The above commenter is wrong about it being capitalist, but they’re right about there being a ruling class in the USSR. The ruling class was the communist party, the “intelligentsia.” Communist party members pre-selected candidates for all political appointments, and becoming a member of the communist party involved passing through multiple stages of party-administered education and then having your past scrutinized and approved by committees of existing communist party members.
At its’ highest level of membership it never surpassed roughly 3% of the population. That is a politically privileged class that enjoyed better wages, benefits, general living conditions, and political influence than the general population.