/* Group 16529940864.y downloaded from the LMFDB on 24 July 2026. */
 
/* 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([24, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 73836703008, 788726420257, 121, 132190577570, 228239875587, 715905595611, 42576533619, 267, 897340573444, 634792829788, 424558463812, 56120169700, 667016140613, 609111428285, 351997077221, 60506128301, 501282965, 413, 1291993016838, 1354502507934, 514070686134, 99327082254, 23481094998, 2911241238, 1424895446023, 431909853727, 595045778743, 137632843087, 64391753191, 40072740607, 20591180503, 559, 3019774919048, 33526441760, 674506927352, 114478723088, 58157831624, 28395593408, 9589675688, 1428513608, 1505099370249, 177637518753, 676576428537, 266605897041, 127358153385, 8392135809, 16315503993, 7766255697, 3545805081, 705, 2480280168970, 1115297194210, 186710100250, 209526495634, 86292537514, 49891020034, 8027449210, 5092987858, 3512024410, 2162747464715, 1208395438883, 393169645499, 61925015891, 126674585963, 8200538627, 22945638683, 1595521331, 3831396107, 291111203, 449640539, 851, 5093495986188, 1039899534372, 1145260726332, 148550837844, 74606987628, 24412752132, 12434498076, 703729908, 687810468, 3455238850573, 1856986435621, 17102969917, 36512985685, 87921179245, 21219480709, 27510150685, 1041393205, 4792483789, 749262757, 119764789, 4410301, 290036090894, 830144609318, 1230721827902, 46223032406, 165790696430, 39924316934, 28735430558, 4959066422, 4789238606, 826511270, 401397374, 13238, 44091326, 734671503375, 2122216464423, 345349951551, 152641511511, 54745030767, 50607618183, 31075633311, 11771827383, 2151069903, 1188974823, 801239295, 278005527, 5049519, 7839711, 2304823569424, 1919383423528, 1064889047872, 386787446872, 180443666416, 35977903624, 25679794336, 14490064696, 7448285008, 211820776, 588286480, 301077352, 75313024, 903640, 100744, 2253372825617, 2622801005609, 804321073217, 504072917081, 23598604913, 143327369, 3009685409, 7261291193, 882856145, 709072937, 559776353, 165294713, 6419393, 1924889, 214217, 36689, 28905818130, 542090465322, 433250415426, 246672200538, 174097983858, 19908799626, 3264551586, 14179976826, 8150790450, 1404175626, 450570210, 13622826, 6316362, 55958370, 9345162, 6217938, 78378, 14106, 5019230085139, 1420454983723, 422513003587, 77633095771, 149874002035, 18522846859, 24069208483, 9777127867, 3488573011, 3004318315, 1272309379, 176293723, 4199347, 19712515, 6221179, 2657203, 30667, 109891, 6891148680212, 102852965420, 239990252636, 75711210764, 1899802460181, 2157978848301, 165826248261, 485552973405, 71833817205, 69012041613, 43904602533, 2436749757, 7442145429, 2110724589, 1454967621, 225153213, 4619277, 11932629, 5774061, 2994165, 71709, 347349, 8397, 8528474188822, 1420253429806, 1241348198470, 528185359966, 37549495414, 33042287374, 29990663590, 18615930814, 4868063926, 3232876558, 760551382, 275174494, 13279798, 26156878, 10060582, 1565326, 149470, 248854, 17038, 6112404799511, 1594049642543, 1528101199943, 528958107743, 108122480783]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.8, GPC.10, GPC.12, GPC.14, GPC.15, GPC.16, GPC.17, GPC.18, GPC.19, GPC.20, GPC.21, GPC.22, GPC.23, GPC.24]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "d2", "e", "e2", "f", "f2", "g", "g2", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r"]);
GPerm := PermutationGroup< 36 | (1,23,31)(2,22,32,3,24,33)(4,6)(7,26,36,8,25,34)(9,27,35)(10,21,14,11,20,15)(12,19,13)(16,28)(17,30)(18,29), (1,23,9,16,15,34,32,4,3,24,8,17,14,35,31,5,2,22,7,18,13,36,33,6)(10,19,28,25,12,20,30,26,11,21,29,27) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_16529940864_y := 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>;