/* Group 12754584.he 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([16, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 155868480, 211840801, 81, 18752546, 48354946, 805854531, 238706323, 48830435, 179, 670426564, 330125780, 49899396, 26272868, 1132296197, 232895253, 188699941, 52250933, 15085893, 10715413, 1320996102, 117441430, 133584230, 57783542, 21574, 1430, 804142087, 503884823, 208410663, 14556727, 43847, 21975, 227256200, 348641304, 1944040, 272504, 46018440, 15260488, 10040, 1848, 568, 1285839369, 125971225, 311081, 44789817, 51913, 2116414090, 69269402, 156017706, 92817530, 61414922, 14070762, 10349962, 2656490, 537114, 3338, 2047527947, 463085595, 396389419, 67399739, 39191115, 28226971, 6547499, 1462011, 1054219, 2475, 763, 1738309260, 720959644, 10917548, 96572796, 1819660, 1515386893, 776901917, 329204781, 43271485, 38211341, 20085501, 744045, 48557, 6237, 2984117774, 831928350, 484989166, 151260542, 34642158, 24669454, 913822, 6654, 17470, 179159055, 416655391, 47029295, 69599295, 53747791, 10637663, 394127, 96943, 37055]); a,b,c,d,e,f,g,h,i,j,k,l := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.7, GPC.8, GPC.9, GPC.11, GPC.12, GPC.14, GPC.15, GPC.16]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "e", "f", "g", "g3", "h", "i", "i3", "j", "k", "l"]);
GPerm := PermutationGroup< 36 | (1,4,15,28,2,6,14,29,3,5,13,30)(7,34,8,35)(9,36)(10,33,24,21,12,31,22,20,11,32,23,19)(16,26,18,25)(17,27), (1,33,12,2,32,11)(3,31,10)(4,29)(5,28)(6,30)(7,23,27,21,35,14,9,22,26,19,36,15,8,24,25,20,34,13)(17,18) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_12754584_he := 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>;