The Cthulhu is a secondary kingdom set in another planet, it's ruler is Matheus (Matheuzinho),in this
republic there are no rules one can be or do whatever he/she wants, Matheus built this in response to the Purity Act estabilished at Bellmaina. He wasn't there a the time and did not agree with that, as such he can't stand to live at Bellmaina under this act therefore he teleported to a barren planet and built a ginormous kingdom there.
Matheus used to live in a Republic called Mathmaina, a rather small republic set on earth, this peaceful republic was once a great kingdom but in an attempt to stop Belo's army Matheus blew it up destroying 100 soldiers of Bellmaina but still losing his army which he loved like his family, later he was force to join Bellmaina and lived there until the Great War where the Purity act was settled without his consent which led to the events of The Cthulhu Empire.
Inside the Republic
There isn't much inside there, only a huge castle where it's ruler lives and thousands of houses built by him alone where outsiders can come to live in, also there are his Cthulhu servants that are treated well and help maintain everything in order.