/* Group 2654208.dt downloaded from the LMFDB on 09 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([19, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 38, 32746900, 12703478, 31016343, 14995600, 81431267, 7005702, 22611409, 212, 121130324, 91565583, 15714182, 10060960, 15675461, 76026168, 30589435, 25718918, 12097989, 141516262, 106336185, 55016292, 16961819, 7955078, 8616639, 386, 94439431, 111375898, 72347181, 15131968, 11590995, 904198, 18911240, 2134107, 96925582, 20169857, 1998732, 4207, 3603434, 1999815, 207619849, 17182108, 104843567, 21532386, 2736085, 34304, 2807943, 278872, 93071, 560, 439348106, 3130013, 7463856, 20284771, 8186198, 30201, 2362660, 393371147, 157987614, 116487985, 21242372, 12016599, 10440682, 7645877, 2634912, 905095, 676, 5216652, 80241439, 8678642, 24044037, 18993400, 5655419, 5015214, 1467325, 359444749, 93768224, 49642035, 4136902, 9652697, 4826412, 2930383, 1206722, 143824, 67235, 24162, 11413, 425502734, 183202593, 56142772, 19206791, 22900410, 11450269, 5540528, 2585667, 123305, 66894, 51523, 24182, 151289871, 3151906, 115306037, 788040, 459739, 14413358, 98625, 3160228, 1182119, 167443216, 90419363, 129210390, 47721385, 25604948, 24523563, 6174598, 5346122, 1395528, 104839, 35090, 52551, 22531, 460961297, 212751396, 99284023, 3545930, 11524125, 5762128, 6870227, 1440654, 369548, 191043, 59734, 13583, 284456466, 270108901, 2183384, 60821355, 30020854, 234041, 8441034, 3801481, 156122]); a,b,c,d,e,f,g,h,i,j,k,l,m,n := Explode([GPC.1, GPC.3, GPC.4, GPC.6, GPC.7, GPC.9, GPC.10, GPC.12, GPC.14, GPC.15, GPC.16, GPC.17, GPC.18, GPC.19]); AssignNames(~GPC, ["a", "a2", "b", "c", "c2", "d", "e", "e2", "f", "g", "g2", "h", "h2", "i", "j", "k", "l", "m", "n"]);
GPerm := PermutationGroup< 24 | (1,23,16,10,5,21,14,7,3,20,18,11)(2,24,15,9,6,22,13,8,4,19,17,12), (1,15)(2,16)(3,18)(4,17)(5,14)(6,13)(9,12)(10,11)(21,24)(22,23), (1,22,17,11,4,23,13,10,5,20,15,8)(2,21,18,12,3,24,14,9,6,19,16,7) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_2654208_dt := 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>;