetry. Symmetries are extremely useful in simplifying very complex things. The best example I can think of is physics, where the symmetry of space or time yields very nice and useful invariants, such as energy or momentum by Noether's theorem. More complex symmetries also occur in particle physics. Besides that there is the whole field of cryptography, which is basically one huge application of group theory. So I consider my point about group theory proven.
Now the problem with pure group theory is that research progress is extremely slow and has not really yielded many useful results lately. Sure, there is the classification of simple groups, but the proof is extremely contrived and in itself not very useful, because most group theoretic properties do not really have a reduction theorem that lets you reduce the problem to simple groups and group extensions.
Now representation theory offers exactly that and even allows to substantially simplify some proofs for purely group theoretic theorems, such as Burnside's pq theorem. Fixing a field seems to allow a much better way to reduce the complexity of investigating certain groups. Group representations is a very rich field and has some very nice results.
tl;dr: group theory too hard, representation theory easier
