Baylor’s president, athletic director and head football coach were fired amid the program’s myriad sexual assault allegations. (LM Otero/Associated Press)

A federal lawsuit filed Friday alleged that at least 31 football players at Baylor University committed at least 52 “acts of rape” over four years — including five gang rapes, two of which involved 10 or more players at the same time, some of whom videotaped the rapes on their phones and passed the recordings around to teammates.

The lawsuit, filed by a Virginia woman who alleges that she was gang-raped by two Baylor players in 2013, is the latest fallout in a sexual-violence scandal that has embroiled the Baptist university in Waco, Tex., for more than a year. Baylor’s president, athletic director and head football coach all lost their jobs last year after an independent investigation found that athletic department leadership left women on campus at risk by discouraging victims from reporting assaults and keeping accusations against Bears players quiet.

That previous investigation, conducted by a law firm hired by Baylor’s board of regents, found 19 players accused of domestic or sexual assault by 17 women. Lawyers for the Virginia woman — Elizabeth Doe in the lawsuit — claim to have uncovered evidence of far more sex crimes committed by Baylor players as the program rose to national prominence from 2011 to 2014.

Late Friday night, the school responded with a statement calling the assaults “reprehensible and inexcusable” and noting that school has made “great progress in implementing 105 recommendations to strengthen the safety and security of all students and restore faith in the University.”

John Clune, a Colorado attorney representing Doe, released a statement via email.

“We have been working with Baylor on these football cases since the start of this, and though we have appreciated their efforts to fix the problems, this is one that needed to be filed,” Clune wrote. “As hard as the events at Baylor have been for people to hear, what went on there was much worse than has been reported. We do still appreciate the progress that Baylor has made and know that the school will be a better place when this case is over.”

Baylor athletics officials created a “culture of sexual violence,” the lawsuit alleged, by using the promise of sex to entice top football recruits.

“Do you like white women?” one Baylor assistant asked a recruit from Dallas, the complaint alleged. “Because we have a lot of them at Baylor, and they love football players.”

The Baylor Bruins, the school’s female hostess program, figured prominently into this culture of sexual violence, the complaint alleged. Doe, the plaintiff, was a member of the Bruins in April 2013 when she attended a football party where she became “very intoxicated.” Several hours later, Doe’s roommate returned home and heard “a loud bang and a slapping noise accompanied by hearing a woman’s voice loudly saying ‘no.’ ”

When the boyfriend of Doe’s roommate yelled into Doe’s bedroom, according to the complaint, two Baylor players emerged — Tre’Von Armstead and Shamycheal Chatman — one of whom said Doe was fine. The roommate’s boyfriend looked into the room, however, and “saw Ms. Doe partially unclothed on the floor of the bedroom and [she] said ‘she is not fine.’ ”

Waco Police responded to the scene but did not aggressively investigate the case, and neither did Baylor Police, the lawsuit alleged. Neither Armstead nor Chatman was charged with a crime.

Chatman later transferred to Sam Houston State University. When Baylor commissioned an independent investigation of the incident two years later, the lawsuit stated, the school found Armstead responsible and expelled him.

In an interview in October on “60 Minutes,” Baylor Chief Financial Officer Reagan Ramsower was asked about the 2013 incident.

“There was a police report. I suppose it stayed with the police department,” Ramsower said. “It never came out of the police department. That was a significant failure to respond by our police department; there’s no doubt about it.”