You get 1 point each for a 50+ relationship with each of the four members of the rep group, and another point for having 100 with the king of that group. You get 1 point for giving the king the group trophy, and 1 for getting to level 10 in the preferred skill. You get 1 point for having a negative relationship with the enemy king, and 2 points for completing the rep mission.
You can LOSE points for living in the group's hated district (there is no favorite district for a group, just an UNfavorite one). You can also lose points for having a roommate from the enemy group.
Streeties: King Darius, Crystal, janitor Kris Thistle, mechanic Ewan Watahmee; hate Richies and Sim Quarter, like Body skill. Trophy is in the graveyard.
Nerdies: Queen Polly Nomial, inventor Sue Pirnova, Dr. Max Moore, journalist Lincoln Broadstreet; hate Artsies and Sim Quarter, like Logic skill. Trophy is near the carnival.
Richies: King Luthor Bigbucks, Lily Gates, Lottie Cash, lifeguard Misty Waters; hate Streeties and Urbania. Trophy is in the 2nd floor of the Glasstown Megamall.
Artsies: Queen Roxie Moxie, saxophonist Cannonball Coleman, theater owner Theresa Bullhorn, Prichard Locksley; hate Nerdies and Glasstown, like Creativity skill. Trophy is behind double SimEating plants in Bayou.