I hope this doesn't sound too negative, but if not a single one of these topics is even mentioned in an outline, I wouldn't have much hope that opening an issue (let alone making a PR) would make a difference.

This would be like asking the Nano developers how they plan to support Emacs-Lisp macros.

In other words, adjusting the title (to prevent wrong expectations) would be more productive than expanding the scope far beyond what the author(s) had in mind.

The problem is that the author of the book and the previous comment are talking about different books with a different scope, because each one has a different idea of what "group theory" means, it depends a lot of your background.

This book is about symmetry and group definitions, but it has no or very little details about generic properties of groups.

The previous comment is about a book that no one has written, that is a coloring book for students of a math major in the university, probably in the 2nd or 3rd year. In this (unwritten) book the idea is to study the general theorems about groups, and in each case give some visual examples to color and apply the theorem.

Only one of those is group theory.

As a mathematician, I agree. But when you talk with people that work in the applications, they usually have weird definitions.

In particular, in this book they don't use $Z_2$ that is the usual notation in math (at least here). They use $C_2$ that is more usual in physics. And for the selection of the groups I guess the author has some interest in crystallography.

Yes the motivation was crystallography and giving a small amount of group theory background was about providing the groundwork for talking about it.