Starting in 1600 bc, describe the groups who controlled babylon and how each group or person came to power.

The Babylonians called it the dynasty of Babylon, for, though foreign in origin, it may have had its actual home in that city, which it gratefully and proudly remembered. It lasted for 296 years and saw the greatest glory of the old empire and perhaps the Golden Age of the Semitic race in the ancient world. The names of its monarchs are: Sumu-abi (15 years), Sumu-la-ilu (35), Zabin (14), Apil-Sin (18), Sin-muballit (30); Hammurabi (35), Samsu-iluna (35), Abishua (25), Ammi-titana (25), Ammizaduga (22), Samsu-titana (31). Under the first five kings Babylon was still only the mightiest amongst several rival cities, but the sixth king, Hammurabi, who succeeded in beating down all opposition, obtained absolute rule of Northern and Southern Babylonia and drove out the Elamite invaders. Babylonia henceforward formed but one state and was welded into one empire. There were apparently stormy days before the final triumph of Hammurabi. The second ruler strengthened his capital with large fortifications; the third ruler was apparently in danger of a native pretender or foreign rival called Immeru; only the fourth ruler was definitely styled king; while Hammurabi himself in the beginning of his reign acknowledged the suzerainty of Elam.