Cthulhu (クトゥルフ Kutourufu?) is a fictional cosmic entity appearing in H.P. Lovecraft's short story "The Call of Cthulhu", part of a shared fictional universe named after the entity; the Cthulhu Mythos.
In Toaru Majutsu no Index, Cthulhu is a being which can be brought into existence through certain spells based off the Cthulhu Mythos.
Cthulhu is described as a giant being hundreds of meters tall, possessing a mixture of octopean, anthropoid and draconian features.
Like the other evil gods of the Cthulhu Mythos, Cthulhu is a being which no human can handle, however like them it gains its role and terror from the story it represents. Spells which use Cthulhu cannot ignore this story aspect - as such it's terror only lasts during the 'story' and it can't do anything once that story comes to an end, until the next story begins.
In The Call of Cthulhu, Cthulhu was trapped in the sunken city of R'lyeh and emerged after the sunken city came to the surface. As such, the entity is an inescapable aspect of any spells that involve the summoning of R'lyeh and it will emerge during such a ceremony.
Necessarius Special Admission Test SSEditNecronomicon, Arlands Darkstreet of Dusk Waiting to Awaken carries out a ceremony on an ocean salvage terminal in the Strait of Dover with conditions made to mimic those of the underwater city of R'lyeh.
As the ceremony progresses, Cthulhu begins to appear as a mental presence, overwhelming Itsuwa. However the Amakusa manage to use the story aspect of the Cthulhu Mythos and make the evil god leave before it could gain a physical form by interfering with the twisted landscape which had been used to deceive it.