The dihedral groups are both very similar to and very dissimilar from the quaternion groups and the semidihedral groups. Together the dihedral, semidihedral, and quaternion groups form the 2-groups of maximal class, that is those groups of order 2n+1 and nilpotency class n.
The dihedral groups are both very similar to and very dissimilar from the quaternion groups a.nd the semidi,hedra:l groups. Together the dihedral, semidihedral, and quaternion groups form the 2-groups o:f maximal class, that is those groups of order 2n+1 and nilpotency class n.