In a recent preprint [1302.1929](http://arxiv.org/abs/1302.1929) my co-authors and I make use of some results about the character theory of extraspecial groups. These were largely gleaned from haphazard Googling, comments made by people on MO, and playing around by ourselves.


Because the paper is probably going to be read by people in Banach algebras/harmonic analysis rather than by finite group theorists, the referee has requested that we provide references for the following assertions: if $G$ is a group with prime power order where the centre and derived subgroup coincide and have order $p$, for $p$ a prime, then each non-linear irreducible character has degree $p^n$ where $|G|=p^{2n+1}$, and is supported on $Z(G)$.


Now while this does not look hard to prove directly, just using fairly basic character theory, I would like to know if this is written down *explicitly* somewhere where I can cite it. The Wikipedia page for extraspecial groups lists Gorenstein's book on finite groups as a reference, but my library doesn't have a copy.


Can anyone suggest a suitable reference? (I would like to check that no such convenient reference exists before writing out a proof in the paper.)



reference request for character theory of p-extraspecial groups
I'm sure you'll correct me quickly if I'm off the mark, but isn't this proven in the appendix of [Threads Through Group Theory](http://www-stat.stanford.edu/~cgates/PERSI/papers/threads_Diaconis.pdf)? (article by Persi Diaconis, appendix by Marty Isaacs, published in "Character Theory of Finite Groups".)


Quite apart from the proof itself, the context how it ended up in this appendix is quite interesting, as Diaconis writes in the intro:



> 
> Marty Isaacs believes in answering
>  questions. They can come from
>  students, colleagues, or perfect
>  strangers. As long as they seem
>  serious, he usually gives it a try.
>  This paper records the path of a
>  letter that Marty wrote to a stranger
>  (me). It led to more correspondence and a growing set of extensions. All of this work can be traced back to Marty’s letter. [...] We are still meeting, writing, and following the thread together. I am truly thankful.
> 
> 
> 


