/* Group 49800.b downloaded from the LMFDB on 26 June 2026. */
 
/* 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, -2, -2, -3, -5, -5, -83, 167300, 13973, 36, 41918, 58, 111779, 108, 419164, 207, 423365, 250]); a,b := Explode([GPC.1, GPC.2]); AssignNames(~GPC, ["a", "b", "b2", "b4", "b12", "b60", "b300"]);
GPerm := PermutationGroup< 119 | (1,2,4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55,58,61,64,67,70,73,76,79,82,81,83,78,80,75,77,72,74,69,71,66,68,63,65,60,62,57,59,54,56,51,53,48,50,45,47,42,44,39,41,36,38,33,35,30,32,27,29,24,26,21,23,18,20,15,17,12,14,9,11,6,8,3,5)(84,85,86)(87,88,89,91,93,95,97,99,101,103,105,107,109,111,110,108,106,104,102,100,98,96,94,92,90)(112,113,115,118)(114,117,119,116), (1,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,79,73,67,61,55,49,43,37,31,25,19,13,7,2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47,50,53,56,59,62,65,68,71,74,77,80,83,82,76,70,64,58,52,46,40,34,28,22,16,10,4)(84,85,86)(88,90)(89,92)(91,94)(93,96)(95,98)(97,100)(99,102)(101,104)(103,106)(105,108)(107,110)(109,111)(112,114,115,119)(113,116,118,117) >;
GLFp := MatrixGroup< 2, GF(499) | [[436, 74, 132, 63], [287, 49, 7, 287]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_49800_b := 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>;