Hi guys, I've been set this question and I'm a bit stuck.
Find which pairs of the following groups are isomorphic:
(i) the dihedral group D6 of symmetries of a regular hexagon
(ii) Z6
(iii) Z12
(iv) the group of rotations of a regular hexagon
(v) the group of rotations of a regular tetrahedron.
I've worked out that Z6 and the rotations of a hexagon are isomorphic from comparing the Cayley tables (and they're both cyclic of order 6) but I'm not sure if there's anymore.
I know that the rotations of a tetrahedron has order 12 but I'm not sure if it's cyclic and I wouldn't know where to start with a Cayley table.
Thanks in advance!