/* Group 39930.c downloaded from the LMFDB on 17 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([6, 2, 11, 3, 11, 5, 11, 12, 78014, 132074, 887043, 3975, 20986, 178, 60497]); a,b,c,d := Explode([GPC.1, GPC.3, GPC.4, GPC.5]); AssignNames(~GPC, ["a", "a2", "b", "c", "d", "d5"]);
GPerm := PermutationGroup< 38 | (1,3,10)(2,7,19)(4,14,24)(5,17,29)(6,18,30)(8,11,23)(9,22,31)(12,26,21)(13,25,16)(15,28,33)(20,27,32), (34,37,35,38,36), (1,8,4,20,15,9,5,21,16,6,2)(3,7,18,13,12,17,22,28,27,14,11)(10,19,30,25,26,29,31,33,32,24,23), (1,16,9,4,2,21,15,8,6,5,20)(3,13,22,14,7,12,28,11,18,17,27)(10,31,19,33,30,32,25,24,26,23,29), (1,5,8,21,4,16,20,6,15,2,9)(3,17,11,12,14,13,27,18,28,7,22)(10,29,23,26,24,25,32,30,33,19,31), (3,10)(7,19)(11,23)(12,26)(13,25)(14,24)(17,29)(18,30)(22,31)(27,32)(28,33) >;
GLFp := MatrixGroup< 4, GF(11) | [[3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3], [0, 3, 2, 7, 3, 9, 2, 2, 4, 1, 10, 8, 0, 4, 8, 8], [1, 8, 0, 0, 1, 7, 6, 7, 1, 1, 8, 2, 7, 7, 9, 6], [3, 2, 4, 10, 8, 6, 8, 0, 1, 1, 8, 3, 10, 6, 2, 10], [4, 0, 0, 0, 5, 9, 4, 0, 2, 2, 10, 0, 2, 2, 6, 4], [3, 2, 9, 8, 10, 6, 4, 9, 6, 4, 1, 9, 0, 6, 1, 4]] >;
GLZq := MatrixGroup< 2, Integers(121) | [[60, 23, 46, 60], [27, 0, 0, 27], [56, 0, 0, 1], [34, 110, 22, 23], [111, 0, 0, 111], [120, 0, 0, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_39930_c := rec< RF |  
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>;