/* Group 250000.bm downloaded from the LMFDB on 05 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([10, -2, -2, -5, -2, -5, -2, -5, -5, 5, 5, 153200, 3850761, 51, 204482, 9728803, 1771613, 8223, 113, 2002004, 4014, 252005, 546015, 93025, 95435, 15345, 175, 5636, 3257, 3600008, 1800018, 18058, 20400009, 10200019, 1220039, 33059]); a,b,c,d,e,f,g := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.8, GPC.9, GPC.10]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "d2", "e", "f", "g"]);
GPerm := PermutationGroup< 30 | (1,2,6,3,7,10,4,8,9,5)(11,12)(13,14)(16,17,20,19,23)(26,27,30,29,28), (1,5,6,8,7,10,4,3,9,2)(11,12,14,15,13)(18,21,22,24,25)(27,28)(29,30), (1,3,6,2,7,5,4,8,9,10)(12,13)(14,15)(16,18,17,21,20,22,19,24,23,25)(26,28,29,30,27), (1,4,6,9,7)(2,8,3,5,10)(11,12,14,15,13)(16,19)(17,20)(18,22)(24,25)(26,29,27,28,30) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_250000_bm := rec< RF |  
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>;