Kagutsuchi appears as a large draconian creature with fiery wings and a sword through his mouth. He makes sounds akin to dolphins and waves and has several abilities, including shooting fire from his mouth and, in one instance, resurrecting himself (protecting Mai through apparently absorbing her at the same time). Kagutsuchi is presumed to be the most powerful of the Childs.
Kagutsuchi is based on the Japanese legend of Kagutsuchi (カグツチ), a fire god born to the creator deities Izanami-no-Mikoto and Izanagi-no-Mikoto. The legend is narrated in the Kojiki: -
Next they gave birth to the Fire-Burning-Swift-Male-Deity, another name for whom is the Deity Fire-Shining-Prince, and another name is the Deity Fire-Shining-Elder. Through giving birth to this child her august private parts were burnt, and she sickened and lay down (i.e. died).
So then His Augustness the Male-Who-Invites said: Oh! Thine Augustness my lovely younger sister! Oh that I should have exchanged thee for this single child!" And as he crept round her august pillow, and as he crept round her august feet and wept, there was born from his august tears the Deity that dwells at Konomoto near Unewo on Mount Kagu, and whose name is the Crying-Weeping-Female-Deity. So he buried the divinely retired Deity the Female-Who-Invites on Mount Hiba at the boundary of the Land of Idzumo and the Land of Hahaki. Then His Augustness the Male-Who-invites, drawing the ten-grasp sabre 1 that was augustly girded on him,  cut off the head of his child the Deity Shining-Elder.
- Kojiki: Volume I, Sections 6-8 at Sacred Texts dot com