How to find just one permutation in s8

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SUMMARY

The discussion focuses on finding a single permutation of order 15 in the symmetric group S8. A permutation of the form (abc)(defgh) has an order of 15, and there are a total of 896 permutations of this order within S8. The calculation for the number of permutations is derived from the factorial of 8 divided by the product of 3 and 5. The user seeks clarification on how to identify one specific permutation among these 896 options.

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  • Understanding of symmetric groups, specifically S8
  • Knowledge of permutation order and cycle notation
  • Familiarity with factorial calculations
  • Basic combinatorial principles
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  • Research how to construct permutations in symmetric groups
  • Learn about cycle decomposition in permutations
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Mathematicians, combinatorial theorists, and students studying group theory or permutations who need to understand the structure and identification of specific permutations in symmetric groups.

Charles007
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Hello, can anyone tell me how to find order 15 in S8.

I only know. Permutation (abc)(defgh) have order 15.

Next, I would think about 8*7*6*5*4*3*2*1 = 13440

Number of permutations, for order 15 in s8. would be

8*7*6*5*4*3*2*1 / 3*5 = 896.

There are 896 permutation of order 15 in s8.

But how to find just one permutation in s8?
 
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