col16.z

#############################################################################
##
#W  col16.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1716 ] :=
[ 96116692410292187, 96858787547632439, 164936971840389960503, 14045049771995
, 77007906527195, 63007957309689, 132873668918039351, 7008160452337,
132145671558727895, 108121734239819349, 228011217529972608263, 1748974685447,
226701723696281278427, 389020158586986072691511, 96858250309140743,
14037692055815, 14469823660295, 24087353997459719, 132103592196298715,
226690488813236310839, 226689760815876999383, 389000878803431406849287,
818565040963847, 90991675442471, 1405580840587100423, 63008195937861,
1404657920174948615, 1716786787929882887, 2411976722542107623687, 33634124039
, 20991817913328, 96312577316031947, 44877349127, 36723622173, 77431916003591
, 4108715413, 77007922201895, 63007972984389, 132873668925751559, 263 ]; 

PROPERTIES_SMALL_GROUPS[ 1716 ] := rec(
isNilpotent := [ 12, 40 ], 
isSupersolvable := [ 1, -30, 33, -40 ], 
isAbelian := [ 12, 40 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 15, -18, 23, -40 ], [ 1,
-14, 19, -22 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 ]
, pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ] ) );

SMALL_GROUP_LIB[ 1720 ] :=
[ 19022415049769196747, 259879595781757249409, 447538161463760486861447,
792753190458004103, 32693196824408854076619, 2417965955510880136680721031,
817322554261697327591, 817322554261566636359, 1405794793646256657801863,
817322554263527004839, 1405794793646258618170343, 1405794793646258487479111,
2417967045071877365975690375, 446992746440326982533301, 151092698162710037,
259879503709914779669, 151092698032018805, 151092699992387285,
32718535451718057133671, 11059548164312007, 19022404345239492039,
11059548033620775, 11059549993989255, 769765636926252144190690439,
260196604992214325735, 447538161003394741036007, 260196604992083634503,
260196604994044002983, 460367836885319, 460369797253799,
1362744114828935797895, 1405806822133951617495527, 19007673647042108199,
1405794160180501779556679, 475187347485462695, 87807779426471, 6440463914685,
151276853348038823, 167 ]; 

PROPERTIES_SMALL_GROUPS[ 1720 ] := rec(
isNilpotent := [ 4, 29, -31, 39 ], 
isAbelian := [ 4, 29, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 35, -39 ], [ 7, -34 ], [
1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35 ],
pos := [ 1, 2, 3, 4, 5, 6, 13, 18, 23, 28, 31 ] ) );

SMALL_GROUP_LIB[ 1722 ] :=
[ 277669724161839, 6778142723165, 478147110789121839, 1638403165, 51200001839
, 6635523165, 88294154241839, 1392649561, 88079196168079, 11294597182445,
152042698321921839, 1839 ]; 

PROPERTIES_SMALL_GROUPS[ 1722 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1725 ] :=
[ 2759079355, 1035925030033, 12187 ]; 

PROPERTIES_SMALL_GROUPS[ 1725 ] := rec(
isNilpotent := [ 1, 3 ], 
isSupersolvable := [ 1, 3 ], 
isAbelian := [ 1, 3 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 2, -3 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 3 ], pos := [ 1 ] ) );

SMALL_GROUP_LIB[ 1734 ] :=
[ 58286280689, 1528245333000703, 2649993286118015487, 33817087,
26127249908300405801471, 15414477964144804351, 15536620569087,
1528196310237695, 873324351263, 35655665, 881310302719, 505414143, 511 ]; 

PROPERTIES_SMALL_GROUPS[ 1734 ] := rec(
isNilpotent := [ 4, 13 ], 
isSupersolvable := [ 1, -4, 8, -13 ], 
isAbelian := [ 4, 13 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -8, 10, -11, 13 ], [ 1,
-4, 9, 12 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1736 ] :=
[ 6004075691987883005, 34816996258566435029, 60591193755406978500179,
150153589628100179, 185996322689059800179, 185996322689035500179,
322889616247535266500179, 185996322689400000179, 322889616247535631000179,
322889616247535606700179, 560536373805780508301700179,
60442284085777498504529, 20055862359004529, 34816983916815004529,
20055862334704529, 20055862699204529, 10423070560379175326105,
3458568893426105, 6004072905384626105, 3458568869126105, 3458569233626105,
105186312209483887623300179, 34902761285021400179, 60591193669012872600179,
34902761284997100179, 34902761285361600179, 86394494700179, 86394859200179,
260516737062144900179, 8402383007457633000, 107140704652800179,
11548915200179, 1993766400875, 20105232134400179, 179 ]; 

PROPERTIES_SMALL_GROUPS[ 1736 ] := rec(
isNilpotent := [ 4, 27, -29, 35 ], 
isSupersolvable := [ 1, -29, 31, -35 ], 
isAbelian := [ 4, 27, 35 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 30, -35 ], [ 5, -29 ], [
1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29 ], pos := [
1, 2, 3, 4, 11, 16, 21, 26, 29 ] ) );

SMALL_GROUP_LIB[ 1740 ] :=
[ 13255349449849611, 1473319867335795, 23092801952932426287, 491484068835313,
23064328714774682999, 2563576938992281439, 40181475514985651052415,
122658998361983,
[ (1,2,3,4,5), ( 3, 4, 5)( 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,
     22,23,24,25,26,27,28,29,30,31,32,33,34) ],
23055481053486840587, 2561611715432498291, 69915652800238924563477039,
69915652814467366376960559, 129257155648612667748911, 40116565281729828090415
, 40116536808491670347127, 4457204139974906390367,
121653235872415661661642760063, 121653235897173150417104084863,
224907450828641604433551231, 69802823590204142748901247, 42692949771158399,
14236066144192871, 74343616104187954047, 1473336372056783,
74285754334240670591, 123800715486777377663, 129357892019003704542079,
1472193053570288, 7615518999423, 848126936583, 13271705064899455,
284177599525, 13255350534080871, 1473320951567055, 23092801953465926527, 895
]; 

PROPERTIES_SMALL_GROUPS[ 1740 ] := rec(
isNilpotent := [ 8, 37 ], 
isSupersolvable := [ 1, -8, 10, -28, 30, -37 ], 
isSolvable := [ 1, -8, 10, -37 ], 
isAbelian := [ 8, 37 ], 
lgLength := rec( lgLength := [ 4, 5, false ], pos := [ [ 22, -37 ], [ 1, -8,
10, -21 ], [ 9 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17 ], pos := [ 1, 2,
3, 4, 5, 6, 7, 8 ] ) );

SMALL_GROUP_LIB[ 1746 ] :=
[ 7961382831695865023, 4559879572300991, 132949110210518113, 7217334114591935
, 269270672648655882145, 4218364634303, 2585680001639615, 2585765615772863,
4514577788644107455, 1489414137023, 4133939586239, 46204471201,
7217335303677119, 76062042971233, 12601472981340791999, 9407 ]; 

PROPERTIES_SMALL_GROUPS[ 1746 ] := rec(
isNilpotent := [ 6, 16 ], 
isAbelian := [ 6, 16 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, 10, -11, 14, -16 ], [ 1,
-6, 8, -9, 12, -13 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1748 ] :=
[ 3566396046549, 4405489792329, 7777987541813147, 52413609115, 81977058871179
, 2526217099, 2046460895, 4449630876811, 395 ]; 

PROPERTIES_SMALL_GROUPS[ 1748 ] := rec(
isNilpotent := [ 4, 9 ], 
isAbelian := [ 4, 9 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -9 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1750 ] :=
[ 3597685524064616318265, 1952408014416203, 6292382952780408219872529,
1565133420875, 1115660201099, 1561314300683, 2732295694191755,
1174741972926033, 669498437649, 390839352920913, 2732354773976907345,
2058162871979413653, 1955529363490763, 4781520594283853579,
1196949426871981404309, 2055814948583607225, 393522449901753,
3601785142120140306069, 692572699403463957, 891830219, 893805323,
1561568124875, 638006027, 383202069, 1117444295435, 670772939601,
1955538281862923, 1173859586971833, 3422192057098468619, 779 ]; 

PROPERTIES_SMALL_GROUPS[ 1750 ] := rec(
isNilpotent := [ 4, 20, -22, 30 ], 
isAbelian := [ 4, 20, 30 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 23, 28, -30 ], [ 5, -7,
10, 14, 16, -22, 24, -27 ], [ 1, -4, 8, -9, 11, -13, 15 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32 ],
pos := [ 1, 2, 3, 4, 7, 11, 15, 17, 19, 22 ] ) );

SMALL_GROUP_LIB[ 1752 ] :=
[ 10747432175108381244928583, 6134492491676297998919, 97475280296063196673,
6912960215889593774663, 12111510366192824586436751, 12177443564157763727,
21217642516447496849777766983, 18829501166733764765872919687,
6134379100915372725383, 10747432172800127060219015, 6134379100913437807751,
6134379100942461572231, 12106928750014985956766279,
21211339174080326293471985807, 7107468379861165867151, 7107468379859230949519
, 12452284606284312572952719, 7107468379888254713999,
12452284606284341596717199, 12452284606284339661799567,
21816402630214879818769858703, 3501427941414868103, 3501427968503714951,
10747626789731368071173255, 299711826097548675857542656,
560987419893690348815724127224, 12111502245582802736485511,
3945751157467059335, 6912957901691342099591, 3945751155532141703,
3945751184555906183, 170776524099093852265921, 55636718336777665,
97475185216119545281, 55636716401860033, 55636745425624513,
21219366149412552490738876559, 6912962530231028613263,
12111510359250183394492559, 6912962530229093695631, 6912962530258117460111,
6942672150626447, 6942701174390927, 21322724498723532275855,
37162264512846710645614415983175, 12110526550505109341901959,
21211338095568929085750784583, 37162264343440790066377151840399,
12111499639776129712423055, 341260845042250622988864,
597889016053710962278223808, 3501372707256139919, 14219201809304053461575,
10761833825662249967399495, 6910347473508187280519,
12106928752329325456687247, 4056771464345419919, 2013057345650831,
166658758901714880, 6142599217741182644807, 2251067693727887, 31949359944697,
3945751277431947407, 143 ]; 

PROPERTIES_SMALL_GROUPS[ 1752 ] := rec(
isNilpotent := [ 6, 42, -44, 64 ], 
isSupersolvable := [ 1, -24, 27, -49, 52, 55, -58, 61, -64 ], 
isAbelian := [ 6, 42, 64 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 52, 57, -58, 61, -64 ],
[ 8, -12, 15, -44, 46, 49, -51, 53, -56, 59, -60 ], [ 1, -7, 13, -14, 45, 47,
-48 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38
, 41, 44, 47, 50, 53, 56 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 21, 24,
25, 26, 31, 36, 41, 44 ] ) );

SMALL_GROUP_LIB[ 1755 ] :=
[ 100547904388293095, 465863191542911, 57292194967943, 100547798393074055,
100547851392299399, 57292194719111, 100547798392825223, 57292198451591,
264996398207, 265000130687, 465333202773119, 150782278788005341, 8185600127,
22655 ]; 

PROPERTIES_SMALL_GROUPS[ 1755 ] := rec(
isNilpotent := [ 2, 9, -11, 14 ], 
isSupersolvable := [ 1, -11, 13, -14 ], 
isAbelian := [ 2, 9, 14 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 12, -14 ], [ 3, -11 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 8, 11 ] ) );