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SymmetricGroup

SymmetricGroup[n]
represents the symmetric group of degree n.
  • The degree n of SymmetricGroup[n] must be a non-negative integer. Degrees 0 and 1 correspond to the trivial or identity group.
  • SymmetricGroup[n] is represented by default as a permutation group on the points .
Number of elements of a symmetric group:
Permutation generators of a symmetric group:
Elements of a permutation representation of a symmetric group:
Number of elements of a symmetric group:
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Permutation generators of a symmetric group:
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Elements of a permutation representation of a symmetric group:
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Symmetric groups of degree 0 or 1 are the trivial group, only containing the identity:
In all other cases the symmetric group of degree n contains n! elements:
Test whether two random permutations generate the symmetric group of degree 100:
Permutations returns the permuted forms of an expression under the elements of a symmetric group:
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