/* Group 512.10494213 downloaded from the LMFDB on 29 December 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([9, -2, 2, 2, 2, 2, 2, 2, 2, 2]); a,b,c,d,e,f,g,h,i := Explode([GPC.1, GPC.2, GPC.3, GPC.4, GPC.5, GPC.6, GPC.7, GPC.8, GPC.9]); AssignNames(~GPC, ["a", "b", "c", "d", "e", "f", "g", "h", "i"]);
GPerm := PermutationGroup< 18 | (1,2), (3,4), (5,6), (7,8), (9,10), (11,12), (13,14), (15,16), (17,18) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_512_10494213 := rec< RF |  
Agroup := true,
Zgroup := false,
abelian := true,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := true,
solvable := true,
supersolvable := true>;