/* Group 2821109907456.j downloaded from the LMFDB on 05 October 2025. */ /* Various presentations of this group are stored in this file: GPC is polycyclic presentation GPerm is permutation group GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups Many characteristics of the group are stored as booleans in a record: Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable */ /* Constructions */ GPC := PCGroup([32, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 64, 34825003307041, 74993185568642, 41489806639714, 258, 279301681800195, 116444865282595, 20377934937187, 436715491383044, 16886967348516, 421422925508, 32064798667940, 7811790163332, 122151642547205, 62692889705509, 20969982779973, 56100002016101, 13867524727813, 549, 293210975748102, 255502164112422, 79920103173190, 31583279961958, 7750980988038, 6415941365766, 201985672122375, 111185662599207, 50928484947015, 84173269530727, 5583002551431, 22530836006567, 3102596048839, 743, 415954103869448, 249153093863464, 105584234987592, 44477998649960, 18966630041992, 13692495049512, 8437093857992, 392737984392, 578178424401929, 249096575508521, 100005544345673, 1129573739625, 53422139911817, 5266035429289, 13020592671561, 834517668713, 61280033545, 937, 203529601273866, 149865889738794, 100797609949770, 123480142866538, 14119415304330, 2599668910250, 4517565377098, 4685237411946, 2366267393162, 106623095370, 156137988562955, 258813453754411, 34081243066443, 20697901830251, 54316387593355, 26404153210539, 13976931801803, 2725564923883, 2712773607819, 272300205611, 457722152395, 1131, 296764607746060, 571415412252716, 231487004636236, 95194769799276, 36509561727116, 16859035395244, 11729534559180, 925147012844, 2923466143372, 633745986732, 133400669708, 18865447308, 441797804195341, 241415487258669, 165630334464077, 36709865128045, 20621910113421, 30517603587245, 7586341701325, 338456531181, 1459035632141, 486228460333, 387636048909, 153011177453, 20324200909, 1325, 1274364223488014, 603854867497006, 336701486776398, 20014582947950, 19763038679182, 27052030909614, 16263297469646, 1241573598958, 2546029325070, 993533990702, 121294, 102926874606, 24186473678, 1353802529636367, 39560609267759, 218112120078415, 59211202756719, 8276024918159, 5814757933231, 4679713751247, 1873385791727, 557257937167, 142533955887, 48138983759, 44296096111, 20897916303, 3871620527, 2149910479, 1519, 922775118151696, 94913872920624, 13172059275344, 23772326363248, 23728468230288, 16920752, 986861574384, 1410320, 164781029680, 164781264720, 4568804016, 414265882305041, 461973415108657, 49128983488593, 128482832074865, 29347916931217, 4650292353201, 569631688913, 2006251670257, 1149370187025, 729279200177, 53700092113, 32419450737, 33668525201, 969221809, 259665, 806316401, 403130833, 1713, 254108862775314, 21208417173554, 52942145273938, 2058752360562, 514688090290, 332913328338, 18911474, 525682, 15090, 574461671961619, 152494728192051, 381202200207443, 209038001909875, 82888307389587, 14959268974259, 6232405524691, 3989396632563, 2195072461715, 438795544627, 397040146899, 259134474611, 30646564243, 28486426035, 18005553107, 985951219, 15041843, 1907, 1480712487174164, 129159621771316, 212199004717140, 29310132289652, 11703134306452, 732151333044, 8776974495956, 2194261042420, 609561760020, 386768535860, 213330039892, 60951647604, 15238347668, 1881218804, 16692, 711156082779669, 42295313313845, 69191582220373, 180873578907765, 108349088196245, 9550527402421, 2729397648597, 4358152808309, 3039028090837, 120884430261, 436396695317, 214094555509, 15965808021, 30485487029, 20036409301, 1281747957, 213625141, 2809589, 2101, 77063994998806, 289092173561910, 136123492515926, 6408721907830, 16911180103830, 20026534846646, 1023571427542, 267842765046, 356093522230, 255927195990, 33388775798, 33383052694, 1240013238, 2679064054, 446511158, 5741430, 2155845730959383, 56104202797111, 473548126888023, 23499407425655, 25356928352407, 12685319995575, 10034482839767, 1556963721463, 836529389847, 143841153335, 129645453655, 50988663159, 48767091095, 12905423287, 3227849175, 1075950071, 358484535, 59858551, 14944407, 11967671, 2989015, 2295, 1130006362521624, 278642869862456, 1194393688, 69660717465720, 17415179366552, 483754982712, 241877145944, 115832, 19896, 1443411474186265, 396712037449785, 81561741281369, 16381832822905, 86190438776985, 68791340427449, 10204188254425, 9418904681721, 3830384443673, 501474834745, 315252228441, 63389454713, 48386378137, 9820901817, 8753412569, 1986177529, 389256761, 73502841, 19499417, 4463545, 554841, 455033, 2489, 2333789363994650, 1078857398845498, 130541797933146, 44048453640314, 112433284528282, 40999457913018, 2673129019610, 6710375716090, 5443407028506, 482775759674, 315156428122, 92472938874, 43777511834, 859963898, 143327802, 18289786, 2924474, 664314, 1889718030434331, 1118813742563387, 57356787253339, 41755004928123, 112690666561691, 41536738123963, 2772091994331, 6922789687547, 5663073927451, 506676087099, 329838760283, 97904443771, 45900546459, 919683579, 153281083, 19741307, 3290811, 710395, 32525917618204, 355529505374268, 171783602454620, 8080216031356, 20200540078236, 25250675097788, 1010027004124, 476957196604, 294591209820, 46760509820, 44422484380, 3247258108, 541210172, 2506364, 34236, 52222710251549, 133741506723901, 166407255982173, 25076532510845, 48063353979037, 24031676989629, 2089711042781, 1393140695293, 116095058237, 130606940509, 111257764221, 9674588573, 3090493949, 515082813, 2385405, 69949, 61638258327582, 103649667711038, 529129639821406, 77737250783358, 8637472309406, 3239052116158, 12416366444766, 3239052116222, 89973670206, 59982446942, 555393534, 92566078, 429310, 411518, 713991294812191, 1335773195403327, 657149625630815, 240734712103039, 42930529763487, 41774731002047, 21567881871583, 13026917007615, 6492771827999, 1043422249279, 743008371039, 407622648191, 118674948511, 318505599, 53084863, 738111]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s := Explode([GPC.1, GPC.3, GPC.5, GPC.6, GPC.8, GPC.10, GPC.12, GPC.14, GPC.16, GPC.18, GPC.20, GPC.22, GPC.24, GPC.26, GPC.28, GPC.29, GPC.30, GPC.31, GPC.32]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "d", "d2", "e", "e2", "f", "f2", "g", "g2", "h", "h2", "i", "i2", "j", "j2", "k", "k2", "l", "l2", "m", "m2", "n", "n2", "o", "p", "q", "r", "s"]); GPerm := PermutationGroup< 36 | (1,23,25,34,15,12)(2,24,26,36,13,10,3,22,27,35,14,11)(4,19,6,21)(5,20)(7,18,8,17)(9,16)(28,33,30,31)(29,32), (1,27,2,25)(3,26)(4,29,18)(5,28,17,6,30,16)(7,21,8,19,9,20)(10,12)(13,14,15)(22,23)(31,32)(34,35), (1,21,15,7,26,32,3,20,14,9,27,31,2,19,13,8,25,33)(4,23,18,35,30,11)(5,22,16,34,28,12,6,24,17,36,29,10), (1,29,25,16,13,5)(2,30,26,18,15,6)(3,28,27,17,14,4)(7,11,20,35,32,23,8,12,21,34,33,24)(9,10,19,36,31,22) >; /* Booleans */ RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; booleans_2821109907456_j := rec< RF | Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, nilpotent := false, perfect := false, quasisimple := false, solvable := true, supersolvable := false>;