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How to find (describe) all groups which have 3 conjugacy classes?

Thanks in advance!

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    $|Z(G)| \leq 3$. So there is not any p-Group with $p \not= 3$. I'll try to obtain more.2012-12-26
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    It's good to post the work you've done up until now, whenever you post a question.2012-12-26
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    I would guess that this is very difficult (probably impossible) for infinite groups. There are many infinite groups with just two conjugacy classes. Perhaps the exercise was just about finite groups?2012-12-26
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    http://math.stackexchange.com/questions/52350/finite-groups-with-exactly-n-conjugacy-classes-n-2-3?rq=12012-12-26

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