/* Group 29400.c downloaded from the LMFDB on 23 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, -5, -7, -2, -2, -3, -5, -7, 16, 89, 35298, 468163, 91, 1170404, 116, 1397765, 189, 1599366, 334, 1612807]); a,b := Explode([GPC.1, GPC.4]); AssignNames(~GPC, ["a", "a2", "a10", "b", "b2", "b4", "b12", "b60"]);
GPerm := PermutationGroup< 31 | (2,3)(4,5)(7,8)(10,11)(12,13)(14,15), (1,2,4,5,3)(6,7,8)(9,10,12,14,15,13,11)(23,24)(25,26), (1,3,5,4,2)(6,8,7)(9,11,13,15,14,12,10)(16,17,18,19,20,21,22)(23,25,24,26)(27,28,29,30,31) >;
GLFp := MatrixGroup< 2, GF(421) | [[4, 0, 0, 316], [0, 1, 1, 0], [2, 0, 0, 32]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_29400_c := rec< RF |  
Agroup := true,
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>;