The phrase "what class of" is correct and usable in written English.
It is used to ask what type or group something belongs to. For example: "What class of animal is a koala?".
"What class of a name is Pavel, anyway?" he said.
What "class" of people live in your neighborhood?
What class of terrorists should be subject to preventive detention, and for how long?
Were I forced to say to what class of things it belongs I should call it Immense.
All of them require a lot of information, such as where you are leaving from and when, what class of car you want to drive or -- in Amtrak's case -- what class of seat you want.
Then there were the inevitable questions, as society's norms of discourse shifted, about what class of words, if any, to banish.
Their first step will be to sequence the DNA present in my swabbed gunk, in order to identify what classes of organism are generally present.
In the descriptive agenda, more emphasis should be placed on establishing what classes of learning rules actually model learning by multiple humans or animals.
Fifty-one years later, we are still debating what classes of people have the right not to suffer from discrimination.
If any state can determine that a gay marriage is not a valid marriage, it would logically follow that any state should also be able to determine what classes of people can marry one another.
From the first moment when we strategized over what classes of characters to take (I played a fighter, because I'm basic), to coordinating together at the boss battle at the end of our crypt, I knew this game wasn't like the ones I've previously played.
