Nadezhda Tolokonnikova (left) and Maria Alyokhina, two members of the dissident Russian punk group "Pussy Riot" (CNN)

SOCHI, Russia (CNN) -- After several tumultuous days that included police detentions, interrogations and a public flogging from angry Cossacks, the dissident punk band Pussy Riot struck back.

The controversial Russian musicians released an angry music video on Thursday slamming Russian President Vladimir Putin's crackdown on free speech and political expression. They also took aim at the Sochi Olympics' whopping $50 billion price tag.

Titled "Putin Will Teach You To Love Your Country," the music video included footage filmed Wednesday of Cossacks -- modern-day descendants of 19th-century horsemen who pushed the boundaries of the Russian empire -- flogging the women moments after they began lip-synching their song next to a large "Sochi 2014" sign in the Olympic city.

"The goal is to show what it's like to be a political activist in Olympic Sochi," Pussy Riot member Maria Tolokonnikova told CNN.

The band invited foreign media to a news conference at a hotel in Sochi for the unveiling of the new video on Thursday. But upon arrival, a bizarre scene unfolded.

An employee at the hotel informed journalists a conference room would not be available.

Outside, uniformed police and security officers in civilian clothes awaited the arrival of the band, alongside several dozen journalists.

Also waiting, at least five male university students accompanied by a man dressed in a giant chicken suit.

When four women from the band walked up, arms locked, the university students pulled out raw chickens and began chanting "We like sex with chicken" in mangled English.

The students and costumed chicken then attempted to disrupt the makeshift news conference given by the women in the park outside the hotel.

"We don't understand their behavior and that's why we're protesting," said 23-year old Sergei Barashov, one of the members of the anti-Pussy Riot demonstrators. Barashov said he was afraid the punk band would desecrate a Russian Orthodox cathedral that had been recently constructed on the outskirts of Sochi's Olympic Park.

Pussy Riot rocketed to international fame after the provocative musicians stormed into a Moscow cathedral in 2012 and performed an expletive-ridden song denouncing Putin.

Tolokonnikova and her band mate Maria Alekhina were sent to prison on charges of hooliganism and inciting religious hatred. Russian authorities released the pair shortly before the start of the Olympics in Sochi along with several other high-profile critics of the Russian government.

Prison failed to silence the two young women. They immediately went back to denouncing the Kremlin, as well as conditions inmates endure in Russian prisons.

In the new song, Pussy Riot sings about the "constitution being lynched," government pressure against Russia's lone independent TV station and of last week's sentencing of environmentalist Evgeny Vitishko to a penal colony for three years.

Vitishko, an outspoken critic who drew attention to environmental damage caused by the massive construction around the Sochi Olympics, has gone on hunger strike, according to his defense attorney.

On Tuesday, police in Sochi detained members of Pussy Riot, along with at least seven human rights activists and journalists in connection with the investigation into an alleged theft at the band's hotel. Hours later, all charges were dropped and the detainees were released from the police station, located just a few minutes' drive from the Olympic Torch.

The detention, as well as the televised attack by the Cossacks, have put the International Olympic Committee on the defensive.

"Personally I found the video and pictures very unsettling," said Mark Adams, a spokesman for the IOC.

"It happened in Sochi, but it was unrelated to an Olympic venue and was not, as far as I know, a demonstration against the Olympics," Adams said on Thursday.

In its new song, Pussy Riot also takes aim at a quirk of bathroom interior designing in Sochi that became a social media joke in the Olympic Village and around the world.

"They took gay pride to the washroom," the band sings. "And made a two-seat toilet a priority."