col18.z

#############################################################################
##
#W  col18.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1827 ] :=
[ 8633665340999, 577187228049, 63885523575, 2045598071, 963804105, 22903 ]; 

PROPERTIES_SMALL_GROUPS[ 1827 ] := rec(
isNilpotent := [ 3, 6 ], 
isAbelian := [ 3, 6 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 4, -6 ], [ 1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7 ], pos := [ 1, 2, 3 ] ) );

SMALL_GROUP_LIB[ 1830 ] :=
[ 422771140592643839, 401029263363839, 97539240963839, 97550645770919,
178490387566090919, 146109588483839, 146932185603839, 267377968811523839,
129392643839, 81285123839, 391910403839, 20321287143, 717652016643839,
7050254341, 716842483210919, 36462804692463, 1313304076604163839, 3839 ]; 

PROPERTIES_SMALL_GROUPS[ 1830 ] := rec(
isNilpotent := [ 18 ], 
isAbelian := [ 18 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -18 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1836 ] :=
[ 368015821103784972886224077073, 1634171144569330434375967,
675700653043121496719257843539729, 1009779639408488616223,
2999791814765400382999953695, 167018304968551440225229760530906881809,
367831172937873796206197481233, 326691704900326355046656,
890071428046763594015, 200444347006418587266117905,
367828778939162120588393193233, 549984512507908383, 890071428046646218783,
1008609688693359317023, 1851806291116269120851999, 109173964292979798700049,
59398485667425153041, 108936823173281893969937, 399907077416945392187207697,
204801578848023536036020721, 1634171144569334595125535,
3399916350492114292255555871, 734233752317917726546736513521,
200443872595404252592931089, 109055620146723325673745,
376015707773887066964603441649, 204801465160034419224875505,
557162124296589599, 557162399107387679, 1008681465061595681055,
1633873537456861878489119, 1634169883108452992094239,
3000335904281724539551944735, 16515855213311094153180067463665,
2999791814765400387160703263, 5508616720261240825089859059999,
30323470187803390525491859666567665, 30323110171539300387695835467485681,
376013850813831049663442063857, 367815051844278304217683132689,
1267509111247018743811356134773625329, 692586904482584448856011816571377,
111962552526868718817777, 1008609688744949190943, 1851925991517069508612383,
200010914278853315431240177, 205569652382304079766884849,
111906740173305200775665, 326691930801653971742993,
200008007087762417626706193, 10194958089005773165745410545,
205563251316230065242509809, 367219927130677830320356594161,
377425881778787158024433701361, 377225980214312268023591866865,
177936658340374507776, 326691704759589352370432, 177936658340357730560,
326691704759589335593216, 177936658340877824256, 484787879550128415,
549351477076824351, 1008609090816849219871, 59462943441604845329,
32352038792732433, 59333782161154121489, 217814312319074336513809,
111547668614504056361457, 890071428050924343583, 1851806291116533177389343,
200010499394940950768783857, 109174222546273061368081, 59398487864250528017,
204801524453424092409762289, 111547638971937799016945, 299067229868319,
299342040666399, 549386652926087455, 484787879432753423, 32352038742466305,
890071428050874077215, 59398485671686565905, 1634171144569336709054751,
109055620144532892352785, 3000338221437349396958155039, 8074813411168543,
889909342440458883343, 1633873537456866106347551,
2999791814765400389274632479, 5507617771909281143341449220383,
200225821238571263032684561, 10113828093915372090336276662780191,
6249442565014554413589426405663, 1102842626263280705962482008337,
18591936327510046106165794651206848799, 34421923630789670213759451132858655,
549351270918394143, 1009771828589335941407, 32352171869609745,
1008609688747029565727, 1853941077982311526437151, 1853945534646001562816799,
59398485802666225937, 1851807391085348410888479, 5561822262576512925438239,
6249457586957283701104765309215, 109411234609925535625489,
3414941316496135929135632671, 96915365804711680, 263891380605215,
17600775983601, 484787883710877983, 32352043020590865, 890071428053004718367,
59398485673817207057, 1634171144569337765957919, 4383 ]; 

PROPERTIES_SMALL_GROUPS[ 1836 ] := rec(
isNilpotent := [ 4, 12, 28, -30, 76, -78, 86, 117 ], 
isSupersolvable := [ 1, -7, 9, -39, 43, -55, 61, -90, 97, -108, 110, -117 ], 
isAbelian := [ 4, 12, 28, 76, 86, 117 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 102, -110, 115, -117
], [ 45, 47, -63, 66, 70, 72, -79, 84, -87, 90, 94, -101, 111, -114 ], [ 7,
-15, 18, 22, 24, -33, 36, 38, -44, 46, 64, -65, 67, -69, 71, 80, -83, 88, -89
, 91, -93 ], [ 1, -6, 16, -17, 19, -21, 23, 34, -35, 37 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 32, 38, 44, 50, 56, 62, 68,
74, 33, 39, 45, 51, 57, 63, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172,
178, 184, 190, 196, 202, 208, 214, 220, 143, 149, 155, 161, 167, 173, 179,
185 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 19, 23, 25, 27, 30
, 33, 37, 39, 40, 41, 42, 46, 48, 50, 53, 55, 60, 63, 67, 71, 73, 75, 78, 79,
80, 81, 82, 83, 84, 85, 86 ] ) );

SMALL_GROUP_LIB[ 1840 ] :=
[ 2223844181866602510816659, 15562073953234702770486917,
28668311928863458257732962327, 46338481715261364652055,
4088908840635578788290893203, 173039828509111338573170557913111,
51110555497239619955899863, 51110555497239619842519959,
94043422114947282786559903767, 94043422089790699170620114391,
94043422089790699170506734487, 173039896645214912849336534044695,
173167922902662700215140138975575, 173039896691477883797576939509207,
173167922948925671163366258572183, 318628978140899368408334757908288983,
318628978140899368408334757794909079, 173039896691477870125520624588247,
318393409912319281043647944089837591, 173167922995213785023162660748183,
318628978311193339312197770685779991, 586277319779254837871348431036320292887
, 318393409912319306200231563544403991, 318628978226023209810172390681939991,
51110580640151182755405591, 51110555497239623130537175,
51110580640151186156802711, 94043468428204054149276362519,
94043422114933610733419620119, 94043468377890886910367229719,
94043468403047470529821796119, 8457648881742335533917,
15562068916449159640951645, 28634216058863262299593886557,
28634216058865996710856870749, 52686957548313436540187110921629,
8457648881742222154013, 15562068916449159527571741, 8462677464054169803677,
15562073945031471475221405, 15571331567803430755656605,
8457648881745056651613, 31358169730690371560169912029,
57699032304470285836320560365853, 57699032304470285836320673745757,
106166219440225325940995230603138461, 8462677464057571200797,
1208610967172659564539, 2223843086913226138294267,
4091873291354334522070185979, 4091873291354928959301269499,
7529046856093069737350420283963, 1208610967172546184635,
2223843086913226024914363, 1209704137239828498491, 2223844180083293307228219,
2225856706772849672540219, 1208610967175380682235,
6815834204342113940895998843, 12541134935989489676882175765947,
12541134935989489676882289145851, 23075688282220661005488628554973755,
1209704137243229895611, 15580604309135288812895703,
28668311903679530529163331031, 52749693949033320625901814076887,
52749693949033334297958128997847, 97059436866221335121733613874372631,
15580604309135288699515799, 28668311903679530529049951127,
15580629452046851612401431, 28668311928822442091962836759,
28668358216936301888365012759, 15580604309135291987533015,
288380658753985948983216137552215, 530620412107334146142395256846797719,
530620412107334146142395256960177623, 976341558277494828902020549953466261527
, 15580629452046855013798551, 25183927732424548119, 50326839298965590679,
92626554558891996702487, 25183927732651307927, 46313297787532681640855,
85216467942724599069081943, 156798301014626699983195671447,
288508873866913141406567728095255, 94044865499075364270225923863,
94044865473932452710601055447, 173042552472035718859366248474391,
94044865473932452707426418135, 173042552472035718859363073837079,
173042552472010575947803448968663, 318398296548499459749829372386218007,
4088908839540647699799759419, 7523592264753644424452193100347,
2222233065591298485782587, 4088908839540647702520877115,
2222233065591299166062011, 4088908839540647703201156539,
2222233065591301887179707, 173039828509086154648689302112279,
318393284456718499417354907891421207, 94043385059299614609383939863,
173039828509086154648692476749591, 94043385059299614609610699671,
173039828509086154648692703509399, 94043385059299614612785336983,
94113001577520397355982896599, 94043422089777027117933350359,
173167922902637543631517283012055, 94043422089777027117819970455,
173167922902637543631517169632151, 173039896645189742593664392714263,
318628978140853080294474957991335959, 51110555483567567042376023,
94113001577520397359384293719, 173167922902637543631513654855127,
27777475799378877786455, 51148370422558641541982551,
51110555483567570670532951, 94113001577520397363012450647,
27777475799378651026647, 51110555483567570443773143,
94113001577520397362785690839, 27777475799378537646743,
51148370422558641201842839, 51110555483567563300839191,
27777475799382052423767, 51110555483567566815616215,
51110555483567566702236311, 94043422089777027113965053719,
27798027396772222042199, 27777475799385680580695, 51148370422558648344776791,
15562068913714751439194369, 4596545391580458689, 8457646147337648553665,
8457646147337421793857, 5033813534412998081, 17042483546552529523583553,
17042483546552522720789313, 31358169725659054709066715969,
4596545391240318977, 4596545398383252929, 2223843086318791968254711,
656853198851330231, 1208610372742004302007, 1208610372741777542199,
1094121341683869623, 3704257719156570052643895, 3704257719156563249849655,
6815834203248349308489856311, 656853198511190519, 656853205654124471,
28668311903665858476363187095, 8467719718452251257175,
15580604295463239527528791, 15580604295463239300768983,
46292715874155181359191, 156728618888022162562467390679,
156728618888022162555664596439, 288380658753960792399593281588695,
8467719718451911117463, 8467719718459054051415, 13672056428300951,
13672059943077975, 46313284115476139960087, 25170255679851163991,
51111339931485549023237335, 8892553493490028959853168, 1207735420573976015351
, 51110535358315093062371991, 15096447330497888343, 2496694421061719,
356720389161425, 4602014242678161495, 87 ]; 

PROPERTIES_SMALL_GROUPS[ 1840 ] := rec(
isNilpotent := [ 4, 80, -87, 166, -169, 178 ], 
isSupersolvable := [ 1, -170, 172, -178 ], 
isAbelian := [ 4, 80, 83, 166, 178 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 171, 174, -178 ], [
25, -31, 39, -42, 47, 55, -58, 63, 71, -74, 79, -82, 88, -90, 97, -98, 101,
104, -105, 108, -170, 172, -173 ], [ 7, -24, 32, -38, 43, -46, 48, -54, 59,
-62, 64, -70, 75, -78, 83, -87, 91, -96, 99, -100, 102, -103, 106, -107 ], [
1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46,
131, 135, 139, 143, 147, 151, 155, 159 ], pos := [ 1, 2, 3, 4, 5, 6, 31, 47,
63, 79, 87, 94, 101, 108, 135, 145, 155, 165, 169 ] ) );