What is the main governmental building in Mexico?
The Palacio Nacional, where the president works. The other one would be the Palacio Legislativo de San Lazaro, where the congress sessions.
Rome had many classes of people and none of them could be considered the main "group". You could loosely say that the two main groups of the Roman republic were the citizens and the non-citizens. If you are asking about the governmental groups in the senate, they were the populists and the optimates.