The T-Rogorans were a species native to the Gamma Quadrant. During the 16th century, they conquered a race of farmers known as the Skrreeans. The T-Rogorans killed most of the Skrreean leaders, and forced the rest of the population to work as laborers and servants.
At some point before 2370, the T-Rogorans were invaded and conquered by the Dominion, allowing the Skrreeans to escape. (DS9: "Sanctuary")
The T-Rogorans were also referred to as "Tirogorans" in the episode script.
It's unclear how long the Skrreeans had been looking for the wormhole, and thus when exactly the T-Rogorans were conquered.
According to the Star Trek: Star Charts, on pages 70 and 74, the T-Rogoran were from the T-Rogoran system. This was a trinary star system. Primary was a Class F star. It had a magnitude of +1, which was 100 times brighter than Sol. The stellar companions were Class M and Class G stars. T-Rogoran was a M-class planet. The official name for the planetary government was T-Rogoran Prime, and this government was annexed by the Dominion in 2370. The dominant species were the T-Rogoran and the humanoid Skrreea. There was no information on the population of the T-Rogoran. The T-Rogoran were warp-capable in 1570.