The Fellowship of the Holy Fallout has been suggested as the name of the religious congregation of telepathic mutant humans who lived beneath the ruins of New York City and worshipped in St. Patrick's Cathedral in the latter half of the 40th century.
The mutants' name for their own society was never indicated in Beneath the Planet of the Apes or in the script, but their leader, Mendez XXVI, prays during one of his sermons, "May the Blessings of the Bomb Almighty, and the Fellowship of the Holy Fallout, descend upon us all. This day and forever more."
Marvel Comics' adaptation of the film identified the mutants as The Children of the Bomb.
See Also: Mutants (Beneath the Planet of the Apes)