In the afternoon, Harry takes his History of Magic exam. He has a vision of Sirius being tortured in the Department of Mysteries and tries to figure out what to do. After a delay trying to contact Grimmauld Place and being caught by Umbridge (OP32), Harry takes off for the Ministry of Magic Headquarters to find Sirius. Ron, Hermione, Ginny, Neville, and Luna come along (OP33). Snape, meanwhile, sends word to the Order of the Phoenix that the kids have gone (OP37).
The date for this event is taken from the Real World calendar. The Thursday in the third week of June, 1996, was the 20th.