According to The Communist Manifesto, would a communist society consist of classes?

According to Marx and Engels, a communist society would
have no classes.  The class struggles that typified all of previous history would end
with the triumph of the proletariat.  After that, there would be no need for classes
because everyone would be equal and no one would be
oppressed.

In The Communist Manifesto,
Marx and Engels state this point quite clearly.  They tell us that (I have added the
bold face)

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When, in the course of
development, class distinctions have disappeared, and all
production has been concentrated in the hands of a vast association of the whole
nation, the public power will lose its political
character.

To them,
political power is the organized power of one class oppressing another class.  During
our time, the proletariat are oppressed by the bourgeoisie and we have class struggle. 
However, once the proletariat wins this struggle, they will not oppress anyoe and so
there would be no politics and no classes.  As the authors tell us, by the time it is
over, the revolution will

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... have swept away the conditions for
the existence of class antagonisms and of classes
generally...

From
this, it is quite clear that Marx and Engels believe that a communist society will be a
classless society.