# Permutation11

Classify groups of order 6
Subgroups of finite index force the existence of normal subgroups of bounded index
The quaternion group is not a subgroup of Symmetric group for any n less than 8
Compute a permutation representation of Dihedral group of order 8
Compute permutation representations of Dihedral group of order 8
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
Compute the orbits, cycle decompositions, and stabilizers of some given group actions of Sym(3)
A group action is faithful precisely when the kernel of the corresponding permutation representation is trivial
The kernel of a group action is precisely the kernel of the induced permutation representation