As pointed out by Mikko Korhonen in this answer, Özdem Çelik proved (in 1976 here) that a finite group whose Sylow subgroups are cyclic (called a Z-group) is determined by its character table.

Now there are many results and conjectures relating character tables and Sylow subgroups (see this paper of Gabriel Navarro), the most famous being perhaps the McKay conjecture.

This leads to wonder whether Çelik's theorem can be extended:

Question 1: Is a finite group determined by its character table iff its Sylow subgroups are so?

If not, let us include the class types, in other words:

Question 2: Is a finite group not in a Brauer pair iff its Sylow subgroups are so?