On rational groups with Sylow 2-subgroups of nilpotency class at most 2

A finite group G is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on G and also via nilpotency and nonnilpotency assumption of G .