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<table
style="text-align: left; margin-left: auto; margin-right: auto; color: rgb(0, 0, 102);"
border="0" cellpadding="20" cellspacing="10">
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 <tr align="center">
 <th style="vertical-align: top;">
 <table style="width: 100%; text-align: left;" cellpadding="2"
cellspacing="2">
 <tbody>
 <tr>
 <td style="vertical-align: top;"><a
href="aboutCoefficientSequence.html">Previous</a> 
 </td>
 <td
style="text-align: center; vertical-align: top; color: rgb(0, 0, 102);"><big>About HAP: Third homology of some
superperfect groups 
 </big></td>
 <td style="text-align: right; vertical-align: top;"><a
href="aboutPeriodic.html">next</a> 
 </td>
 </tr>
 </tbody>
 </table>
 <big></big> 
 </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 superperfect if it is perfect and
its second integral homology is trivial. Using the library of perfect
groups
compiled by Holt and Pleskin, we (very
partially) 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 
 <div style="text-align: center;"> 
DisplayInformationPerfectGroup(order,number);

 
 </div>
 </div>
 
where "order" is the order of the group and "number" is the number of
the group given in the table. 
 
 (Work on the table is to be
continued ... ) 
 </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;"> 
 </td>
 <td style="vertical-align: top; text-align: center;"><big><big>List
of superperfect groups 
 
 
 </big></big> </td>
 <td style="vertical-align: top;"> 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; font-family: helvetica,arial,sans-serif; text-align: left;"><big>Order

 
 </big></td>
 <td style="vertical-align: top; text-align: left;"><big>Perfect
Group
Number 
 </big></td>
 <td style="vertical-align: top; text-align: left;"><big>Third
integral
homology 
 </big></td>
 </tr>
 <tr>
 <td style="vertical-align: top; text-align: left;"> 
 </td>
 <td style="vertical-align: top; text-align: left;"> 
 </td>
 <td style="vertical-align: top; text-align: left;"> 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; text-align: left;">120 
 </td>
 <td style="vertical-align: top; text-align: left;">1 
 </td>
 <td style="vertical-align: top; text-align: left;">[ 8, 3, 5 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">336 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[16,3] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">504 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
2, 9, 7 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1320 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 5 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2160 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
16, 3, 3, 5 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2184 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 7 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2688 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 8, 3 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3840 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">6 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">??? 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3840 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">7 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">??? 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">4080 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
3, 5, 17 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">4896 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
32, 9 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">5376 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">??? 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">5616 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">6048 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 9, 5 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">7920 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">9720 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 9, 5 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">12144 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
16, 3, 11 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">14400 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 8, 3, 3, 5, 5 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15000 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">2 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 5, 25 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15000 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">??? 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15120 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
16, 3, 3 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15360 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">4,6-7:
Not
yet checked if these are superperfect 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);"> 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">15600 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
16, 3, 13 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">19656 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 7, 13 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">21504 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">5-22:
Not
yet checked if these are superferfect 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);"> 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">24360 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
8, 3, 5, 7 ] 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">29160 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">??? 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">29160 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">3:
Not yet checked if this is superperfect 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);"> 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">29760 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">1 
 </td>
 <td
style="vertical-align: top; text-align: left; color: rgb(0, 0, 0);">[
64, 3, 5 ] 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top;">32256 
 </td>
 <td style="vertical-align: top;">1-2: Not yet checked if these are
superperfect 
 </td>
 <td style="vertical-align: top;"> 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">32736 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">[ 3,
11, 31 ] 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">34560 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">4 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">??? 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">37500 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1:
Not yet checked if this is superperfect 
 </td>
 <td style="vertical-align: top;"> 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">40320 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">[ 8,
16, 3, 3, 5 ] 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">40320 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">3 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">??? 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">43008 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1-25:
Not yet checked if these are superperfect 
 </td>
 <td style="vertical-align: top;"> 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">46080 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1:
Not yet checked if this is superperfect 
 </td>
 <td style="vertical-align: top;"> 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">50616 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">[ 8,
9, 19 ] 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">51840 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">??? 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">57624 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1-2:
Not yet checked if these are superperfect 
 </td>
 <td style="vertical-align: top;"> 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">58320 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">2:
Not yet checked if this is superperfect 
 </td>
 <td style="vertical-align: top;"> 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">62400 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">??? 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">64512 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1-4:
Not yet checked if these are superperfect 
 </td>
 <td style="vertical-align: top;"> 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">68880 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">1 
 </td>
 <td style="vertical-align: top; color: rgb(0, 0, 0);">[ 16,
3, 5, 7 ] 
 </td>
 </tr>
 </tbody>
 </table>
 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top;">
 <table
style="margin-left: auto; margin-right: auto; width: 100%; text-align: left;"
border="0" cellpadding="2" cellspacing="2">
 <tbody>
 <tr>
 <td style="vertical-align: top;"><a
style="color: rgb(0, 0, 102);" href="aboutCoefficientSequence.html">Previous
Page</a> 
 </td>
 <td style="text-align: center; vertical-align: top;"><a
href="aboutContents.html">Contents</a> 
 </td>
 <td style="text-align: right; vertical-align: top;"><a
href="aboutPeriodic.html">Next
page 
 </a> </td>
 </tr>
 </tbody>
 </table>
 <a href="aboutTopology.html"> 
 </a> </td>
 </tr>
 </tbody>
</table>
 
 
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