/* Group 6718464.qj downloaded from the LMFDB on 23 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([18, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 104575536, 212344633, 91, 64725050, 49742678, 14227203, 184369557, 47333847, 201, 528940804, 31570582, 76885600, 256, 381957125, 67060247, 99146633, 1679711, 184672662, 322837728, 84984522, 102010668, 4020486, 12511644, 366, 67836679, 236928409, 58000939, 3605821, 6756559, 4509601, 421, 340573256, 527775290, 68356268, 29699198, 7566128, 2526002, 476, 84602889, 57231387, 56033325, 39214143, 19595601, 5859, 917002954, 372534652, 91973422, 99057088, 42229522, 25670404, 6372550, 515728, 733150, 586, 21897227, 262766621, 53775407, 33689153, 23563091, 8418917, 2519543, 425225, 1475003, 567171084, 90215454, 368948784, 140714562, 35313492, 3774054, 5537496, 3661770, 236028, 78816, 258061, 156828703, 36578353, 1741891, 1850809, 1252075, 54589, 9265, 1192181774, 271226912, 121513010, 22394948, 8644442, 4438940, 175118, 116834, 769720335, 38486049, 125632563, 8971899, 3366285, 560031, 690923536, 45121570, 274228, 76162246, 4768792, 19035754, 1204540, 1197214, 1189888, 1028505617, 285161507, 126406709, 182145095, 104322905, 47029355, 33468029, 10785455, 2939489, 1049957]); a,b,c,d,e,f,g,h,i,j,k := Explode([GPC.1, GPC.2, GPC.4, GPC.7, GPC.11, GPC.13, GPC.14, GPC.15, GPC.16, GPC.17, GPC.18]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "c4", "d", "d2", "d4", "d8", "e", "e2", "f", "g", "h", "i", "j", "k"]);
GPerm := PermutationGroup< 36 | (1,33,7,31,9,34,3,36)(2,30,4,32,8,28,6,35)(5,29)(10,27)(11,23,18,22,12,19,14,20)(13,24,15,25,16,21,17,26), (1,13,7,17,3,10,6,18)(2,16)(4,12,5,15,9,14,8,11)(19,34,27,31,24,30,25,33)(20,36,22,29,23,28,21,35)(26,32), (1,26,6,27,4,24,7,19,2,23,9,22,8,25,5,21)(3,20)(10,36)(11,33,15,35,13,32,18,31,12,30,17,34,16,28,14,29), (1,31,8,30,6,35)(2,33,9,29,4,34)(3,32,7,28,5,36)(10,21)(11,23)(12,25)(13,20)(14,22)(15,27)(16,19)(17,24)(18,26) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_6718464_qj := 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>;