He eventually gave up on that and used "Noldor", a term he'd been kicking around for a while in various contexts. That's much more comfortable, but he kept using "gnome" way longer than seemed reasonable.
What do you mean by "high-class" here? Do you mean they're Calaquendi, or are you saying they were esteemed greater than the other houses?
The Vanyar (also Calaquendi) were probably "higher" than the Gnomes, but they were never seen in Middle-earth again. We learn very little about them, and I don't think they're even passingly alluded to in The Lord of the Rings. Some of the Gnomes returned to Middle-earth, so they outrank everybody who never left.
He renamed the Gnomes "Noldor", and most of The Silmarillion is about them (and the Men who hung out with them). They came back to Middle-earth to retrieve the Silmarils, which had been stolen by Morgoth (the Big Bad of the First Age, and Sauron's boss).
Galadriel is one of the very few we meet who were part of that go-and-return trip. It was a nasty business, and that's why her turning down the Ring and returning to the West was such a big deal. (Though she wasn't part of the story at the time they were called Gnomes, and she had to be retroactively inserted into it. He never did finalize that story, and we're left with a conflicting mess of unpublished stories.)
All children of Feanor (the main contingent of the Noldor) are dead by the end if the first age).
The few Noldor that outranked Galadriel left by the end if the second era after the last alliance of men and elves and the war with Sauron.
[1] which I think is also half Teleri.
This makes it sound like most Noldor were children of Feanor or that most of them followed Feanor and his sons, but that's not the case. The sons of Feanor and their followers were first to Middle-Earth - is that what you mean by 'main'? It's stated a few times that there weren't as many of them. The Noldor were an entire people, and most were neither Feanor's children nor followers of his children. (They were technically all under Feanor as high king of the Noldor for a time, though.) This is from the Silmarillion, describing their travel through Valinor on the way to Middle-Earth:
> Fëanor and his following were in the van, but the greater host came behind under Fingolfin; and he marched against his wisdom, because Fingon his son so urged him
and then after those who didn't follow Feanor cross to Middle-Earth in the north, many die, but there are still more of them:
> for the agony of those that endured the crossing of the Ice had been great, and Fingolfin held the sons the accomplices of their father. Then there was peril of strife between the hosts; but grievous as were their losses upon the road, the people of Fingolfin and of Finrod son of Finarfin were still more numerous than the followers of Fëanor,
Yes, Galadriel's father, Finarfin, was of the Noldor, and he married Earwen of Alqualonde, the daughter of Olwe, who was one of the two leaders of the Teleri.
So his gnomes were not of the, aehm, garden variety.