The Gurren-dan (or Gurren Brigade) was formed by Kamina with the original goal of breaking through the surface from the underground.
The Gurren-dan (or Gurren Brigade) was formed by Kamina with the original goal of breaking through the surface from the underground. When it reached that goal-- at the time its only members were Kamina and Simon --it moved on to a new task: allowing humanity to move to the surface by defeating the beastmen who attempt to destroy and surface dwellers. Eventually that goal was accomplished as well, and the Gurren-dan split up, most of its members becoming a part of the newly-formed government of Kamina City. Then the Anti-Spirals and their program to tear humanity back down appeared, and the Gurren-dan reunited (with some new members) to take on the threat.
Over time, the Gurren-dan took on several different names, and each iteration had different members:
Break through to the surface (episode 1), defeat the beastmen (episodes 2-7).