# Group theory

1. Apr 29, 2014

### tableshark

Can one set up a multiplication table for the symmetry group C3V of the equilateral
triangle.
Then show that it is identical to that of the permutation group P3.

I need some clarification....

What about a matrix representation (2x2) for these groups?
→ Here was thinking to use Cartesian coordinate
system in the xy plane, with origin at the center of the triangle.

2. Apr 29, 2014

### Zondrina

The symmetry group of the equilateral triangle is indeed isomorphic to the dihedral group of order six (degree three) $D_3$.
It is also isomorphic to $SL(2, 2)$ I believe.