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In Chapter Twelve of Philosopher's Stone the following sentence appears:

"And you're not sitting with the prefects today, either," said George. "Christmas is a time for family."

It appears from this sentence that the rest of the year (i.e. besides Christmas) the prefects sit separately from other students. I am trying to figure out what this is referring to.

I know that there is a special prefect carriage on the Hogwarts Express. From Philosopher's Stone Chapter Six:

"Can't stay long, Mother," he said. "I'm up front, the prefects have got two compartments to themselves —"

And from Order of the Phoenix Chapter Ten:

"We’re — well — Ron and I are supposed to go into the prefect carriage,” Hermione said awkwardly.

And from Half-Blood Prince Chapter Seven:

"We can't, Harry," said Hermione, looking apologetic. "Ron and I've got to go to the prefects' carriage first and then patrol the corridors for a bit.

However, George is clearly not referring to the Hogwarts Express. They don't go on the Hogwarts Express that day, and they have not been on it for nearly four months at this point. George is obviously referring to some more recent occurrences of Percy sitting with the prefects as opposed to his family.

I also know that there is a prefect bathroom. From Goblet of Fire Chapter Twenty-Three:

"Tell you what," Cedric said, "use the prefects' bathroom.

And from Half-Blood Prince Chapter Six:

"That gives you equal status with prefects!" cried Hermione happily. "You can use our special bathroom now and everything!"

But it is also pretty clear that George is not talking about which bathroom Percy uses.

So what is he talking about? What else is there where prefects sit separately from other students? I would have assumed that it might be referring to sitting in the common room, or sitting in the Great Hall, but as far as I know there is never mention of a special seating area for prefects in either of those locations. And if we are to assume that it means that the prefects simply unofficially sat together, there are other occasions where we see Percy sitting with the others both in the Great Hall, and in the common room. From Philosopher's Stone Chapter Seven:

On Harry's other side, Percy Weasley and Hermione were talking about lessons

From Chamber of Secrets Chapter Nine:

Harry, Ron, and Hermione chose seats as far as possible from Percy in the common room that night.

(Implying that otherwise, prefects and regular students sat intermixed.)

From Chamber of Secrets Chapter Fourteen:

Percy Weasley was sitting in a chair behind Lee, but for once he didn't seem keen to make his views heard. He was looking pale and stunned.

From Chamber of Secrets Chapter Sixteen:

"If you've finished eating, I'll take that seat, Ginny. I'm starving, I've only just come off patrol duty."

Ginny jumped up as though her chair had just been electrified, gave Percy a fleeting, frightened look, and scampered away.

From Prisoner of Azkaban Chapter Eleven:

Ron and Hermione watched Harry nervously all through dinner, not daring to talk about what they'd overheard, because Percy was sitting close by them.

And, of course, once Ron and Hermione became prefects they continued to always sit with Harry in the Great Hall and the common room.

So what phenomenon involving Percy sitting with the prefects was George referring to?

George is talking about Christmas dinner.

The house prefects would normally all sit together at regular mealtimes throughout the year, so George is telling Percy that he should sit with family and not friends for Christmas.

It's well known that Rowling modelled Hogwarts on a stereotypical British boarding school (with the houses and sports teams, etc). Some schools have rules that segregate prefects from non-prefects for things like mealtimes. Even if such a rule is not in place, students would normally sit with their peers and contemporaries, rather than their siblings.

No, the prefects aren't segregated. Percy sat with other prefects because he was big-headed.

There's no evidence that there were any separate seating arrangements for prefects in the Great Hall or in lessons, as there was on the Hogwarts Express. Prefects can sit with whoever they want. The most compelling evidence for this is that Ron and Hermione continue sitting with Harry (and others) after they are made prefects, throughout Order of the Phoenix and Half-Blood Prince.

“Morning,” Harry said brightly to Ron and Hermione, joining them at the Gryffindor table in the Great Hall.
_{(Order of the Phoenix, Chapter 14, Percy and Padfoot).}

When at long last the bell rang, Harry was first out of the dungeon and had already started his lunch by the time Ron and Hermione joined him in the Great Hall.
_{(Order of the Phoenix, Chapter 12, Professor Umbridge).}

As the quotes in the question demonstrate, they reluctantly followed prior convention by sitting away from Harry on the train. That they didn't do this throughout the year shows that there was no such convention in the school itself.

George's comment can best be understood as relating exclusively to Percy rather than to prefects as a whole. Percy was seemingly in the habit of sitting with fellow-prefects. However, this wasn't something that he did without exception. He sits next to first-years like Harry and Hermione during the Sorting Ceremony.

Percy the Prefect got up and shook his hand vigorously, while the Weasley twins yelled, “We got Potter! We got Potter!”.
_{(Philosopher's Stone, Chapter 7, The Sorting Hat).}

Nevertheless, he did make a habit of sitting alongside other prefects on other occasions.

Percy could be heard telling the other prefects, “My brother, you know! My youngest brother! Got past McGonagall’s giant chess set!”
_{(Philosopher's Stone, Chapter 17, The Man With Two Faces).}

In my view, this was a byproduct of Percy's deep-seated ambition and his desire to curry favour with people of influence. Percy valued the status that came with being a prefect and saw it as a pathway to greater things.

...and in a tiny junk shop full of broken wands, lopsided brass scales, and old cloaks covered in potion stains they found Percy, deeply immersed in a small and deeply boring book called Prefects Who Gained Power.

“A study of Hogwarts Prefects and their later careers,” Ron read
aloud off the back cover. “That sounds fascinating...”

“Go away,” Percy snapped.

"’Course, he’s very ambitious, Percy, he’s got it all planned out...He wants to be Minister of Magic...” Ron told Harry and Hermione in an undertone as they left Percy to it.
_{(Chamber of Secrets, Chapter 4, At Flourish and Blotts).}

This probably explains why Percy was in the habit of sitting with other prefects - when this wasn't required by any rule. George is saying that he should give up this practice for Christmas Day in order to sit with his family. He's saying that, even if Percy wants to sit separately from them at other times in the year, that he should at least sit with them at Christmas in order to prioritise family.

The prefects didn't always sit separately. They had the luxury of sitting separately and had many other privileges because they earned it, but they weren't forced to. Percy just always sat with the prefects because he was snobby and it was his way to brag that he was a prefect.