Turks

Department of Public Safety or General Affairs also known as the Turks. They do kidnapping and assassinations (to put it negatively); they also go on missions to check places out or to completely destroy places (Gelnika and Benora). The Turks don't consist of four members at a time it seems. There is Tseng, Reno and Rude the male members of the group. Then Elena and Cissnei, the females. However, Elena is in Final Fantasy VII along with the males and Cissnei is there in Crisis Core. The Turks also recruit members for SOLDIER.

Final Fantasy VII
The Turks antagonized Cloud and his group. They were always one step ahead of him and there to delay his progress. However, there are a few times you can see the Turks on their days off and they DON'T work on their days off. They don't do more work than needed. Elena is actually promoted to the Turks in the game after Reno sustains a bad injury.

There is a time when you get to work with the Turks, though they are not playable and will not join the party. It’s in Wutai and you must have gotten optional character Yuffie. While it doesn’t add a lot to the story, you do get to learn a little about the Turks.

Crisis Core
The Turks (actually Tseng and Cissnei) helped Zack through his missions they best they could. Tseng, current leader of the Turks was probably considered as one of Zack's friends too. He even joked with him about getting paid more because he was a Turk. Cissnei also helped Zack through his days and gave him information. Reno and Rude on the other hand told him to get out of Turk jurisdiction. But later did everything they could for him.

Dirge of Cerberus
It’s a little different here. Vincent himself is an ex-Turk and the only one that appears in the game. You view flashbacks of Vincent’s and in them it’s when he was Turk working in Nibelheim with Hojo and Lucrecia.