/* Group 4251528.kp 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([15, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 49395420, 73488421, 76, 142132592, 5162162, 115479543, 65279178, 19700133, 168, 237149104, 66325519, 44979784, 4604914, 354592085, 62737220, 57301595, 9616370, 10235585, 148009686, 74826381, 2842596, 24492771, 12027396, 5571171, 449971207, 22124182, 79742917, 17243572, 1170787, 6367762, 2125897, 488916008, 123881423, 89025518, 20753873, 8325248, 7166153, 2366918, 6593, 307929609, 102643224, 31881654, 314665570, 37582435, 539835851, 246996026, 70124441, 10251416, 11722391, 10045706, 3484721, 635156, 37931, 368465772, 124717347, 3411777, 482373373, 32039308, 61349443, 41831218, 9219493, 6974188, 2341813, 160768, 54943, 12778, 97912814, 289105229, 24227144, 30440759, 4993724, 3080114, 1008554, 508394, 166184, 15029]); a,b,c,d,e,f,g,h,i,j,k,l,m := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.7, GPC.8, GPC.9, GPC.10, GPC.11, GPC.12, GPC.13, GPC.14, GPC.15]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m"]);
GPerm := PermutationGroup< 36 | (1,3,2)(4,21,36)(5,20,35)(6,19,34)(7,24,30,9,23,28,8,22,29)(10,16,32,11,18,33,12,17,31)(13,15,14)(25,27,26), (1,22,17,26,10,6)(2,24,18,27,12,4)(3,23,16,25,11,5)(7,21,9,20,8,19)(13,34,30)(14,36,28)(15,35,29)(31,33,32) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_4251528_kp := 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>;