The Study of Groups

The study of groups has gone from something rather simple and then blossomed into very complicated ideas nowadays I'm guessing. So a lot of it starts with finite groups That is Can you figure out What are the possible group structures you can put on a finite set? Like if I say There's a group and it has five elements in itcan you write down the multiple occasion table for these five elements? Mm, and it's going to look like a little Sudoku because Everything has an inverse so there should be one of each element in every row and one of each in every column But this composition Has its own little structure, which is if you do three things It shouldn't matter which two