class equation of order $10$ Is it a class equation of order $10$


$10=1+1+1+2+5$.


As far as I know for being a class equation each member on RHS has to divide $10$ and should have at least one $1$ on RHS, which is the case. So I think it is a valid class equation.Is it correct?

This cannot be a class equation of a group of order 10 because the $1's$ in the class equation correspond to all those elements which lie in the center $Z(G)$ of the group. But $Z(G)$ is a subgroup, so by Lagrange it's order (which in this case will be $3$) must divide $|G|=10$. This is a contradiction.
