/* Group 14700.c downloaded from the LMFDB on 20 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([7, -2, -5, -7, -2, -3, -5, -7, 14, 78, 80, 137, 250]); a,b := Explode([GPC.1, GPC.4]); AssignNames(~GPC, ["a", "a2", "a10", "b", "b2", "b6", "b30"]);
GPerm := PermutationGroup< 31 | (3,4)(5,6,7)(13,14,15,16,17)(25,26,27,28,29,30,31), (1,2)(8,9,10,11,12)(18,19,20,21,22,23,24) >;
GLFp := MatrixGroup< 2, GF(211) | [[1, 0, 0, 2], [8, 0, 0, 132]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_14700_c := rec< RF |  
Agroup := true,
Zgroup := false,
abelian := true,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>;