On rational 2-groups and their nilpotency classes

A finite group G is called a rational group if all the generators of every cyclic subgroup of G are conjugate. In this article we discuss about nilpotency class of rational 2-groups and we give an upper bound for nilpotency class of a rational group G of order 2n. Furthermore we show that an irreducible character of a rational 2-group G does not appear as a constituent of character 2 except for = 1G, the principal character of G .