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How many and which distinct groups of order 20 that are not isomorphic? Why are they not isomorphic? I have the $Z_{20}, Z_2+Z_{10}, D_{10}$.

There are more than 4. I don't know the limit.


marked as duplicate by Dan Shved, clark, dfeuer, Shuchang, user61527 Nov 29 '13 at 7:01

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  • 2
    $\begingroup$ There are more than 4. $\endgroup$ – newyorkwedge Nov 29 '13 at 6:22
  • $\begingroup$ There are exactly $5$ non-isomorphic groups of order $20$. If you are aware of semi-direct products, look at SnowAngel6147's answer in the link Dan provided. If you know about presentations, the remaining two can also be found here and here. $\endgroup$ – NotAwake Nov 29 '13 at 6:38

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