Homework 4. Due Tue. March 7

(1) Let G be the group of 3 by 3 upper triangular matrices with entries in a finite field F_q
with 1 on diagonal. Show that there are exactly $q^2$ homomorphisms from G to C^*.
Show that there are exactly (q-1) irreducible representations of G of dimension q (up to isomorphism).
Each of these is induced by a one dimensional representation of a commutative subgroup of G of order q^2.
Compute the character of each irreducible representation of G.