/* Group 1430.10 downloaded from the LMFDB on 22 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([4, -2, -5, -11, -13, 4385, 45, 15722, 142]); a,b := Explode([GPC.1, GPC.2]); AssignNames(~GPC, ["a", "b", "b5", "b55"]);
GPerm := PermutationGroup< 29 | (2,3)(4,5)(6,7)(8,9)(10,11)(13,14)(15,16), (17,18,19,20,21,22,23,24,25,26,27,28,29), (12,13,15,16,14), (1,2,4,6,8,10,11,9,7,5,3) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1430_10 := rec< RF |  
Agroup := true,
Zgroup := true,
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>;