# Direct Product30

Compute all Sylow subgroups of Dihedral group $D_{12}$ and $S_3\times S_3$
Use direct products to construct groups with some given properties
Basic properties of n-ary direct products of groups
Definition of the n-ary direct product of groups
A quotient by a product is isomorphic to the product of quotients
Symmetric group acts on the n-fold direct product of a group by permuting the factors
Finite direct products are isomorphic up to permutation of the factors
In the direct product of the quaternion group and an elementary abelian 2-group, all subgroups are normal
The direct product of groups with no nonnormal subgroups may have nonnormal subgroups
The Sylow numbers of a direct product are products of the Sylow numbers