#eg consider computing equivariant (ie Bredon) homology of a point for that dihedral group. I dont think anyone has done this(!)

[locally-normal]

Don't worry, if you spend a while considering a space with a group action up to homotopy you can conclude that no one really understands group actions.

Seeing that the Weyl group W_G(H) := normalizer of H in G / H is the set of equivariant (ie group action preserving) maps from G/H to G/H is pretty neat though, would recommend, it's a fun exercise. G/H here is the set of H cosets of G, with a G action given by g . H = gH. (Remember that for G/H to be a group H must be normal, but you can always write a set of cosets G/H).

I did that one a while ago and then recently had to remind myself and do it for the case G=O(2) and H=Z/2 generated by a map with determinant -1, ie a flip. Good stuff.

Finally understanding group actions and all it took was looking at this picture (from Michael Artin’s Algebra)