Interesting group theory problem

[betty2301]

Homework Statement

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Homework Equations

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The Attempt at a Solution

i can do part a.
can you give me hints on part b and c?

 

[jbunniii]

For (b), you are asked to show that the sizes of these two sets are the same: $\{gag^{-1} | g \in G\}$ and $G / C(a)$. The natural thing to do is to try to find a bijection between the two. There's only one obvious candidate that I can see.