col16.z

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

SMALL_GROUP_LIB[ 708 ] :=
[ 4119940307989, 234166740597869, 165790814042898563, 5805369118,
242360234509939, 8222294784556, 330622747251, 6156177131, 234166910342003,
115 ]; 

PROPERTIES_SMALL_GROUPS[ 708 ] := rec(
isNilpotent := [ 4, 10 ], 
isSupersolvable := [ 1, -5, 7, -10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -10 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 712 ] :=
[ 1356142039080317015, 21923243857856, 964699527024486854743,
965571187389442011223, 1904688235028567, 1356139306808287319,
1904688175059031, 1904688594845783, 30764379624, 31184166376,
15587305485094376, 687097581241100173258839, 1355374167912157271,
2673202036823, 87 ]; 

PROPERTIES_SMALL_GROUPS[ 712 ] := rec(
isNilpotent := [ 2, 9, -11, 15 ], 
isAbelian := [ 2, 9, 15 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 14, -15 ], [ 4, -11, 13
], [ 1, -3, 12 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11
] ) );

SMALL_GROUP_LIB[ 714 ] :=
[ 407793303903, 24136122869, 291162786103647, 41943541, 505413983, 169869813,
362223239519, 35653105, 359941539103, 120027352853, 258629143363935, 351 ]; 

PROPERTIES_SMALL_GROUPS[ 714 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 726 ] :=
[ 3732820991, 24692833800199, 17927443021400199, 5160199,
119521395954501040199, 141141035568480199, 212236160199, 46400199,
33961440199, 5440991, 33510880919, 24656277040199, 199 ]; 

PROPERTIES_SMALL_GROUPS[ 726 ] := rec(
isNilpotent := [ 4, 13 ], 
isSupersolvable := [ 1, -4, 8, -13 ], 
isAbelian := [ 4, 13 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -7, 9, -10, 12, -13 ], [
1, -4, 8, 11 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 728 ] :=
[ 10824194899658309, 23806086074670539, 17443379263257732167, 2976112595952,
17317828127362719179, 12602772516016510755911, 140476725900712007,
140476725900463175, 102267056710574761031, 140476725904195655,
102267056710578493511, 102267056710578244679, 74450417285553105282119,
17330792107860698843, 32700554386139, 23806033078672091, 32700554137307,
32700557869787, 7879993115722787381, 14868353490485, 10824166364831285,
14868353241653, 14868356974133, 12698779833903299503175, 23960684830169159,
17443378892266887239, 23960684829920327, 23960684833652807, 4077113172,
4080845652, 2163644457035604, 17443129585037331527, 8651618062196544,
23779323503300315, 17317982726117968967, 192962185003079, 44877348935,
20416168073, 32912566714439, 71 ]; 

PROPERTIES_SMALL_GROUPS[ 728 ] := rec(
isNilpotent := [ 4, 29, -31, 40 ], 
isSupersolvable := [ 1, -32, 34, -40 ], 
isAbelian := [ 4, 29, 40 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 33, 36, -40 ], [ 7, -32,
34, -35 ], [ 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[ 732 ] :=
[ 163838641641123659, 223837668003659, 4877535092401, 286980032163659,
210070285414560119, 6648487140, 153596579931338403659, 58681635840119,
210011192583843659, 153589528082432160119, 296681978880119, 82944000119,
9734930348400, 43554923631576059, 391910400119, 7050243541, 286980226560119,
119 ]; 

PROPERTIES_SMALL_GROUPS[ 732 ] := rec(
isNilpotent := [ 6, 18 ], 
isSupersolvable := [ 1, -12, 15, -18 ], 
isAbelian := [ 6, 18 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, 11, -18 ], [ 1, -7, 9,
-10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 735 ] :=
[ 363832928423, 669095, 705383, 492418151, 501707879, 359 ]; 

PROPERTIES_SMALL_GROUPS[ 735 ] := rec(
isNilpotent := [ 2, 6 ], 
isAbelian := [ 2, 6 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 4, -6 ], [ 1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) );

SMALL_GROUP_LIB[ 736 ] :=
[ 733692534093516568555362773, 47528181256307647854992,
996864856075659119759253, 733691048837882034420602773,
397438310937959035235201537673109, 397439113308713035389211921483669,
292514596850337849935780242431676885, 996864856075658326099925,
733691048837882033626943445, 734781226495507958490992597,
539996611938654488430761860757, 803367620868756600785890453,
591279657655848087903702759637, 591280747833505713828566808789,
591278568953377994260579700373, 435181026749686206282695589451989,
996864856075659006379349, 733691048837882034307222869,
996864856075658779619541, 734781230515092515077754837,
733691048837882034080463061, 539999881000464887302272229333,
539997700637104997524554471637, 539997700639117524214110836949,
397438307667424044361907720258005, 998344063192485769381269,
733695490489754714194089365, 435181828030264564071867869454805,
591278568953377994252869866901, 435181026749686206282687879618517,
435181026749680176905861049448341, 320765619435900351061544929621766933,
236083495904822658381299484276240350549,
236083495904822658381299484276353730453,
173757452985949476568636422843304297042389, 998344063192485656001365,
996864856075661500737237, 591278568953377994260466320469,
591278568953377994143911779157, 803367620868756491827802709,
435181026749680176905860709308629, 435181026749680176905744154767317,
435181026749680176905860936068437, 257691155202491207736,
64576331937666947640, 47463604924372810932792, 257691155204078526392,
47463779689396532403128, 34933341763777710160641976,
25710939538052775205609444408, 34933341763777477051559352,
25710939538052774972500361784, 25710939538052774974087680440,
189660865466214204011576, 35075345909495823459172920,
35075345996996983874667064, 25815454396361589715760113208,
64576331939254266296, 47463604924374398251448,
18948822754736259899078337038200, 13946333547485887285291870888726968,
10264501490949613041974387105710810680, 733692528036795623766495189,
540798982694658965882060316629, 540798981215451849058131812309,
1356445723230983994773, 996864847872431680081301, 996864847872428051924373,
734781226487304731844973973, 734781224477512453551592853,
735871402135138378415642005, 1091534103349271835685717,
803369102082931172355752789, 803370583299840274350878421,
1483062636879341267221, 1091532093556997057081621, 1091534106083690241603861,
1091534106083690014844053, 1091536118610379571209365,
803370581290047999572274325, 803369100073138897577148693,
1605741339312520967488260053, 591279659131030151235592148949,
591279657651820300000400660437, 591280749308687777160456198101,
1091534103349271949065621, 803367620860553247721278869,
803367620860553244093121941, 803369100070404482912767381,
803369102080196761206148501, 803370581290047996397637013,
803369104092723450762513813, 591279657649810507725622056341,
1354435930953370893077, 996862838080154066979605, 996862838080150438822677,
733692528039530053737163541, 733692528042264465000147733,
539997700637096794294733815701, 539997700639109320984176801109,
1091532093556994335963925, 803367618850760966480020245,
591278568953372525325807627029, 435181026749682181229204343996309,
803463897949854696639287829, 591349428891094126460467831317,
435233179663845278139301256997397, 591349428891094126453665037077,
435233179663845278139298082360085, 435233179663845278139297855600277,
320331620232590124711587452213252885, 435233179663845278139291052806037,
320331620232590124711587448811855765, 235764072491186331787729426222453614485
, 1354435930953030753365, 996862838080153726839893, 1354435930952577233749,
996864847872431566701397, 734781224474778041948468949,
996862838080153273320277, 996862838080153046560469, 1354435930959720167701,
1354435930956092010773, 998344054989259009982741, 998344054989258783222933,
803367620860555003975991829, 435232307617998454227565443389077,
591278568953369792655719828565, 1483062636879001127509,
1091534103349278638479957, 1605741339312520974291054293,
1483062636886144061461, 1091534103349278751859861, 1091534103349282153256981,
803369100067670074824420501, 591278568953369792656059968277,
320330978406846862312712395144937365, 435181026749680168704256189576533,
1181823445380715312744990922709, 803367618850760962284963797,
803369100067670071649783189, 591279657649807773314359072149,
1091532093556993995824213, 591348244046193550276046455317,
591278568953369792655833208469, 435232307617998454227565330009173,
1354435930959380027989, 1356445723241188186133, 87738935648077428,
175121212018751988, 128976829343852891764, 128976829344079651572,
128889328183664157428, 94991434868273141757812, 87738946192408500,
64576094172638352436, 47528005540670071250548, 64576094172865112244,
47528005421782965173556, 34980611990661537274677108, 47528005659557857606964,
47527918039509995896116, 34980547677308631886481268, 87738937235396084,
64488593006667242996, 64488593119140107764, 47463604568204468310964,
34933212961950705619459572, 25710844739995471469643985524,
34933212961950705959599284, 34933148648597807374197684,
25710797405367733111074781236, 996862835345749720169557, 1840258838945911317,
1354433196556167016981, 1354433196555713497365, 2015025241593774101,
1091532090824338193893653, 1483059902482137391125, 1091532090824324588305173,
803367618848028307616832277, 803367618848026565421227413,
1483059902584179304725, 1091532090822597132087829,
591278567472150147394030219157, 1840258838152251989, 1840258852551499797,
118887559597070, 118891074374094, 64488474117633697934, 87620051943387854,
64488474247907207630, 34933148561096275752888142, 2496694421061653, 21 ]; 

PROPERTIES_SMALL_GROUPS[ 736 ] := rec(
isNilpotent := [ 2, 44, -62, 149, -172, 188, -193, 195 ], 
isAbelian := [ 2, 45, 58, 149, 164, 188, 195 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 194, -195 ], [ 37,
44, 63, -93, 117, -125, 129, -135, 139, -142, 147, -163, 173, -193 ], [ 8,
-16, 19, -31, 36, 38, -43, 45, -57, 94, -116, 126, -128, 136, -138, 143, -146
, 164, -172 ], [ 3, -7, 17, -18, 32, -35, 58, -62 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 6, 11, 17, 22, 58, 63, 209, 214 ], pos := [
1, 2, 43, 62, 148, 172, 187, 193 ] ) );