The most common and most likely answer to this crossword clue is the 6 letter word CASTES
I've seen this crossword clue in Financial Times
C
A
S
T
E
S
More clues leading to the result CASTES
Buddy explains!
The straight part
We know that "Classes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case classes = castes.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CASTES mean?
CASTES noun- Any of the hereditary social classes and subclasses of South Asian societies.
- A separate and fixed order or class of persons in society who chiefly associate with each other.
- A class of polymorphous eusocial insects of a particular size and function within a colony.