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Math Help - Conjugation classes

  1. #1
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    Conjugation classes

    I want to calculate the conjugation classes of A_4 and prove that A_4 doesn't have subgroups of order 6.

    How can i do? Is there any relationship or implication with Lagrange or Cauchy Theorems?

    Thanks a lot!
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  2. #2
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    Quote Originally Posted by roporte View Post
    I want to calculate the conjugation classes of A_4 and prove that A_4 doesn't have subgroups of order 6.
    Hint: The conjugacy class equation is 1 + 3 + 4 + 4 = 12.

    This means we cannot have a subgroup of order six because it is normal and none of the summand combinations can give us six.
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