/* Group 331776.br downloaded from the LMFDB on 09 October 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([16, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 32, 3568913, 2666306, 392946, 130, 5449219, 7156499, 99844, 7886740, 691556, 320052, 4329989, 2002197, 4386853, 500597, 6405, 277, 872710, 2623510, 3067046, 655926, 31741959, 9391127, 8484903, 2347831, 3527, 375, 24908552, 4188696, 604840, 1047224, 245769, 17280025, 4701481, 4112697, 161369, 72105, 24121, 13577, 473, 236554, 17943578, 304874, 836410, 32016395, 4976667, 7465003, 2488379, 228187, 103787, 107259, 50251, 58406412, 23722012, 8132012, 6739260, 2426188, 292124, 134892, 93724, 50684, 21372, 11404, 32269, 6096429, 1306429, 217821, 12205, 4157, 18285, 59719694, 31726110, 362926, 7465022, 3732558, 82206, 10942, 39038, 17454, 3981327, 9263, 497743, 29343, 2479]); a,b,c,d,e,f,g,h,i,j,k := Explode([GPC.1, GPC.3, GPC.5, GPC.6, GPC.8, GPC.10, GPC.12, GPC.13, GPC.14, GPC.15, GPC.16]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "d", "d2", "e", "e2", "f", "f2", "g", "h", "i", "j", "k"]);
GPerm := PermutationGroup< 20 | (1,2,4,7)(3,5,9,14)(6,11)(8,12)(10,13)(15,16), (1,3,6,9,4,8,13,16)(2,5,10,14,7,12,11,15)(17,18,19,20) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_331776_br := 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>;