/* Group 1320.133 downloaded from the LMFDB on 24 February 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 */
GPerm := PermutationGroup< 12 | (1,4,3,9,5,7,10,11,6,8,12), (1,10,3,12)(2,5,8,9)(4,11,6,7) >;
GLFp := MatrixGroup< 3, GF(11) | [[7, 4, 10, 5, 4, 6, 9, 5, 9], [5, 7, 10, 1, 10, 6, 10, 8, 7]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1320_133 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := true,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := false,
supersolvable := false>;