# Converse of congruence condition on Sylow numbers for the prime two

From Groupprops

## Statement

For any odd number , there exists a finite group where the number of 2-Sylow subgroup (?)s of (i.e., the Sylow number (?) for the prime ) equals .

## Proof

`Further information: Dihedral group, subgroup structure of dihedral group`

We take as the dihedral group of degree and order . It is given by the presentation:

.

The two-element subgroup is a 2-Sylow subgroup, and it is a self-normalizing subgroup. It has conjugates, given by , with .