Conjugacy classes - two problems.
Hi, I was wondering if I could get some help with these questions?
1.Let G be a non-abelian group of order 21. Show that if m is the number of conjugacy classes of size 3 and n is the number of conjugacy classes of size 7 then 3m+7n = 20. Deduce that m = n = 2.
2. Let G be a group of order p^2 where p is a prime number. Show that all conjugacy classes in G have size 1 or p.
I guess that I need to use The Class Equation or The Orbit-Stabilizer Theorem but I do not know how?
Can anyone help me, please?