Question

Example:

Let D6 be the group of symmetries of the regular hexagon (see Exercise 6.2.15). 7. Determine the orders of the elements of De, and count the elements of each order. Decide which ones are a. conjugate (make a table summarizing your results, as in the text) What are the normal subgroups of D6? b. order of element geometric description #(conjugates) identity 180° rotations preserving edges 180° rotations preserving faces 1 1 2 2 3 3 +120° rotations 8 +90° rotations 4 6

Answer 1

7. { . D& 3 1, r r AY NOw C1) 2 2 (r)3 2 9 (sA) O order of ele ment theye 2 conjugaey clamn NOw, the 4 s

(b The normal Subgroups One <5e u u> 7