The Khômiss was a Binet that had 12 undisclosed participants every year.
They intentionally projected the idea of a semi scary and cool secret society/cult/Fascist/Gestapo/non-racist Ku Klux Klan-like organization
Khômiss members would wear a face cover whenever they would go out "on duty", notably to break a student's door with a fire axe when some student had fucked up particularly bad.
The Khômiss had an ambivalent character: while on one hand they would punish students that they felt had fucked up, they were actually semi approved by the school's head.
And conversely, they could also play pranks on the school head, e.g. vandalizing their office with funny objects if they had made some decision that was particularly unpopular to the students. This also likely with tacit approval, and as a way to be a "cool independent organization that also represents the students".
As such, the Khômiss aimed to be a sort of a "conscience" of the cohort, punishing the evil deeds of either side.
They were apparently unfortunately disbanded by the school in 2013 it seems, just after Ciro Santilli left. They took some poor student out by car and left him more than 1km outsie of the school for some reason. But he had a cell phone and walked came back, so doesn't feel that serious. Likely the political correctness of the times just caught up with them.
Figure 1. The logo of the Khômiss. Source.
Figure 2. Low resolution image of Khômiss members standing on top of a roof in Paris. Source. They are wearing their official unmasked clothing in that photo. It appears that ex-Khômiss are allowed to reveal their identities from this. The one with a French military cap is the their leader, and is known as the "GénéK" in their jargon.