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maximal Maximal set of non commuting elements in a conjugacy class of $S_8$

Thanks for any comments

Can some onesomeone calculate by computer or prove the subset of maximal order of paiwisepairwise non commuting elements in the set of conjugacy class containing $(123)(45)$ in $S_8$?

I mean a subset of conjugacy class containing $(123)(45)$ of maximal order all of its elements do not commute pairwisely.

maximal non commuting elements in a conjugacy class of $S_8$

Thanks for any comments

Can some one calculate by computer or prove the subset of maximal order of paiwise non commuting elements in the set of conjugacy class containing $(123)(45)$ in $S_8$?

I mean a subset of conjugacy class containing $(123)(45)$ of maximal order all of its elements do not commute pairwisely.

Maximal set of non commuting elements in a conjugacy class of $S_8$

Can someone calculate by computer or prove the subset of maximal order of pairwise non commuting elements in the set of conjugacy class containing $(123)(45)$ in $S_8$?

I mean a subset of conjugacy class containing $(123)(45)$ of maximal order all of its elements do not commute pairwisely.

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maximal non commuting elements in a conjugacy class of $S_8$

Thanks for any comments

Can some one calculate by computer or prove the subset of maximal order of paiwise non commuting elements in the set of conjugacy class containing $(123)(45)$ in $S_8$?

I mean a subset of conjugacy class containing $(123)(45)$ of maximal order all of its elements do not commute pairwisely.