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Results tagged with conjugacy-classes
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user 92209
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Finite groups with lots of conjugacy classes, but only small abelian normal subgroups?
Let $G$ be an extraspecial group of order $p^{2n+1}$. Then
$$
cp(G)=\frac{p^{2n}+p-1}{p^{2n+1}}=\frac1p+\frac{p-1}{p^{2n+1}}.
$$
All maximal abelian subgroups have index $p^n$ in $G$. Hence, the answe …
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