Possible Class equation for a group Determine the possible class equation for a group of order 21?

Until now I have found the following:

$1+3+3+7+7$

$1+1+1+3+3+3+9$

$1+1+1+1+1+1+1+7+7$

$1+1+1+1+1+1+1+1+1+3+3+3+3$

$1+1+1+\cdots +1 \ (21 \ \text{times})$

Is there any way to eliminate the choices from this equation? More importantly, how would we know that this is a complete list (Until now my attempt has just been guess and check after I found possible occurences of 1's) Is there any easier way to determine the class equation?
Hint: the number of 1's is the order of $Z(G)$, the center of $G$. Also, $|G/Z(G)|$ can not be a prime number. And of course $|Z(G)|$ divides the order of $G$. This leaves you with the first and last possibilities. In the last case the group is abelian.
I think $G$ is abelian. So $|Z(G)|=21$. Hence class equation is all of $1$'s.