Korah did not just challenge Moses. According to the Targum Jonathan, he manufactured a theological argument using the very fabric of his clothing, hid treasure he had looted from Joseph's royal stores in Egypt, and provoked a miracle that had been planned since the six days of creation.
The Targum says Korah "took his robe which was all of hyacinth" and staged a legal demonstration. Moses had taught that fringes should be white with one thread of hyacinth. Korah made garments with fringes entirely of hyacinth—arguing that if one thread of blue makes a garment holy, a garment entirely of blue should need no fringe at all. Two hundred fifty leaders supported him.
Their accusation stung: "All the congregation are holy, and the Lord's Shekinah (the Divine Presence) dwells among them; why should you be magnified over the church of the Lord?" The Targum adds that Moses heard their words "as if every one of them was jealous of his wife, and would have them drink of the trial-water on account of Moses." The comparison to the Sotah ritual is deliberate—they treated Moses like a suspected adulterer of power.
Dathan and Abiram refused to appear before the court. The Targum adds their backstory: these were the men "who had been worthy of death from their youth in Egypt, for they betrayed my secret when I slew the Egyptian." They also "provoked the Lord at the sea" and "at Alush profaned the Sabbath."
Korah brought two treasure chests he had found "among the treasures of Joseph, filled with silver and gold," and used them to turn the people against Moses. Moses then announced the test: "If a mouth for the earth, which has not been made from the beginning, be created now"—the Targum implies this was a brand-new act of creation—"and the earth open her mouth and swallow them, you will understand that these men have provoked the Lord."
The earth split. They descended alive into Sheol. Their last words, as they fell, were: "Righteous is the Lord, and His judgment is truth, and the words of His servant Moses are truth; but we are wicked who have rebelled against him." Then fire consumed the 250 incense-bearers.