/* Group 3168.c downloaded from the LMFDB on 21 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([8, -2, -2, -2, -3, -3, -11, -2, -2, 47841, 41, 48482, 66, 2563, 123, 9604, 156, 34565, 166]); a,b,c := Explode([GPC.1, GPC.2, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "b4", "b12", "b36", "c", "c2"]);
GPerm := PermutationGroup< 28 | (2,4)(3,5)(6,9)(7,8)(10,11)(21,22)(23,25)(24,27)(26,28), (1,2,5,8,9,10,11,6,7,3,4)(12,13,14,15,16,17,18,19,20)(21,23,26,24), (1,3,6,10,8,2,4,7,11,9,5)(21,24,26,23)(22,25,28,27) >;
GLFp := MatrixGroup< 2, GF(397) | [[5, 0, 0, 219], [282, 0, 0, 252], [0, 1, 1, 0]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_3168_c := rec< RF |  
Agroup := false,
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>;