A group Shiena is in. It's an organization composed of bullied people who aid each other. From how its functions are described, when a bullied person joins, a member of the Collective kills their bullies for them. The bullied person then has to kill the bullies of another bullied person, thus paying it forward, or "avenging" another. However, in the event the bullied person that is supposed to be avenged is killed, another task may be assigned, as is the case with Shiena. Due to the person she was supposed to avenge being killed prematurely by Otoya, Shiena is sent to participate in the Black Class so she can win the wish for the Collective.
In chapter 23, Yuri compares Datura to the Collective, saying the former organization is "not cute." Nio responds in saying the level is incomparable and Datura is more aggressive than the Collective.
In chapter 5 of Koakuma no Riddle, Nio mentions that the Collective is an organization with meager resources.