Converse of congruence condition for Sylow numbers for the prime two

Statement

Suppose $m$ is an odd natural number. Then, there exists a finite group where the number of $2$-Sylow subgroups is $m$.

Related facts

• Converse of congruence condition for prime power Sylow numbers
• Congruence condition for Sylow numbers

Proof

Proof idea

We take the dihedral group of order $2m$.