/* Group 532400.d downloaded from the LMFDB on 18 November 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([9, -2, -5, -2, -11, -2, -2, -5, -11, -11, 18, 12620072, 3441296, 74, 1221123, 88572, 26166, 18423904, 2578963, 565312, 130, 2399765, 962294, 49919, 158, 2550246, 720735, 116448, 375, 633607, 633616, 316825, 7840808, 7840817, 3920426, 178244]); a,b,c,d := Explode([GPC.1, GPC.3, GPC.5, GPC.9]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "c2", "c4", "c20", "d"]);
GPerm := PermutationGroup< 46 | (20,21,22,23,24), (1,2,5,3,4,9,7,8,11,6,10)(20,22,24,21,23)(26,32,35,43,34,40,37,44,36,46,45), (2,7,3,8,6,10,9,11,4,5)(12,13,14,16)(15,19,18,17)(20,23,21,24,22)(25,26,33,34,28,40,41,36,27,37)(29,35,42,45,38,32,31,44,30,43)(39,46), (12,14)(13,16)(15,18)(17,19)(20,21,22,23,24), (1,3,7,6,2,4,8,10,5,9,11)(20,24,23,22,21)(25,27,38,31,29,41,30,39,33,42,28)(26,34,36,32,40,46,35,37,45,43,44), (1,4,9,11,7)(2,8,3,5,10)(12,15,14,18)(13,17,16,19)(20,23,21,24,22)(25,28,38,29,42,41,30,31,27,39)(26,35,44,43,34,32,45,40,46,36), (1,2,3,8,4,6,11,7,5,9)(12,14)(13,16)(15,18)(17,19)(20,21,22,23,24)(25,29,27,30,41,31,28,38,33,42)(26,34,32,37,40,43,45,35,36,46), (1,5,4,7,11,10,2,3,9,8,6)(12,14)(13,16)(15,18)(17,19)(20,23,21,24,22)(25,30,27,39,38,33,31,42,29,28,41)(26,34,36,32,40,46,35,37,45,43,44), (1,6,10,4,8)(2,3,5,11,9)(20,23,21,24,22)(25,31,39,41,30)(26,36,34,37,40)(27,33,28,42,29)(32,35,44,45,43) >;
GLFp := MatrixGroup< 4, GF(11) | [[2, 0, 0, 0, 5, 7, 4, 0, 10, 10, 10, 0, 8, 10, 6, 4], [4, 0, 0, 0, 5, 9, 4, 0, 2, 2, 10, 0, 2, 2, 6, 4], [8, 2, 9, 5, 10, 5, 10, 8, 8, 5, 4, 0, 3, 5, 7, 5], [3, 2, 9, 8, 10, 6, 4, 9, 6, 4, 1, 9, 0, 6, 1, 4], [9, 0, 0, 0, 7, 5, 10, 0, 6, 6, 5, 0, 3, 6, 4, 1], [2, 9, 1, 9, 8, 8, 9, 5, 10, 5, 2, 0, 3, 6, 0, 10], [3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3], [8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8], [0, 10, 3, 5, 10, 8, 3, 3, 6, 7, 4, 1, 0, 6, 1, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_532400_d := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>;