size of centralizer

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Computing with Magma David A. Craven
MSE
Find all permutations that commute with ω=(1 9 7 10 12 2 5)(4 11)(3 6 8) in S₁₂
In Magma CAS:

1. G := Sym(12);
2. omega := G!(1,9,7,10,12,2,5)(4,11)(3,6,8);
3. #Centralizer(G, omega);

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Output:
42