/* Group 2821109907456.cx downloaded from the LMFDB on 27 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, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 34130183872512, 80310943994241, 161, 45239925412226, 34514624732226, 190277572232195, 36496405205539, 60336191447363, 15018930569315, 251018174609924, 132339947805476, 91381739602628, 39957206372900, 452, 29588890048517, 189568620432421, 45009541953093, 54982253261669, 7864057829541, 453895238092806, 40665621742630, 157896285134406, 57407424870758, 3524217338118, 2352770171750, 646, 91664089251847, 212742452363303, 92184292892743, 65293669642343, 10492033366151, 16151107015847, 2386520534247, 656876325740552, 376649862783016, 53693165113416, 9124197378152, 11222273793160, 19487489239464, 1945699527368, 1384220286952, 2645113024776, 849516960399369, 160705019658281, 200525502095433, 5747114649705, 19417421706377, 23304301831849, 5730296161481, 6351506793833, 3429721631305, 937, 568812944375818, 396260789354538, 2691571841098, 382590591082, 23174275289226, 25863360534698, 7033222254282, 7252888195050, 1284422872394, 22437124079627, 39592247525419, 96994390696011, 64292725936235, 57940013512843, 33022758122667, 5391954922187, 160467927787, 3090995365515, 762325394987, 419555415499, 1131, 1111091721732108, 1595083509804, 132874779062348, 128435254738028, 63369667951756, 20733638575276, 7155497095756, 1680891324140, 429135558028, 84506652972, 619570803404, 21563373708, 90409911975949, 37033463513133, 160305684811853, 139429416075373, 76852161663117, 3715228532909, 10019105300941, 4750307348205, 1977196096781, 754274605, 377113293, 25674781805, 111205158349, 1325, 195452479733806, 154793410638, 79357660692590, 5288774860942, 9674588366, 4232022681838, 3899244096270, 11886, 1291066862469135, 97911309271087, 89232563208271, 88234237575279, 63698408685711, 31742736040111, 2141548787919, 7664797864175, 3229312168207, 1625339990319, 88456873295, 38009413999, 62529500559, 34791361967, 1519, 491347717521424, 499470139707440, 357386944745552, 106848432918640, 9943286304400, 15125586776240, 22254102875344, 2649156351216, 563912741648, 1633658112304, 853863144528, 292991374064, 65757608464, 3996082992, 853079568, 343305077981201, 481577413312561, 333206912065617, 101428382269553, 59646002835601, 47141988305073, 1345239664337, 5752855001329, 745107082257, 852335011889, 629333484241, 33503124465, 156679065041, 47686185649, 2786189681, 462954193, 1713, 1316804314005522, 761866196484146, 16012820938834, 201104159146098, 23919863390354, 36277157892274, 13618829168850, 13232813101298, 4683428329234, 1170759702834, 906548516690, 24745347442, 3214909842, 35564191922, 1249994994, 1297413233049619, 735099565588531, 65919099740243, 86431367331955, 78520727582867, 16626057892019, 26310134377171, 3187535155443, 362756621075, 56112514867, 980212700499, 351421371251, 143605267603, 55808179635, 338312179, 118345491, 1054038323, 801702355, 1907, 637277050109972, 476478051409972, 222672925569108, 83433994592372, 62126854218388, 16722864378036, 5091083730644, 7845443827444, 6843043856148, 2329151376692, 156343227636, 110825584532, 10312525940, 1408507156, 363469236, 257649428, 36167700, 302253053313045, 39071801032757, 203750548734037, 14984267341941, 80121181713557, 2269515055285, 11755340974293, 902209093877, 729867055381, 243289018677, 1105015634261, 25783972213, 168299569557, 5172305333, 2317151733, 1736799509, 204197173, 85169109, 98622581, 24675157, 2101, 427862746202134, 853246504599606, 73578477994070, 27176568201334, 9339059110038, 3296526518, 2838309811414, 4690132844790, 587193753878, 195731251510, 802944534870, 92852158838, 78407122582, 7100504502, 900758518, 197236790, 18294, 1394336744865815, 229465460736055, 491723654234199, 246561192345719, 119367847784599, 28583280083127, 15191296782551, 255624118519, 2624393613591, 42854842679, 837926830423, 245490352503, 123240683927, 7413203383, 2939701751, 570572311, 381100599, 315602519, 90792055, 11315607, 6336695, 2295, 2030709856665624, 662544462643256, 415133016883288, 142737677107320, 139962625228952, 57668972544184, 17549525145816, 1653190041848, 1549277971480, 276054221112, 1255904870744, 364078886776, 235830874008, 5889024440, 1281485304, 163584568, 78125432, 1904394664673305, 102672749297721, 432556145049689, 18334419517561, 30363587444889, 59512333271225, 14671011963097, 1320115470585, 5256006672665, 1752002224441, 144441004377, 413280092537, 24073501081, 12939769, 2157113, 1828721039376410, 500601913638970, 595923695861850, 246499739467898, 43330025889946, 2249682149562, 30551437191386, 778320617722, 1645647632922, 626590826810, 1351781831002, 181170847098, 252359318426, 6467641786, 1601234426, 1238437402, 179657274, 135821434, 39222810, 3982010, 3302970, 241945540558875, 864458710843451, 382856593932379, 285670816284795, 57532161835163, 47038389092539, 20647776780507, 1047435411707, 567862493499, 517614741883, 116507511195, 1502614011, 58254971, 55513243, 5441211, 3457531, 2462504026374172, 1234211433873468, 544813815398492, 133063636377724, 104206795923612, 21451758944444, 27025217188060, 6416581017852, 5984046305564, 1389393285436, 181370161500, 265611640700, 280527176860, 3167880700, 1266431004, 33675836, 140180604, 35179292, 3152252, 1851939127296029, 622673056235581, 199306097786973, 3266706309245, 15250876784797, 19307631329469, 21788249149661, 2802943181053, 2249341954845, 447360123197, 1376210166109, 227816479101, 124440883613, 10679869885, 3023309309, 598441501, 296663613, 9838717, 60065949, 7523261, 3571965, 1353682538201118, 1130615498833982, 46404705337438, 193112211582, 109793946452126, 21557775642814, 955338568926, 6445891436798, 959719574302, 302781763902, 677301793118, 511455693694, 220267330974, 20814382526, 2486412798, 930798110, 578177854, 134646782, 11511870, 881662, 462903387881503, 380997501714495, 244735162712159, 147611003388031, 50986320003231, 2685379018943, 434569937119, 8239022604543, 1881886556447, 721318183231, 1880262181215, 100456464767, 20265099679, 96889209279, 13900530175, 4508172831, 1176404543, 411697791, 90944159, 31912639, 6384383]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u := Explode([GPC.1, GPC.2, GPC.4, GPC.5, GPC.7, GPC.9, GPC.10, GPC.12, GPC.14, GPC.16, GPC.18, GPC.20, GPC.22, GPC.24, GPC.26, GPC.27, GPC.28, GPC.29, GPC.30, GPC.31, GPC.32]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "d2", "e", "e2", "f", "g", "g2", "h", "h2", "i", "i2", "j", "j2", "k", "k2", "l", "l2", "m", "m2", "n", "n2", "o", "p", "q", "r", "s", "t", "u"]); GPerm := PermutationGroup< 36 | (1,27,15,2,26,14,3,25,13)(4,30,16)(5,28,17)(6,29,18)(7,33)(8,32,9,31)(10,23)(11,22)(12,24)(34,36), (1,35)(2,36)(3,34)(4,7,29,20,5,9,28,19)(6,8,30,21)(10,13,24,26,12,15,22,27,11,14,23,25)(16,33)(17,32,18,31), (1,17,32,22)(2,16,33,24)(3,18,31,23)(4,8,35,26,30,21,12,14)(5,7,34,25,29,20,11,13,6,9,36,27,28,19,10,15), (1,31,25,19,15,9,3,32,26,20,13,8,2,33,27,21,14,7)(4,34,17,10,28,22)(5,35,18,11,29,23)(6,36,16,12,30,24) >; /* Booleans */ RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; booleans_2821109907456_cx := rec< RF | Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false>;