/* Group 2048.cqy downloaded from the LMFDB on 04 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([11, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 133, 56, 17251, 5822, 1521, 740, 1247, 158, 34502, 12337, 3724, 974, 226, 19027, 35220, 158762, 87141, 34880, 17467, 8766]); a,b,c,d,e,f,g,h := Explode([GPC.1, GPC.2, GPC.4, GPC.5, GPC.7, GPC.9, GPC.10, GPC.11]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "d2", "e", "e2", "f", "g", "h"]);
GPerm := PermutationGroup< 26 | (3,9)(6,12)(10,15)(13,16)(17,18)(19,21)(20,22)(23,24)(25,26), (17,19)(18,21)(20,23)(22,24), (1,3,4,9)(2,6,7,12)(5,10,11,15)(8,13,14,16)(17,20)(18,22)(19,23)(21,24)(25,26), (1,4)(2,7)(3,9)(6,12)(17,21,19,18)(20,24,23,22), (1,4)(2,7)(8,14)(10,15)(17,19)(18,21), (1,2)(3,6)(4,7)(5,8)(9,12)(10,13)(11,14)(15,16)(17,19)(18,21)(20,23)(22,24), (1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)(17,22)(18,20)(19,24)(21,23), (25,26) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_2048_cqy := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := true,
solvable := true,
supersolvable := true>;