# Conjugacy Classes and Group Order

1. The problem statement, all variables and given/known data
Is there a proof that the number of elements in a conjugacy class of a group has to divide the order of the group?
Everyone seems to cite it left and right but I've not seen a proof of it anywhere.

2. Relevant equations

3. The attempt at a solution
I'm guessing Langrange's Theorem may come into play but since conjugacy classes themselves aren't subgroups I'm not sure how.

Related Calculus and Beyond Homework News on Phys.org

#### matt grime

Homework Helper
It is a trivial* consequence of the orbit-stabilizer theorem, or the class equation if you want to be fancy.

If G is a finite group acting on a set X, then |G|=|Orb(x)||Stab(x)|. Let X be G, and let the action be conjugation.

* Trivial in the sense of an immediate and obvious corollary, not something that is unimportant and easy.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving