F-class is generic for First Class as most airlines that have multiple classes refer to their forward cabins as F - although depending on airline, it could be listed as F,P, or A - each one meaning a different type of first class fare - one could be Full Paid First class, the other could be Discounted Paid First, and the last could be upgraded/award travel First class.

C & J are generic for Business Class, sometimes it's D or Z - depends on the airline & the value of the ticket (free/full-fare/discount fare)

Y is generic for Economy - Y being the highest economy fare on most (if not all) airlines - a Y-class ticket is often fully refundable & often times will allow the purchaser a 1-cabin upgrade if its available.

If you search each board for Fare Class Definition by airline & you should get some results - I know UA & NW have them.

You're getting there!