The Gamma Quadrant represents one-fourth of the Pocket Universe, between the Beta Quadrant and the Delta Quadrant.  The New Shi'ar Imperium is weakest here.  The strongest interplanetary regime in this quadrant is the Systems Commonwealth with it's capital Muscovy located about 45,000 light years from the Warp Barrier and about 455,000 light years from the black hole at the center of the local universe.  The Sontaran Dominion is the second strongest interplanetary government in this quadrant. 

The Gamma Quadrant is on the opposite side of the Pocket Universe from the Alpha Quadrant

Corellia is located in the Gamma Quadrant.