  We continue studying properties of semisimple Hopf algebras $H$ over
algebraically closed fields of characteristic 0 resulting from their
generalized character tables. We show that the generalized character table of
$H$ reflect normal left coideal subalgebras of $H.$ These are the Hopf
analogues of normal subgroups in the sense that they arise from Hopf quotients.
We apply these ideas to prove Hopf analogues of known results in group theory.
Among the rest we prove that columns of the character table are orthogonal and
that all entries are algebraic integers. We analyze `semi kernels' and their
relations to the character table. We prove a full analogue of the
Burnside-Brauer theorem for almost cocommutative $H.$ We also prove the Hopf
algebras analogue of the following (Burnside) theorem: If G is a non-abelian
simple group then $\{1\}$ is the only conjugacy class of G which has prime
power order.
