Allah is the god of Islam and the Qur'an. Although this god is called by his personal name of Allah, he is generally considerd to be the same god as that of the Christians and Jews, whom the Muslims call "The People of the Book". (Here, "The Book" refers to the first few books of the Old Testemant of The Bible, which all three Faiths have in common. These faiths are also known as the Abrahamic religions, as Abraham is a central figure in all three before the religions supposedly diverged.)
Allah has all the same characteristics of the Christian God. He is omnipotent, omneiscent, omnipresent, and outside of the Qur'an, omnibenevolent.