Pillar of fire
A pillar of fire was the most common teleportation method used by the 456. (TV: Children of Earth: Day Three, Children of Earth: Day Five)
Overview
When the pillar of fire was used to teleport from a location in space, presumably some form of cloaked spaceship, it streaked out of the sky directly down at its target. A hole was burned in the surrounding clouds which closed once the pillar of fire had passed. The pillar of fire could enter buildings, resulting in them shaking, but otherwise causing no visible damage otherwise despite "burning" through at least the roof. The pillar of fire had no effect on the gases in specially-built tank it deposited its occupant into. The space-to-ground transition appeared to be an extended event with the fire still streaking down for several moments after the apex of the pillar entered its destination. (TV: Children of Earth: Day Three)
When reversed so that it went from ground into space, the pillar of fire immediately appeared around the target and streaked upwards back into the sky. As before, a hole opened in the clouds for the pillar of fire to pass through, but the passage caused the surrounding clouds to burn away once it was gone, an effect not seen in the space-to-ground transition. The ground-to-space transition had a shorter duration as well, lasting mere seconds rather than over a minute. The transition took the entire contents of the tank, including the gases that had been put in to act as a breathable atmosphere for the 456. (TV: Children of Earth: Day Five)
History
Upon their arrival on Earth in 2009, the 456 caused every child in the world to point at Thames House, their destination. As the children pointed, the 456 ambassador teleported into the specially-built tank in Thames House using a great pillar of fire. Seen across London, the pillar of fire was covered in news reports about people's panic over the ongoing crisis. (TV: Children of Earth: Day Three)
After Captain Jack Harkness attacked the 456 with the signal they used to kill Clem McDonald, the 456 ambassador appeared to violently explode. Instantly following the ambassador's apparent death, another pillar of fire removed the entire contents of the Thames House tank and sent them streaking back into space, ending the crisis but leaving the human race unable to confirm if the ambassador had been killed. (TV: Children of Earth: Day Five)
