Element structure of quaternion group

This page discusses the element structure of the quaternion group. Notation for the quaternion group differs somewhat from notation for most groups. The multiplication table that we use throughout to identify elements is given below.



In the table below, the row element is multiplied on the left and the column element on the right.



Conjugacy class structure


Automorphism class structure


Directed power graph
Below is a trimmed version of the directed power graph of the group. There is an arrow from one vertex to another if the latter is the square of the former. We do not draw a loop at the identity element.