Conjugacy class size set-determined group

Definition
A finite group $$G$$ is said to be conjugacy class size set-determined if whenever $$H$$ is a group such that:


 * $$G$$ and $$H$$ have the same order (i.e. cardinality)
 * The set of sizes of conjugacy classes of $$G$$ is the same as that of $$H$$

then $$H$$ and $$G$$ are isomorphic groups.