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So the Class Skills in Grand Order and a bit different. Mcjon's theory is that any passive skill is included as a "Class Skill." So let's say you have an Assassin, and it has Magic Resistance. Normally that Magic Resistance would be a Personal Skill, but here, it's a Class Skill.

Furthermore, stuff like Divinity is passive in this game, therefore, it is a Class Skill.

Therefore, it's not really possible for me to go over every single Class Skill, but here are the one's that I have encounter.
The higher the rank the greater the effect. Generally.

Magic Resistance 対魔力
EX: Increases one's resistance against debuffs.
A: Increases one's resistance against debuffs.
B: Increases one's resistance against debuffs.
C: Slightly increases one's resistance against debuffs.
D: Slightly increases one's resistance against debuffs.

Riding 騎乗
A++: Increases Quick card power.
A+: Increases Quick card power
B: Increases Quick card power
C: Slightly increases Quick card power

Independent Action 単独行動
B: Increases the power of critical attacks.
C: Slightly increases the power of critical attacks.

Mad Enhancement 狂化
EX: Increase Buster card power.
B: Increases Buster card power.
C: Slightly increases Buster card power.

Territory Creation 陣地作成
B: Increases Arts card power.
C+: Slightly increases Arts card power.

Divinity 神性
A: Gains the status "damage plus." (increases damage)
B: Gains the status "damage plus." (increases damage)
C: Gains the status "damage plus." (increases damage)
D: Gains the status "damage plus." (increases damage)
E -: Gains the status "damage plus." (increases damage)

Presence Concealment 気配遮断
A+: Increases one's star generation chance.
B: Increases one's star generation chance.

Goddesses Divine Core
EX: Gains the status "damage plus." & Increases one's resistance against debuffs.

Item Creation 道具作成
B: Increases debuff success rate.

If you have a Class Skill you want translated. Put it in the comments.
Yeah.