GATE 2023 MA – Question 58

Algebra · Groups · 2 marks · Numerical answer

In S₈, σ is the product of a disjoint 4-cycle and 3-cycle. How many permutations are conjugate to σ?

Show answer and explanation

Correct answer: 3360 to 3360

Explanation

Conjugacy is determined by cycle type, here (4,3,1). The class size is 8!/(4¹1!·3¹1!·1¹1!)=40320/12=**3360**.

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