This structure (the + singular countable noun) can be used to generalize but is mainly used with animals, plants, things and even certain groups of people.
1. The computer has changed the way we do business.
2. The mountain lion is a member of the Felidae family.
3. The average American speaks two languages.
Normally uncountable nouns are not used in this way and even countable nouns which are abstract and represent concepts rather than things which are tangible cannot be used in this way.
In conclusion, 'the business class' would be incorrect, at least in my opinion.