# Symmetric Group35

Exhibit two Sylow 2-subgroups of Symmetric group $S_5$
Exhibit all of the Sylow 2-subgroups of Symmetric group $S_4$
Compute all Sylow subgroups of Dihedral group $D_{12}$ and $S_3\times S_3$
Classify groups of order 6
The quaternion group is not a subgroup of Symmetric group for any n less than 8
Exhibit quaternion group in Symmetric group via regular representation
Exhibit Dihedral group as a subgroup of Symmetric group via regular representation
Exhibit Sym(3) as a subgroup of Sym(6) via the left regular representation
Exhibit the Klein 4-group as a subgroup of Sym(4) using the left regular representation
Exhibit symmetric group as a subgroup of a general linear group