Oppressor Two was a Skith spaceship that was the successor to the previously destroyed Oppressor One. It was commanded by the Skith General.
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Like the ship's predeccessor, the Oppressor Two contained a portion of a Mindcore that survived on a Skith colony when the Skith home planet was destroyed. The ship was nearly 3 km tall and 300 meters wide.
It carried within a huge Skith army and due to the knowledge acquired from the Doctor it had temporal technology via the Skardis, a crude copy of the Tardis. Which gave it the phase out of time and thereby be invisible to others, but still lacked the ability to actually travel through time.
After the Skith homeworld was obliterated by the Crimson Hand, the Skith used the Opressor Two to track down the Doctor in order to perfect their time travel capabilities in order to combat the Hand. They eventually found the Doctor in Australia, 2010, where it would eventually be destroyed. (COMIC: The Age of Ice)