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Conjugacy Class Problem

  1. Dec 1, 2008 #1
    1. The problem statement, all variables and given/known data
    If a group has order 20 has 4 conjugacy classes, it must have a trivial centre. True or False?

    2. Relevant equations
    The Class Equation

    3. The attempt at a solution
    I believed the answer to be false with this following counterexample:
    20 = lZ(G)l + (20/4 + 20/4 + 20/5 + 20/5) => order of Z(G) = 2 => the centre is non-trivial.
    where 5, 5, 4, 4 is the size of the 4 conjugate classes respectively

    Any feedback on my reasoning and any flaws are very much appreciated
  2. jcsd
  3. Dec 2, 2008 #2


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    Science Advisor
    Homework Helper

    You haven't demonstrated that such a group exists.
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