Question: The group (mathrm{D}_{3}) in Schoenflies notation (32 in international notation, which is read three-two; see Table 5.1 ) consists of the proper (those not reflections

The group \(\mathrm{D}_{3}\) in Schoenflies notation (32 in international notation, which is read "three-two"; see Table 5.1 ) consists of the proper (those not reflections or inversions) covering operations on an equilateral triangle. Label the vertices of a triangle as

a 3 C 2 b

and show that there are six proper symmetry operations and find the corresponding multiplication table. Show from this that the groups \(\mathrm{D}_{3}\) and \(\mathrm{C}_{3 \mathrm{v}}\) are isomorphic.

a 3 C 2 b

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