/* Group 408146688.wu downloaded from the LMFDB on 03 February 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([21, 2, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 105094332, 15423255709, 106, 6820858550, 4361314148, 19194630339, 7576315008, 3981312765, 1721938242, 35047121764, 16021600585, 8842288816, 1398570877, 298, 30562564037, 18000487034, 12251557631, 4048653236, 14016805746, 872417097, 4548909315, 3369785145, 317531556, 47438040, 426, 5079158791, 3454907932, 1105332529, 3715318726, 60397835660, 28135736399, 8237704343, 4180935599, 2593991072, 60994571, 289393532, 554, 43345290249, 29843976990, 21290532531, 4644198792, 2322099453, 387016695, 7830783586, 18784610491, 7825652656, 7216258969, 2719182406, 709546183, 222178708, 118257835, 70959220, 682, 84514183499, 11876421344, 24134516837, 8188532426, 114525023, 602598665, 100433267, 59229994836, 32627659461, 21298204800, 4930196619, 4536880080, 2262071565, 26830578, 377012067, 108845280, 41931363, 414636, 9067392, 810, 71330825677, 13826613058, 11298928087, 9329499724, 254155, 42517, 63198848174, 45210780755, 1971035696, 4192080557, 5199616898, 816620, 74776142, 24619364, 4103456, 115693111311, 46715719716, 560867385, 31352910, 15676515, 2612877, 435639, 12363, 131169568336, 27062970517, 22232494930, 10973037679, 5986204660, 697709518, 30150976, 9009478, 1501810, 93965852753, 22292625638, 28393962971, 10421550800, 6298326821, 890616527, 57480377, 28794755, 805409, 79452110322, 51045059559, 26471645484, 724635153, 6080453670, 83770992, 87821682, 28843140, 4807422, 108254623699, 61689670600, 5272349101, 12440978002, 4493180263, 872000785, 114398107, 20306389, 4450591, 169271584292, 24091396097, 13696484570, 3319862195, 2520473864, 193179314, 32196716, 24115874, 1773092]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o := Explode([GPC.1, GPC.2, GPC.4, GPC.5, GPC.7, GPC.9, GPC.11, GPC.13, GPC.15, GPC.16, GPC.17, GPC.18, GPC.19, GPC.20, GPC.21]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "d2", "e", "e2", "f", "f2", "g", "g2", "h", "h2", "i", "j", "k", "l", "m", "n", "o"]);
GPerm := PermutationGroup< 36 | (1,33,26,21,10,5,3,32,25,20,12,4,2,31,27,19,11,6)(7,35,30,22,17,14,9,34,28,24,16,15,8,36,29,23,18,13), (1,21)(2,19)(3,20)(4,12,8,13,6,10,9,14,5,11,7,15)(16,34,17,35,18,36)(22,31,27,29,23,33,26,28,24,32,25,30) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_408146688_wu := 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>;