在這篇論文中, 我們研究有限群的共軛類數量與有限群的階之關係. 我們特別著重在共軛類數量的界根據有限群的階. 我們會分別討論有限群以及不同類的有限群共軛類數量的上下界. 最後我們獲得了一個針對對稱群共軛類數量可能的上界.

In this thesis, we study the relation between the number of conjugacy classes of a finite group and its order. In particular, we are interested in the bounds for its order by the number of conjugacy classes. We will discuss the lower bounds and upper bounds for the number of conjugacy classes separately for the finite groups and further various classes of finite groups. At last, we obtain a possible upper bound for the number of conjugacy classes of symmetric groups.

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