/* Group 17640.i downloaded from the LMFDB on 26 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([8, -2, -3, -7, -2, -2, -3, -5, -7, 16, 57, 35298, 563139, 91, 702244, 116, 838661, 189, 959622, 334, 967687]); a,b := Explode([GPC.1, GPC.4]); AssignNames(~GPC, ["a", "a2", "a6", "b", "b2", "b4", "b12", "b60"]);
GPerm := PermutationGroup< 33 | (1,2,3,5,4)(6,7,8)(16,17,19,22)(18,21,23,20)(27,28,30,33,29,32,31), (2,4)(3,5)(7,8)(9,10,11,12,13,14,15)(16,18,19,23)(17,20,22,21)(24,25,26)(28,31)(29,33)(30,32), (6,8,7)(9,11,13,15,10,12,14)(24,26,25)(27,29,28,32,30,31,33) >;
GLFp := MatrixGroup< 2, GF(421) | [[2, 0, 0, 211], [1, 0, 0, 286], [0, 182, 1, 0]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_17640_i := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>;