From other thread, me:
That could be right, yeah - off screen he might have phoned ahead.
Regarding the showers though, I'm pretty sure there were actual showers located near to the arrival station; they would be sent left or right by the doctor on charge (one being Mengele), those fit to work would go to Auschwitz 1 and become slave labourers (again), and would often be showered and disinfected to kill lice. The infirm, weak, young and elderly would be sent the other way, to Birkenau, and would be gassed.
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I really didn't think it was three weeks - from the film, it seems like the arrive at night, shower, next morning rollcall, schindler arrives and talks to Hess, they leave - i.e. ~18 hours, not 3 weeks! that's surprised me.