col8.z

#############################################################################
##
#W  col8.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1356 ] :=
[ 109491929890561, 12135308753711471, 16455498947802235103, 27311418179807,
16453732857366524271, 22311261720264395784415, 12353647625109727,
327823249813248, 8947660488927, 85599465617, 12135311113978079, 223 ]; 

PROPERTIES_SMALL_GROUPS[ 1356 ] := rec(
isNilpotent := [ 4, 12 ], 
isSupersolvable := [ 1, -7, 9, -12 ], 
isAbelian := [ 4, 12 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -12 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1364 ] :=
[ 5095691396109, 16417547378129, 22533927776010299, 141420330299,
157836288960299, 12052800299, 3758400879, 16520410080299, 299 ]; 

PROPERTIES_SMALL_GROUPS[ 1364 ] := 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[ 1365 ] :=
[ 21899447, 32516345, 29399005367, 29122967735, 2231 ]; 

PROPERTIES_SMALL_GROUPS[ 1365 ] := rec(
isNilpotent := [ 5 ], 
isAbelian := [ 5 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -5 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1372 ] :=
[ 3115430759611214434934711, 241086723886007, 2269067374626794635607,
175687429463, 1654994248620039611, 1200327093620603, 330237515347503803,
2710248838249197641147, 2270710616705389012535, 337468843562009399,
218494441655, 218510335799, 240037966616759, 3732522981293314940183351,
80614117414514596823, 453136225448548214999, 1205390686010327, 874870450775,
240697910347991, 330237684676738007, 1653837795968124887, 245968529679575,
127433303, 143327447, 174938880599, 874870428497, 1205221368720059,
1653598019446289207, 43698888503, 2268686783423007156923,
21788382008998465533498167, 6118485258455, 8436506515624151,
11574886961097612503, 638005463, 878438172887, 1205246339749079, 215 ]; 

PROPERTIES_SMALL_GROUPS[ 1372 ] := rec(
isNilpotent := [ 2, 4, 11, -13, 23, -25, 29, 38 ], 
isSupersolvable := [ 1, -13, 15, -29, 32, -38 ], 
isAbelian := [ 2, 4, 11, 23, 29, 38 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 33, -34, 37, -38 ], [
15, -16, 19, 21, -25, 28, -29, 31, -32, 35, -36 ], [ 3, -4, 7, 9, -14, 17,
-18, 20, 26, -27, 30 ], [ 1, -2, 5, -6, 8 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 20, 26, 21, 27, 33, 52, 58, 64, 70,
76, 77, 83, 89, 95 ], pos := [ 1, 2, 3, 4, 8, 10, 13, 14, 16, 20, 22, 25, 26,
27, 28, 29 ] ) );

SMALL_GROUP_LIB[ 1380 ] :=
[ 2448930070102713, 349992472061103, 3384892358069933391, 116777183410141,
3379528406430492755, 482989961517503729, 4671151481895836293531,
29130806961563,
[ (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) ],
482523066206037167, 15314948445795534001487, 665881773473910134001,
21134628855211033488021915, 8041877776396859, 2681810243843543,
11108741739015557691, 349997414383565, 11097796493469605435,
18494685803133135419, 15330063599300213779003, 349655048568716, 1773838905915
, 253970985909, 2452814501677627, 85096773499, 2448930394770903,
349992796729293, 3384892358229685819, 571 ]; 

PROPERTIES_SMALL_GROUPS[ 1380 ] := rec(
isNilpotent := [ 8, 29 ], 
isSupersolvable := [ 1, -8, 10, -20, 22, -29 ], 
isSolvable := [ 1, -8, 10, -29 ], 
isAbelian := [ 8, 29 ], 
lgLength := rec( lgLength := [ 4, 5, false ], pos := [ [ 14, -29 ], [ 1, -8,
10, -13 ], [ 9 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17 ], pos := [ 1, 2,
3, 4, 5, 6, 7, 8 ] ) );

SMALL_GROUP_LIB[ 1386 ] :=
[ 103883438553801159, 9453445235401915, 143982395914720201159, 2282393801915,
20455437001519, 11365593801915, 28451260025801159, 3158715616805911,
4447298943408405191, 4409503375382809151, 6164366016875749001591,
126157001159, 24993856001159, 2279129601195, 34641485894401159, 2282400001915
, 34641521936001159, 3158725548801915, 48013099478294401159, 5017601195,
14758401159, 8204801195, 20527532801159, 1651201591, 20455443201519,
11365600001915, 28451260028801159, 2275756805911, 28351271753605119,
15752729417609115, 39433446747364801159, 1159 ]; 

PROPERTIES_SMALL_GROUPS[ 1386 ] := rec(
isNilpotent := [ 12, 32 ], 
isAbelian := [ 12, 32 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, -15, 20, -23, 28, -32 ]
, [ 1, -12, 16, -19, 24, -27 ] ] ),
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[ 1392 ] :=
[ 1365847220865721239276289, 36826888563314198062248219,
51263057314973348056306511927, 85304169320612063309879,
51238468142967027727533551899, 71323947683444898624049162186807,
39550762188246920275058743, 39550762188246919793168439,
55054660966124542173421465655, 55054660904930859636930142263,
55054660904930859636448251959, 76636087979663841422307396513847,
76749836089200970888581753749559, 76636088064784297812355622658103,
76749836174321427278569261715511, 106835771836167751517024567472971831,
106835771836167751517024566991081527, 76636088064784253851376778240055,
106677434586179681401920297301798967, 76749836259503033390159714275383,
106835772073228161369541745432424503, 148715394395945510111738315347529658423
, 106677434586179742595602848731721783, 106835771954655365662207835469082679,
39550823337968491414892599, 39550762188246933767987255,
39550823337968505871601719, 55054746208880375349952458807,
55054660966080581208069976119, 55054746086493010247092613175,
55054746147686692798522535991, 5287414464968313959793923233536,
26456098063972313003483, 36826868136112708996888027,
51263028818968636632808617435, 51263028818983290292423423451,
71358136116024754283562451994075, 26456098063971831113179,
36826868136112708514997723, 26476481304493134939611,
36826888519353229818824155, 36855282388057093303010779,
26456098063983878370779, 55054604096722288503812183515,
76636008902637438422362547283419, 76636008902637438422363029173723,
106677324392471314296753051978827227, 26476481304507591648731,
981212079850602605377, 1365845107706959021583169,
1901259325117382943235222337, 1901259325118898839057443649,
2646552980565508242712421645121, 981212079850120715073,
1365845107706958539692865, 983320690935939218241, 1365847216318044358196033,
1368784513080512994491201, 981212079862167972673,
5692860041168346773601356609, 7924461177306338396144489765697,
7924461177306338396144971656001, 11030849958810423047119751327693633,
983320690950395927361, 36826908990515821091905591,
51263057253691743562126352439, 71358175782259406849238048202807,
71358175782259450810216892620855, 99330580688905155571199724665270327,
36826908990515820610015287, 51263057253691743561644462135,
36826970140237392231739447, 51263057314841465133266186295,
51263142496447576723718746167, 36826908990515834584834103,
229805500678770294780866816786487, 319889256944848250377659362883883063,
319889256944848250377659363365773367, 445285845667228764525744525218454794295
, 36826970140237406688448567, 61281604510564429879, 122431326097606643767,
170485643549279475544119, 61281604511528210487, 85242887716117401260087,
118658099744772123764867127, 165172074844766003832241213495,
229919528183914320541361487835191, 51262982842173794438095777847,
51262982842173794452552486967, 71358072116244769077056617918519,
51262982842173794439059558455, 71358072116244769077043124990007,
71358072116244769077057581699127, 99330436385812657402460576043593783,
7143478322025130117998448364378223550656,
5131809139385869337642650130267181248, 3798419161646718185282358800,
9943721824259376049349170198266823628225600,
7143478322025413828555438426779122527296, 5287399574911582415642217003120,
3985379716170422949812992250688500, 2863060140927027990322469020660,
118601208625798480639717659, 51238468122539920967018481115,
71323947626555025331077986518491, 36809244355664203037246939,
51238468122539920978583848411, 36809244355664205928588763,
51238468122539920981475190235, 36809244355664217493956059,
71323947683383617047173561020471, 99282935175269933779456131143397431,
51238468163394229349117538359, 71323947683383617047187053948983,
51238468163394229350081318967, 71323947683383617047188017729591,
51238468163394229363574247479, 55136376500818776597852479543,
55054660904886898673506213943, 76749836089139777206015867117623,
55054660904886898673024323639, 76749836089139777206015385227319,
76636087979602603778792542662711, 106835771836082569910912962081812535,
39550762144285955887349815, 55136376500818776612309188663,
76749836089139777206000446627895, 28412903809925595283511,
39609465876996116007108663, 39550762144285971307839543,
55136376500818776627729678391, 28412903809924631502903,
39550762144285970344058935, 55136376500818776626765897783,
28412903809924149612599, 39609465876996114561437751,
39550762144285939984969783, 28412903809939088212023,
39550762144285954923569207, 39550762144285954441678903,
55054660904886898656640053303, 28455076032191320293431,
28412903809954508701751, 39609465876996144920526903, 2938002165246527765568,
1905344124405843983361371200, 2652239021172843336872617114688,
36826868121459062393099051, 19005796769058800427, 26456083410340647813931,
26456083410339684033323, 20411537986393473835, 39550721319188803127485227,
39550721319188774214066987, 55054604076324393779321266987,
19005796767613129515, 19005796797972218667, 1365845106191076209828529,
704891805988328113, 981210563982729450161, 981210563981765669553,
2110633023323001521, 4089698303920816944214705, 4089698303920788030796465,
5692860039058219248387797681, 704891804542657201, 704891834901746353,
51263057253647782598220533815, 26456112717752400363575,
36826908946554872124686391, 36826908946554871160905783,
85200611908974403387447, 165090158533555358033588396087,
165090158533555358004674977847, 229805500678709101098300930154551,
26456112717750954692663, 26456112717781313781815, 43960979326308407,
43960994264907831, 85242843755137593061431, 61237643547622391863,
7360263059001605819382087556642928, 51342048942940068581795328283,
3798419240473161168973244528, 36826855490132740136308791,
2728749397919891082776144, 3798419234850195952673532016,
85202017672769262605787, 26443422901050472469291, 36809244370317985052168247,
20411539466760486967, 2110679654883960944, 4089704634806759808030464,
13643309127827511, 505545335243509, 19005796890495156279, 55 ]; 

PROPERTIES_SMALL_GROUPS[ 1392 ] := rec(
isNilpotent := [ 4, 81, -88, 179, -182, 198 ], 
isSupersolvable := [ 1, -31, 33, -95, 105, -145, 149, -182, 186, 190, -192,
195, -198 ], 
isAbelian := [ 4, 81, 84, 179, 198 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 192, 194, -198 ], [
25, -32, 40, -43, 48, 56, -59, 64, 72, -75, 80, -83, 89, -91, 107, -108, 111,
114, -115, 118, -145, 149, -182, 185, -191, 193 ], [ 7, -24, 33, -39, 44, -47
, 49, -55, 60, -63, 65, -71, 76, -79, 84, -88, 92, -106, 109, -110, 112, -113
, 116, -117, 146, -148, 183, -184 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46, 50
, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179 ], pos := [ 1, 2
, 3, 4, 5, 6, 31, 32, 48, 64, 80, 88, 95, 98, 101, 104, 111, 118, 145, 148,
158, 168, 178, 182 ] ) );