“School of No” Principal Marcella Sills finally dragged herself into class on time Monday — sauntering through the doors at 7:30 a.m. in a bid to look good for investigators probing her failing and dilapidated PS 106.

“She hasn’t shown up that early in six or seven years,” a source said of the fur-clad boss of the Far Rockaway, Queens, school.

Sills appeared to be scrambling like a failing student at finals time to put on a show for the city Department of Education probers who showed up following a series of Post exposés.

PS 106 earned its “School of No” moniker because, numerous school sources say, it has no gym, no art classes, kindergarten trailers that smell like animal urine and no reading, writing or math books for the rigorous Common Core curriculum.

Despite the squalor, Sills still forces parents — many of whom live below the poverty line — to cough up more than $200 to attend a bizarre, end-of-year prom in which fifth-graders must dress up like brides and grooms.

Also, sources say Sills frequently fails to attend work.

But on Monday, outraged insiders said she got to school early and staged a rare art class for visitors — and even managed to buy books at the last minute.

It’s not clear how well the principal’s last-minute whitewashing worked — but hours after the inspection the DOE’s new head issued a statement saying her office would be keeping a close eye on the school.

“There is significant room for organizational improvement,” Schools Chancellor Carmen Fariña said. “But [Deputy Chancellor Dorita Gibson reported] that classrooms are orderly, teachers are dedicated, and students are learning. Going forward, I will have field staff at the school weekly to make sure those organizational changes occur.”

A school source said that during the visit, Sills looked “happy, like she doesn’t think there are any problems.”

After the school day ended, she left the building with her lawyer.

Dressed in a fur coat, sunglasses, a revealing short skirt and funky fur boots she looked as if she were headed to a nightclub as she climbed into her shiny red BMW X3 — which goes for a base price of $40,000 — and drove off.

“My client has no comment at this time,” her lawyer said.

PS 106’s terrible conditions drew a response from City Hall.

“The allegations in the paper were deeply troubling, and we’re not going to see our children not get the finest education,” Mayor de Blasio said. “Every school has to provide the best possible education.

So we’re going to take this investigation very seriously and then make decisions based on that.”

Additional reporting by Yoav Gonenand Bob Fredericks