I really need a hint :/ I have been trying all night to solve 5 through 10 but simply can't get started. And I need to hand in tomorrow
Any hints/advice would be welcome.
1. You confessed that this is a homework assignment. We do not do your homework for you.
2. Your question is ill posed. Who is the underlying field K? characteristic 0, algebraically closed? etc. If K has characteristic p, the whole question is moot since there is only one irreducible representation of a p group.
3. For part 5, the character group of G/G' is isomorphic to G/G', so ??
4. There are no questions 6 through 10.