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Math Help - Non-abelian groups of order p^2 q

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    Non-abelian groups of order p^2 q

    If |G| = p^2 q for two distinct primes p, q, then is G necessarily abelian? Are there any non-abelian groups of order p^2 q?
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    Quote Originally Posted by prettyboy View Post
    If |G| = p^2 q for two distinct primes p, q, then is G necessarily abelian? Are there any non-abelian groups of order p^2 q?
    of course! for example A_4 is non-abelian and its order is 12=2^2 \times 3. another example is the dihedral group of order 12. however, if G has order p^2q, \ p <q, and  p \nmid q-1, then G is abelian.
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    refer book

    Refer the book ion abstract algebra by Dummit and Foote. a large behaviour of these groups are well explained
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