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σ₀ = (1,2,3,4)(5,6)(7,8), σ₁ = (1,3,2)(4,5,7)(6,8), σ∞ = (7,6,4,1)(8,5)
Base field: 1 - 2T + 6T^2 - 6T^4
Embedding: 1.094469
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