  The universality class of a phase transition is often determined by factors
like dimensionality and inherent symmetry. We study the magnetic dipole system
in which the ground-state symmetry and the underlying lattice structure are
coupled to each other in an intricate way. A two-dimensional (2D)
square-lattice system of magnetic dipoles undergoes an order-disorder phase
transition belonging to the 2D Ising universality class. According to Prakash
and Henley [Phys. Rev. B {\bf 42}, 6572 (1990)], this can be related to the
fourfold-symmetric ground states which suggests a similarity to the four-state
clock model. Provided that this type of symmetry connection holds true, the
magnetic dipoles on a honeycomb lattice, which possess sixfold-symmetric ground
states, should exhibit a Kosterlitz-Thouless transition in accordance with the
six-state clock model. This is verified through numerical simulations in the
present investigation. However, it is pointed out that this symmetry argument
does not always apply, which suggests that factors other than symmetry can be
decisive for the universality class of the magnetic dipole system.
