Dihedral and dicyclic groups are isoclinic

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Statement

Suppose m \ge 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