Consider the elements σ1 = (152)(34) and σ2 = (163)(45) in S6. Calculate an element τ ∈ S6, written as a product of disjoint cycles so that σ2 = τσ1τ-1. I know from the answers that τ=(56234) and τ-1=(65432), I just don't know how they find these answers, so if able please explain step by step in detail. Thank you in advance.

Consider the elements σ1 = (152)(34) and σ2 = (163)(45) in S6. Calculate an element τ ∈ S6, written as a product of disjoint cycles so that σ2 = τσ1τ-1. I know from the answers that τ=(56234) and τ-1=(65432), I just don't know how they find these answers, so if able please explain step by step in detail. Thank you in advance.

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Question

Consider the elements σ1 = (152)(34) and σ2 = (163)(45) in S₆. Calculate an element
τ ∈ S₆, written as a product of disjoint cycles so that σ2 = τσ1τ^-1.

I know from the answers that τ=(56234) and τ^-1=(65432), I just don't know how they find these answers, so if able please explain step by step in detail. Thank you in advance.

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