1. Let G=D8=('r,slr8=.92=1, T8=ST_1> (whose lattice appear in section 2.5 of your book), and let 6 = G / (r4) be the quotient of G by the normal subgroup generated by 7'4 (this subgroup is the center of G, hence is normal). Recall that for each 9 E G, we denote by g the class of g in E = G/N, i.e. g = 9N. (a) Show that the order of E is 8. (b) Write the elements of E in the form garb for some integers a and b. (c) Find the order of each element of 6 (written under the form of (bl)- (d) Write each of the following elements of E in the form saw"b for some integers a, b as in (b): , srQs, sLrls'r