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Math Help - Group Theory: finding groups of order 160

  1. #1
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    Group Theory: finding groups of order 160

    Hey there, I have received a project in my group theory class that requires me to find all the groups of a bunch of orders... the last one being 160. I know that there are 238=2^5 x 5 groups and so the more I get the more extra credit I get on this project. I know some of the Abelian groups that are obvious. I also know that it is a type 32p, p prime. If people could help me with listing groups along with reasoning that would be great.

    Thank you
    Ghost
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  2. #2
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    Here is a site you might find handy if you can open a zip file. This site lists of them up to 1000. All 238 of yours are there. Problem is, opening the file.

    Generators of Small Groups

    I managed to unzip the file. It is too big to post on the forum.
    Last edited by galactus; May 23rd 2008 at 05:57 PM.
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    Thank you so much that helped a bunch... now all i have to do is find reasons for them
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    Quote Originally Posted by ghostSOU View Post
    Hey there, I have received a project in my group theory class that requires me to find all the groups of a bunch of orders... the last one being 160. I know that there are 238=2^5 x 5 groups and so the more I get the more extra credit I get on this project. I know some of the Abelian groups that are obvious. I also know that it is a type 32p, p prime. If people could help me with listing groups along with reasoning that would be great.

    Thank you
    Ghost
    You might want to include the dihedral group. The nice property of this group is that it exists for every even order \geq 6 and it not abelian. So if you are looking for non-obvious groups i.e. non-abelian you can get many examples using the dihedral group.
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