is the society the characters live in a classless one? why or why not explain

This society is very much not "classless" because the characters act a certain way based on income. Daisy and Gatsby, as well as Tom and Jordan, feel a certain entitlement based on their wealth which allows them to have anything they want (materially) while living a rather dissolute lifestyle. Tom is very jealous, for example, of Daisy's involvement with Gatsby, yet he has had an affair with Myrtle and feels no moral compunction about that. Myrtle is poor as is her husband; Nick, while not rich or poor, has a more Midwestern set of values which do not go along with the shallow lives that the Buchanans live. Certainly the billboard over the Valley of Ashes symbolizes the levels of society.