Sylow number-determined group

Definition
A finite group $$G$$ is said to be Sylow number-determined if given any group $$H$$ such that:


 * The order of $$G$$ is the same as the order of $$H$$
 * The Sylow numbers of $$G$$ are the same as those of $$H$$

Then $$G$$ and $$H$$ must be isomorphic.