Peralitus is classed as Omnipotent^2 and Omniscient^2 on the Omnipotence Hierarchy and he is the only Supergod in his Beyond Bubble in full health. Despite this, he never actually uses his physical abilities, leaving the horribly deformed and physically impaired Abnull to do everything. One can only wonder why she doesn't like him.
Despite claiming to be the ruler, Peralitus does very little ruling whatsoever. All the important tasks such as stabilizing the Beyond Bubble, caring for Monopolum and Binauris, defending the group from Transcendent Ecosystem creatures and gathering energy are performed by Abnull.
Peralitus instead spends most of his time dreaming of what great achievements he could obtain once he becomes strong enough to exit the Logical Desert and enter the local Cohort. He imagines himself becoming a revered hero and leader of hundreds of Supergods, just as he presumed Barelitil to be. Peralitus seems to hold absolutely no regard for the Supergods he lives with and has implied he would abandon them in a heartbeat to benefit himself.
Outside of dreaming up wild fantasies, Peralitus also spends a considerable amount of time talking to a Barelitil fragment he found inside one of the Beyond Bubble's only Monocosms. This Barelitil fragment speaks very highly of Peralitus and it was its words that first suggested Peralitus may be Barelitil's son. Whenever Peralitus tells this fragment about his incredible 'achievements', it responds by telling Peralitus how proud he is, how competent he has become and what a 'perfect fit' he will be. It was this language that convinced Peralitus that Barelitil intended to appoint him as leader.
Abnull finds the amount of time he spends talking to this Barelitil fragment utterly absurd. In fact, she finds everything about how Peralitus acts utterly absurd. From his pitiful idea that he is somehow the 'leader' to his strange obsession with a heritage he doesn't even know exists to his ludicrous ideas about authority. Peralitus, in return, thinks very lowly of Abnull and is astonished and angered at how much the other Broken Supergods seem to respect her and treat her as the leader. Peralitus would gladly exile her if he actually had the means to, though both Peralitus and Abnull know that Abnull would prevail in a physical fight between the two.
Peralitus is also annoyed by Negatil's constant criticism of him and her more general complaints about 'unjust hierarchies', a concept that is completely alien to Peralitus. Surely, it is the strength of the hierarchy and the being at the top that provides its justice? Peralitus holds less resentment for Negatil than Abnull however, as Negatil's anger is not targeted specifically at Peralitus and most of the other Broken Supergods can also agree that Negatil is obnoxious.
Peralitus appreciates Positev's helpful and encouraging praise of his endeavors and pride in his heritage, and considers Positev to be is "second in command". (A role Positev completely ignores.) However, Peralitus is nonetheless annoyed that Positev seemingly also considers Abnull the leader for all practical purposes.
Peralitus also appreciates Schematus's attempts to decipher the Broken Supergods' past, however like Abnull is annoyed at how he wastes his incredible potential. Although it's likely that Abnull and Peralitus have very different ideas of what Schematus putting his skills to good use looks like. While Abnull believes his amazing intelligence and abilities could be used to support the Broken Supergods, Peralitus believes that Schematus could one day monetize and sell his incredible inventions and ideas across the Cohort, gaining recognition for both Schematus and Peralitus.