From: "Ken W. Smith" 
Subject: non-solvable groups of order 120
Date: Tue, 26 Mar 1996 18:57:26 +0000

Hi,
        A recent investigation in combinatorial designs leads me to the
following question.

        How many non-solvable groups of order 120 are there?

There is S_5, the symmetric group on 5 symbols and Z_2 x A_5, the direct
product of a cyclic group of order 2 with the alternating group on 5
symbols.  Are there any other groups?  In particular, if I have a commuting
involution s and G/ is isomorphic to A_5, then is G = Z_2 x A_5?  Why?

Thanks in advance,
Ken
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Ken W. Smith, Professor of Mathematics
Interim Director, Office of Institutional Research   "In the future
Central Michigan University, Mt. Pleasant, MI 48859  computers may weigh
Work phone: 517-774-7222, fax: 517-774-4250          as little as 1.5 tons."
Home phone & FAX: 517-772-5042                       Popular Mechanics, 1949