finding normal subgroups of a dihedral group whose character table is given

Question

my question is about character theory.

for example i have a character table of the dihedral group D12

which has 6 irreducible characters.so the character table is a

6*6 matrix.i also know all these (36 values) components in the

table.i need to find all the normal subgroups in the group

D12 by using the character table.where shall i start?

what are the steps to do that?

thanks for your help...

Answer 1

Hint: each normal subgroup of a group $G$ is the intersection of the kernels of some of the irreducible characters of $G$.