Question

What is the class equation of the dicyclic group of order 12?

A) 1 + 1 + 1 + 1 + 2 + 6
B) 1 + 1 + 2 + 4 + 4
C) 1 + 1 + 1 + 3 + 6
D) 1 + 2 + 4 + 5

Answer 1

The class equation of the dicyclic group of order 12 is represented as the sum of the sizes of its conjugacy classes, which is C) 1 + 1 + 1 + 3 + 6.

Step-by-step explanation:

The class equation of a group is the sum of the sizes of the conjugacy classes of the group. In the case of the dicyclic group of order 12, also known as the dicyclic quaternion group or quaternion group, the class equation can typically be represented in the form of 1 + the sizes of the conjugacy classes other than the identity element. Given the options, the correct answer is C) 1 + 1 + 1 + 3 + 6. This is because, in a group such as the dicyclic group, there is always the conjugacy class of the identity element which contains only itself (thus, '1'), and the other numbers represent the sizes of the other conjugacy classes.