Let $G$ be a group s.t. $|G|\geq 3$.
Is there any example of $G$ such that number of the normal subgroups is equal to number of the conjugacy classes?
2026-04-01 14:24:55.1775053495
Is there any group in which number of the normal subgroups is equal to number of the conjugacy classes?
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With $G=S_3$, there are three normal subgroups (namely $\{e\}$, $A_3$, $S_3$) and three conjugacy classes (namely $\{e\}$, $\{(12),(13),(23)\}$, and $\{(123),(132)\}$).