/* Group 12180.a downloaded from the LMFDB on 10 October 2026. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation, GPerm is permutation group 
	 GLZ, GLFp, GLZN, 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< 30 | (1,2,3)(4,5,7)(6,9,14)(8,12,19)(10,16,24)(11,13,20)(15,22,18)(17,25,26)(21,23,27)(28,30,29), (2,4,6,10,17,19,26,29,24,22,16,25,20,27)(5,8,13,9,15,23,12,14,21,28,30,7,11,18) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; 
booleans_12180_a := rec< RF | 
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := true,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := true,
quasisimple := true,
rational := false,
solvable := false,
supersolvable := false>;