GATE 2021 MA – Question 54
G has order 5⁴ and its center has 5² elements. Find the number of conjugacy classes.
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Correct answer: 145 to 145
Explanation
For noncentral g, its centralizer contains Z(G) and ⟨g⟩, so its order is at least 5³. It is proper because g is not central, hence exactly 5³; the conjugacy class has size 5. There are 25 singleton central classes and (625−25)/5=120 others. Total **145**.