/* Group 5668704.il downloaded from the LMFDB on 19 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([16, 2, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 68779392, 80812353, 81, 180286082, 299401347, 1329043, 1379, 179, 264003844, 4820, 3396, 308, 24012293, 6933, 239070726, 45855958, 12053702, 39080214, 20576374, 326, 140353543, 88639511, 14736423, 23593015, 16798535, 503, 292263560, 186648, 31160, 347431689, 66251545, 53343401, 61430457, 4225033, 4518809, 3343785, 1375321, 473, 689762314, 2052890, 342202, 38122, 88826, 510603275, 746523, 124475, 387179, 3579, 53374476, 14556700, 77635644, 43670092, 7644, 1160054797, 29611037, 4935229, 40429, 238013, 57853454, 83980830, 27993662, 18895758, 77918, 7962639, 483729439, 13436991, 14929999, 248991]); a,b,c,d,e,f,g,h,i,j := Explode([GPC.1, GPC.2, GPC.4, GPC.7, GPC.10, GPC.12, GPC.13, GPC.14, GPC.15, GPC.16]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "c6", "d", "d2", "d6", "e", "e2", "f", "g", "h", "i", "j"]);
GPerm := PermutationGroup< 36 | (1,35,33,29,26,23,19,17,13,11,9,6,3,36,32,30,27,22,20,18,14,12,8,5,2,34,31,28,25,24,21,16,15,10,7,4), (1,28,33,36)(2,29,32,35)(3,30,31,34)(4,8,23,27)(5,9,22,25)(6,7,24,26)(10,13,17,21)(11,14,16,20)(12,15,18,19), (1,18,2,16)(3,17)(4,26,30,15,5,25,28,13,6,27,29,14)(7,12,33,22,9,11,31,24,8,10,32,23)(19,36)(20,35,21,34) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_5668704_il := 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>;