What is the main fundamental characteristic of the Islamic society?
Islamic Society is a broad term. There is a significant difference between Muslim Society in Turkey, to Islamic Society in Iran or Saudi Arabia. Cultural differences and the influence of secular society changes how strictly Islam is adopted. However, Islamic Society should be run to strict adherence to the Koran and the teachings of Mohammed the prophet. Dress of men and women should be modest, drugs and alcohol strictly prohibited. There may be strict censorship of television and music and people should be encouraged to fast during Ramadan, pray five times a day and give to the poor. Certain foods, such as pork, are banned and meat should be killed in a certain fashion and is then considered 'Halal' or permitted food. In strict Islamic societies women and men will be educated separately and women may find themselves unable to drive or hold certain occupations. Certainly any dating is discouraged as women should not be going out with a man who is not a near relative or their husband.
An Islamic Society is a 'Theocracy'. This means that the government is run by God, or 'religious government' (American is a 'Democracy', meaning 'Government') An Islamic society is based on Sharia Law. These were the laws based on the writing by The Prophet Mohammed. Sharia is "based on the Qur'an (the religious text of Islam), hadith (sayings and doings of Muhammad and his companions), Ijma (consensus), Qiyas (reasoning by analogy)
In an Islamic system, Politicians are Mullahs and Imams (Religious men). They make all the decisions for the people. They are not elected. The people cannot control their government. God controls the government and the government controls the people.
Saudi Arabia is an Islamic Theocracy, although many muslims feel that the rulers in Saudi Arabia are corrupt and not genuinely interested in performing the will of Allah.
In the end, the problem with theocracies is that God is not a 'real' president. He doesn't take decisions or answer questions. So Islamic Society is run by unelected, old, religious men, who tend to be either corrupt or very strict.