Conjugacy Classes in Finite Groups

Question

Given an integer $n\geq 1$, it is known that there are only finitely many finite groups with exactly $n$ conjugacy classes.

Question: For $n\geq 3$, does there exists a finite non-abelian group, with exactly $n$ conjugacy classes?

Steve shouldn't that be 2n-6? – Nicky Hekster Sep 27 '12 at 08:42 — Nicky Hekster, Sep 27 '12 at 08:42

score 3 · Accepted Answer · answered Sep 27 '12 at 08:45

3

For $k$ even the number of conjugacy classes of the dihedral group $D_k$ of order $2k$ is $(k+6)/2$. Hence take $k=2n-6$. If $n=3$, then take $S_3$,

answered Sep 27 '12 at 08:45

Nicky Hekster

1 Answers1