Let $P$ be a special $p$-group $p^{n+m}$. So $P$ will have $p^m$ linear characters. How do one describe (or determine) the other ordinary irreducible characters of $P$ and will they be all faithful? How many ordinary irreducible characters will $P$ have in total. Also, what can we say about the orders of elements in the conjugacy classes of $P$  ? I am familiar with the case when $P=p^{1+2k}$ is an extra-special $p$-group, then $P$ will have $p^{2k}$ linear characters and $p-1$ faithful ordinary characters of degree $p^k$.

Let $P$ be a special $p$-group $p^{n+m}$. So $P$ will have $p^m$ linear characters. How does one describe (or determine) the other ordinary irreducible characters of $P$ and will they all be faithful? How many ordinary irreducible characters will $P$ have in total. Also, what can we say about the orders of elements in the conjugacy classes of $P$? I am familiar with the case when $P=p^{1+2k}$ is an extra-special $p$-group, then $P$ will have $p^{2k}$ linear characters and $p-1$ faithful ordinary characters of degree $p^k$.