The class system in A Brave New World, labels classes by the first five letters of the Greek alphabet. People are bred and placed into each class according to intelligence and beauty. The alphas are the most intelligent and beautiful, and are therefore bred for professional and managerial professions, while the least intelligent epsilons can only perform menial labor tasks. Nobody questions their position in society, nobody desires to switch classes, nobody considers life to be fair or unfair.
The idea is a satire of course. The Controllers created this system in order to eliminate class conflict. Of course what is really happening is the complete elimination of free thinking.
The "utopian" society of Brave New World is set up in a pyramid caste system structure. There are two, three, five, or six castes/classes, depending on how you look at the novel. Within the Alpha class, for example, there are classes (plus or minus). Bernard, for example, is an Alpha minus: he's shorter than Henry, an Alpha plus. Later, Bernard will be threatened with outcast status (exile in Iceland).
In the Utopia, there are obviously five castes, but if you include the Savages, there are six:
- Alphas - very small percentage of the population at the very top of the triangle who hold most status and power. They are the top of the elite class.
- Betas - small percentage of the population near the top of the triangle who hold secondary status. They are the bottom of the elite class.
- Gammas - middle of the triangle in terms of population, status, and power. They are the highest of the support/worker castes.
- Deltas - near bottom of the triangle; high population. They are the middle of the support/worker castes.
- Epsilons - highest percentage of the population who hold the least amount of status and power. They are powerless. Their only function is to work to support the other, higher castes.
- Savages (Outcasts) - the non-genetically engineered; those born naturally outside of the utopia. They are interned at the Savage Reservation in New Mexico.
THREE CASTES / CLASSES:
- Upper class: These are the World Controllers, the DHC, and most Alpha pluses
- Middle class: These are primarily the Betas, but also some of the Alpha minuses and even a few of the Gammas
- Lower class: These are most of the Gammas and all of the Deltas, Epsilons, and Savages.
TWO CASTES / CLASSES:
- The Elite: the Alphas and the Betas
- The Workers: the Gammas, Deltas, Epsilons
If I were writing a paper or even a short response about this, I would really focus on the idea that this society does not have classes.
I agree with the first answer that there are all these different ways that you can split up the society. However, I would not call any of these things classes. To me, class is only relevant when there is class conflict. As the second answer points out, the society has been engineered so that there is no class conflict. The classes are all happy with their lot in life because that's how they've been made.
So there is this elaborate system, but it's not a class system in my opinion. It's more like they are different species.