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I have some questions about this post:

Faithful irreducible representations of cyclic and dihedral groups over finite fields

I would appreciate it really if someone could help me.

1) Do I get with this method really just the $\underline{faithful}$ irreducible representations? So there can be still other irreducible representation which are not faithful (and have dimension $>1$). Can one count them too?

2) If an irreducible representation of degree e of the normal subgroup $⟨z⟩$ extends to the whole group, this does mean, that it still has the same degree $e$, not?

3) Where do the condition

" it extends, if $z^{-1}=z^{p^d}$ for some $d$ with $1≤d≤e$ "

come from. Is it a theorem in Clifford's theory or just a conclusion, which you can see, if you work long enough with it? My book does not mention this.

[edit] Could a member please accept the answer. I cannot comment on my own post or accept the answer after 60min.

1 Answers 1