A familial generation is defined as the average time between a mother's first offspring and her daughter's first offspring. Each generation, therefore, lasts 25 years. So since the first novel is set 2,000 years after the starship had left Earth, 2000 / 25 = 80. Hence, all of the younger characters in the novel, like Alcyone, Caroline, Joey, Irene, Razia, etc. were all born in the Centauri Princess' 80th generation.
In Part 2, The True Price of Immortality, a special reference is made to "The Thirty-Niners" on page 159. This is a reference to the 39th generation who had mined a large diamond found buried on a passing ice world, which was used to build the much renowned Diamond Bridge across Eridanus.