Sylow subgroups of S3, S4 and A5

The Sylow

2

-subgroups of

S_{3}

are its three transposition subgroups, while its unique Sylow

3

-subgroup is

A_{3}

. The three Sylow

2

-subgroups of

S_{4}

are dihedral groups of order eight and are the normalizers of the three cyclic subgroups generated by inverse pairs of

4

-cycles. The five Sylow

2

-subgroups of

A_{5}

are Klein four-groups, one fixing each letter.

 Ancestors (7)