I agree they are considered a denomination under the Pentecostal belief system. They are a large denomination with a loose network of 140 groups of over 300,00 churches worldwide. There is only one group in the USA-- AoG USA. This group has a 16 set doctrine:
ag.org/top/beliefs/statement_of_fundamental_truths/sft_full.cfm
The AoG is a loose affiliation, and AoG USA does not own the AoG congregations within the USA.
I like to refer to AoG as ana-baptist Charismatics. But simply put they believe in Salvation through being born again, which means that a person enters a AoG service and during a service accept the Lord Jesus Christ as their personal lord and Savior, a minister lays hands on or near this member who then may be slain by the power of the Holy Spirit and born again (with or without being slain).
Personal means all graces and forgiveness is between the member and God. The emphasis is on showing evidence of this relationship with Jesus through ones inward and outward actions and deeds. Thus a person maintains a relationship through attendance in a congregation and through their own personal belief. There are no sacraments in AoG but they do have communion and baptism and marriage which are in essence not considered to be the Grace of God. Rather to receive God’s Grace a person is Baptized in the Holy Spirit through fire (no one is set on fire and there is no real fire in church). In essence a person feels God Grace and receives a baptism to spread gods ministry through personal witness. Early evidence of this Baptism is the ability to speak in spiritual tongues. There is no written documentation of being born again in spirit or in Baptism in the Holy Spirit but many AoG members write this date down or remember it.
AoG tends to be described as experiential and I tend to feel they are very active in both commitment and activity. They have strong pro life activity. And they have a strong faith formation, youth ministry, and Royal Ranger program.
Because ones must constantly relate to Jesus on a personal level for repentance and their actions, they must essentially spread evidence. AoG members believe that Salvation is a singular event but can be repeated as a sign of evidence which means once saved a person is always saved.
AoG doctrine does not add to or remove any part of the KJV Bible, meaning there are no additional books in the Bible and the Revelation of God is considered to be complete. But they do believe the experience of God is ongoing and can be manifested by God’s Grace in the form of speaking in spiritual tongues, actual tongues, prophecy, spiritual discernment, miracles, healing others, mind reading, dictating future events, being a prophet, levitation, turning objects into new objects, and even being spiritually glued to an object but they do not believe that a person will necessarily experience all of these events. Care should be exercised that one cannot control or command the Holy Spirit but would rather be a tool of the Holy Spirit for a short or long period of time now or at a much later time.
AoG can be a unique experience and quite moving both emotionally and spiritually.