File:D16directedpowergraphcollapsed.png

The collapsed directed power graph of dihedral group:D16. Elements that generate the same cyclic subgroup are collapsed together into one node. An edge from one node to another is there when the latter is the square of the former. No loop is drawn at the identity.

The file was created using Graphviz. The generating code was as follows:

digraph G{       rankdir = "BT"; e[label="Identity element"]; agen[label="{a,a^3, a^5,a^7} -- generators of "]; a2gen[label="{a^2,a^6} -- generators of derived subgroup "]; a4[label="a^4, unique non-identity central element"]; x[label="x"]; ax[label="ax"]; a2x[label="a^2x"]; a3x[label="a^3x"]; a4x[label="a^4x"]; a5x[label="a^5x"]; a6x[label="a^6x"]; a7x[label="a^7x"]; agen -> a2gen; a2gen -> a4; a4 -> e;       x -> e;        ax -> e;        a2x -> e;        a3x -> e;        a4x -> e;        a5x -> e;        a6x -> e;        a7x -> e; }