elements in a finite group with different finite order

Let $\displaystyle a, b$ in a finite group $\displaystyle G$ such that $\displaystyle a \neq b$.

I know $\displaystyle |a|$ and $\displaystyle |b|$ divides $\displaystyle |G|$.

Is there any condition for $\displaystyle |a| \neq |b|$, other than looking at the conjugacy classes?

Re: elements in a finite group with different finite order

For a general finite group? No, I don't know of any general conditions. If you had a specific type of group, then maybe.