The Pedestal is one of two factions among the Geometers. Most of what we know of them comes from explanations by members of the other faction, the Fulcrum, so it's not clear how accurately we understand them. It appears to consist mostly of Urnudians and Troans, with possibly some contingent of Laterrans.
In one Narrative, Erasmas is present when Gan Odru explains that in the Urnudian military, one class of officers were responsible for the strategy, and another for tactics.
The Gan is the chief officer of the strategic side, and nominally in control of the ship; however there is little use for the strategic/tactical divide during the mission of the Daban Urnud and the groups have evolved. Since early in the Daban Urnud's journey, one group has been more inclined to self-preservation; these are the Pedestal, the inheritors of the tactical hierarchy, crowned by the Prag, in the current incarnation a woman named Eshwar. The Pedestal is opposed by the Fulcrum, followers of the Gan, the former strategic arm of the officer corps.
In the Advent, the Fulcrum groups send Lise, spouse of Jules Verne Durand, to Arbre bearing a sample of blood from each of the four worlds the Daban Urnud has visited. However, she is shot with a Pedestal weapon and arrives dead. The landing site is destroyed by a rod on the next orbit of the mother ship, presumably launched by the Pedestal faction.