Dihedral and dicyclic groups are isoclinic

Statement

Suppose $m\geq 2$ is an integer. Then, the following two groups are isoclinic groups:

1. The dicyclic group of degree $m$ and order $4m$.
2. The dihedral group of degree $2m$ and order $4m$.

Further, if $m$ is odd, the nboth of these are also isoclinic to the dihedral group of degree $m$ and order $2m$.

Particular cases

$m$	$2m$	$4m$	dicyclic group of degree $m$, order $4m$	dihedral group of degree $2m$, order $4m$	If $m$ is odd, dihedral group of degree $m$, order $2m$
2	4	8	quaternion group	dihedral group:D8	--
3	6	12	dicyclic group:Dic12	dihedral group:D12	symmetric group:S3
4	8	16	generalized quaternion group:Q16	dihedral group:D16	--
5	10	20	dicyclic group:Dic20	dihedral group:D20	dihedral group:D10