The Group was operative in the North Galaxy for at least thirty years, under the leadership of Freeza and his family. It's unknown how many races and planets have been destroyed or are under the group iron fist: Frieza alone is shown to be in control of at least 79 planets, and Cooler (noncanon) in control of at least 256, with no mention of how many King Cold owns. 
 
There are hundreds if not thousands of races enslaved, most notably the Saiyans. These races are employed in different ways depending on their strength: groups like the Saiyans are given many freedoms for showing their worth by conquering and destroying planets. Other groups are used to compose elite squads like the Ginyu Force, or to serve as "bodyguards" to the leaders, like Zarbon and Dodoria.

The organization has never been given an official name, and it should be noted that "planet trade organization" is a name used just so there is a term for this group. However, Krillin does refer to the organization's members as belonging to the "planet trade."  
 

Members

Freeza: leader of the group 
 
King Cold: father of Freeza.
 
Cooler: leader at the death of Freeza 
 
Ginyu Force: mercenaries, elite squad, Freeza best henchmen. 
 
Cooler's Armored Squadron: Cooler best henchmen.
 
Zarbon, Dodoria: generals, Freeza personal adjutants.
 
Cui, Vegeta: elite soldiers. 
 
Malaka, Planthorr: medical staff
 
Saiyans Race 
Main allies and contributor of the Organization, later eradicated from space by Freeza, who feared a rebellion.
Named: Nappa, Raditz, Tora, Fasha, Shugesh, Borgos, Bardock, King Vegeta 
 
Arcosian Race 
Creators of the "Attack Balls", primary means of interplanetary travel for all the elite soldier of the group.

Foot Soldiers 
Named: Appule, Orlen, Banan, Sūi, Namole, Blueberry, Raspberry, Abo, Kado. 
  

Known Operations

Occupation of Planet Vegeta
 
Occupation of planet Tazba: by Saiyans forces.
 
Kanassan war: by Bardock Team
 
Invasion of Planet Meat: by Bardock Team
 
Genocide of the Saiyans and destruction of Planet Vegeta: by Freeza and his Army
 
Tritek conflict: mentioned by Nappa
 
Attack on Bun's planet: led by Cui
 
Conquering of Shikk: by Vegeta, Nappa & Raditz, three days war.
 
Destruction of Arlia: by Vegeta and Nappa
 
Battle for Planet Namek: to find the Dragon Balls
 
Attack on Earth: Three times, under Freeza, then Cooler, then Abo & Kado.