Beyond its activities within the wide field of tourism, Hamburg international is also well known for reliable services in other business segments: So called ethnic charter flights are frequently operated to destinations such as Pristina in Kosovo or other specific destinations in Turkey.
http://www.hamburg-international.de/neu/english/gesellschaft.html
The little above is all I have gleaned so far
Con Air
On 'Charter Flights' involving Foreign National Prisoners
Con Air, may be the name of a popular movie but there is a real 'Con Air', it is for American prisoners being transported around the USA and its full title is,
Justice Prisoner and Alien Transportation System (JPATS)
They also operate international flights and may have been the operators that removed Jamaicans on the 29th December.
Know nothing about them and googling don't help a lot, can't find a press office.
John O