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Class number (English)

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Definition (undergraduate level)

The number of orbits of the conjugacy action of a group G on itself. It is often written h . If O₁, …, O_h are the distinct orbit, and we set n_i=|O_i|=|G:G_{x_i}| for x_i ∈ O_i , then we have the class equation

|G|=n₁+ …+n_h.

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Relations

broader:: (en) Number; (en) PropertyOfAGroup
references:: (en) Orbit

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