/* Group 408146688.wn downloaded from the LMFDB on 08 November 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([21, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3906643104, 4488967141, 106, 10096220234, 2758725692, 12847561779, 3846065856, 329306841, 234, 29821939564, 2761727245, 7760896336, 1220002648, 6573220421, 18514458170, 10739488079, 1607652212, 855890117, 362, 15317701062, 23841948843, 4142492976, 882712725, 1790052018, 56257689607, 27756380764, 10791887953, 1856457190, 474366907, 80923360, 490, 35460307016, 19312156109, 358951874, 31755095, 366282092, 359416877, 43885084329, 19118267310, 14946898731, 5245238952, 2440080813, 620260314, 639307755, 32358216, 16957887, 618, 65964929194, 20245024831, 8239027156, 664758937, 66622, 316123, 52825, 59560812875, 12436653632, 5453378837, 2020870730, 712732703, 420922772, 20602649, 56945102, 11272139, 10304480, 10049, 746, 110984406636, 9572655489, 6074647542, 8156940867, 923674848, 665748837, 18493221, 33085075981, 11939768098, 12962436535, 342921676, 1524193, 762166, 127168, 3772, 66261222734, 61464629555, 27974245376, 3297147917, 342921698, 240045239, 6668123, 1111565, 17161611279, 45054600228, 17742509625, 6646413390, 1270080099, 318173304, 725922, 8826252, 855030, 82164446800, 62878992661, 8213661850, 7627959103, 1648963108, 637099465, 106183387, 17697409, 2911225, 126406816721, 75263162726, 25178283707, 1042720640, 617585573, 221266202, 154396532, 6132878, 4452332, 123330031794, 29280535239, 3612143868, 2114633049, 828400710, 772553499, 176849733, 21460023, 3921621, 117102867859, 66446997160, 22151646781, 9254431282, 1411240423, 1014975484, 66225766, 28178848, 3314050, 32658413780, 29885257625, 23490891710, 2765013635, 3642208520, 2161358765, 344731631, 101172665, 8599751]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o := 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]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "d2", "e", "e2", "f", "f2", "g", "g2", "h", "i", "j", "k", "l", "m", "n", "o"]);
GPerm := PermutationGroup< 36 | (1,8,2,9)(3,7)(4,36)(5,34,6,35)(10,32,13,30,11,33,15,29,12,31,14,28)(16,26,20,23,18,25,19,24,17,27,21,22), (1,35)(2,36)(3,34)(4,33,8,28)(5,31,9,29)(6,32,7,30)(10,23,11,22,12,24)(13,25,14,27,15,26)(16,18)(19,20), (1,31,26,18,10,8,3,33,27,16,11,9,2,32,25,17,12,7)(4,35,28,22,20,14,5,36,30,23,19,15,6,34,29,24,21,13) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_408146688_wn := 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>;