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            <td style="vertical-align: top;"><a
 href="aboutCoefficientSequence.html"><small
 style="color: rgb(0, 0, 102);">Previous</small></a><br>
            </td>
            <td
 style="text-align: center; vertical-align: top; color: rgb(0, 0, 102);"><big><span
 style="font-weight: bold;">About HAP: Third homology of some
superperfect groups<br>
            </span></big></td>
            <td style="text-align: right; vertical-align: top;"><a
 href="aboutPeriodic.html"><small style="color: rgb(0, 0, 102);">next</small></a><br>
            </td>
          </tr>
        </tbody>
      </table>
      <big><span style="font-weight: bold;"></span></big><br>
      </th>
    </tr>
    <tr>
      <td
 style="vertical-align: top; background-color: rgb(255, 255, 255);">
      <div style="text-align: left;">A group G is said to be <span
 style="font-style: italic;">superperfect</span> if it is perfect and
its second integral homology is trivial. Using the library of perfect
groups
compiled by Holt and Pleskin, we (<span style="color: rgb(255, 0, 0);">very
partially</span>) list below the 
superperfect
groups of order at most 68880 together with their third integral
homology. Further information on these superperfect groups can be
obtained using the GAP command<br>
      <div style="text-align: center;"><br>
 <span style="font-family: helvetica,arial,sans-serif;">DisplayInformationPerfectGroup(order,number)</span>;

      <br>
      </div>
      </div>
      <br>
where "order" is the order of the group and "number" is the number of
the group given in the table. <br>
      <br>
      <span style="color: rgb(255, 0, 0);">(Work on the table is to be
continued ... )</span><br>
      </td>
    </tr>
    <tr>
      <td
 style="vertical-align: top; background-color: rgb(255, 255, 255); text-align: left;">
      <table
 style="margin-left: auto; margin-right: auto; text-align: left; width: 555px; height: 823px;"
 border="0" cellpadding="2" cellspacing="2">
        <tbody>
          <tr>
            <td style="vertical-align: top;"><br>
            </td>
            <td style="vertical-align: top; text-align: center;"><big><big><span
 style="color: rgb(0, 0, 0); font-family: helvetica,arial,sans-serif;"><small
 style="text-decoration: underline;">List
of superperfect groups</small><br style="text-decoration: underline;">
            <br>
            <br>
            </span></big></big> </td>
            <td style="vertical-align: top;"><br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; font-family: helvetica,arial,sans-serif; text-align: left;"><big><span
 style="color: rgb(0, 0, 0);">Order                 

            </span><br>
            </big></td>
            <td style="vertical-align: top; text-align: left;"><big><span
 style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 0);">Perfect
Group
Number</span><br>
            </big></td>
            <td style="vertical-align: top; text-align: left;"><big><span
 style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 0);">Third
integral
homology </span><br>
            </big></td>
          </tr>
          <tr>
            <td style="vertical-align: top; text-align: left;"><br>
            </td>
            <td style="vertical-align: top; text-align: left;"><br>
            </td>
            <td style="vertical-align: top; text-align: left;"><br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; text-align: left;"><span
 style="color: rgb(0, 0, 0);">120</span><br>
            </td>
            <td style="vertical-align: top; text-align: left;"><span
 style="color: rgb(0, 0, 0);">1</span><br>
            </td>
            <td style="vertical-align: top; text-align: left;"><span
 style="color: rgb(0, 0, 0);">[ 8, 3, 5 ]</span><br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">336<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[16,3]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">504<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
2, 9, 7 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1320<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 5 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2160<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
16, 3, 3, 5 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2184<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 7 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2688<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 8, 3 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3840<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">6<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">???<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3840<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">7<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">???<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">4080<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
3, 5, 17 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">4896<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
32, 9 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">5376<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">???<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">5616<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">6048<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 9, 5 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">7920<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">9720<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 9, 5 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">12144<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
16, 3, 11 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">14400<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 8, 3, 3, 5, 5 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15000<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 5, 25 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15000<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">???<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15120<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
16, 3, 3 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15360<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">4,6-7:
Not
yet checked if these are superperfect<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);"><br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15600<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
16, 3, 13 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">19656<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 7, 13 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">21504<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">5-22:
Not
yet checked if these are superferfect<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);"><br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">24360<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 5, 7 ]<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">29160<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">???<br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">29160<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3:
Not yet checked if this is superperfect<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);"><br>
            </td>
          </tr>
          <tr>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">29760<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1<br>
            </td>
            <td
 style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
64, 3, 5 ]<br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top;"><span
 style="color: rgb(0, 0, 0);">32256</span><br>
            </td>
            <td style="vertical-align: top;"><span
 style="color: rgb(0, 0, 0);">1-2: Not yet checked if these are
superperfect</span><br>
            </td>
            <td style="vertical-align: top;"><br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">32736<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">[ 3,
11, 31 ]<br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">34560<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">4<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">???<br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">37500<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1:
Not yet checked if this is superperfect<br>
            </td>
            <td style="vertical-align: top;"><br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">40320<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">[ 8,
16, 3, 3, 5 ]<br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">40320<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">3<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">???<br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">43008<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1-25:
Not yet checked if these are superperfect<br>
            </td>
            <td style="vertical-align: top;"><br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">46080<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1:
Not yet checked if this is superperfect<br>
            </td>
            <td style="vertical-align: top;"><br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">50616<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">[ 8,
9, 19 ]<br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">51840<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">???<br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">57624<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1-2:
Not yet checked if these are superperfect<br>
            </td>
            <td style="vertical-align: top;"><br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">58320<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">2:
Not yet checked if this is superperfect<br>
            </td>
            <td style="vertical-align: top;"><br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">62400<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">???<br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">64512<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1-4:
Not yet checked if these are superperfect<br>
            </td>
            <td style="vertical-align: top;"><br>
            </td>
          </tr>
          <tr>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">68880<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">1<br>
            </td>
            <td style="vertical-align: top; color: rgb(0, 0, 0);">[ 16,
3, 5, 7 ]<br>
            </td>
          </tr>
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Messung V0.5
C=94 H=97 G=95

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