what is the function of the first assembly?
It was ethnic in nature, and thus were organized on the basis of the early Roman family, or, more specifically, on the basis of the thirty original patrician (aristocratic) clans.
Curiate Assembly
The Curiae were ethnic in nature, and thus were organized on the basis of the early Roman family, or, more specifically, on the basis of the thirty original patrician (aristocratic) clans. 
what was the most powerful lawmaking body in the roman republic Assemblies how many types of assemblies are there? Curiate Assembly, the Centuriate Assembly, and the Tribal Assembly. what is the role of the extraordinary magistrates? The dictator of the extraordinary magistrates had "maius imperium" and total authority to command the state; however, since the dictator generally tried to maintain order, this did not conflict with the responsibilities of the other magistrates, who continued to function during a dictatorship.
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Curiate Assembly [SEP] Introduction
The Curiate Assembly ("comitia curiata") was the principal assembly during the first two decades of the Roman Republic. During these first decades, the people of Rome were organized into thirty units called "Curiae". The Curiae were ethnic in nature, and thus were organized on the basis of the early Roman family, or, more specifically, on the basis of the thirty original patrician (aristocratic) clans. The Curiae formed an assembly for legislative, electoral, and judicial purposes. The Curiate Assembly passed laws, elected Consuls (the only elected magistrates at the time), and tried judicial cases. Consuls always presided over the assembly. While plebeians (commoners) could participate in this assembly, only the patricians (the Roman aristocrats) could vote.