the primes dividing 6! are 2,3, and 5 (7 is too big).
the prime factorization of 6! = 720 is: (2^{4})(3^{2})(5).
the sylow 2-subgroups are all of order 16.
the sylow 3-subgroups are all of order 9.
the sylow 5-subgroups are all of order 5.
Question:
What are the orders of the Sylow p-subgroups of the symmetric group ?
Give the possible orders of each Sylow p-subgroup of .
(N.B. If there are many possible orders, then give at least four).
Can anyone help me to understand what is meant by the above question please?
So far i understand that is the symmetric group of degree 6.
that is the symmetric group on { }
and i think that the order is given by .
where do i go from there?
the primes dividing 6! are 2,3, and 5 (7 is too big).
the prime factorization of 6! = 720 is: (2^{4})(3^{2})(5).
the sylow 2-subgroups are all of order 16.
the sylow 3-subgroups are all of order 9.
the sylow 5-subgroups are all of order 5.