/* Group 319440.x 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([9, -2, -5, -2, -11, -2, -2, -3, -11, 11, 18, 3926072, 74, 7203, 2148304, 1068232, 83686, 130, 6866645, 539375, 143780, 158, 10699926, 826080, 992409, 1900807, 90763, 44980, 5893, 23522408, 2352266, 73916, 31643, 13670]); a,b,c,d,e := Explode([GPC.1, GPC.3, GPC.5, GPC.8, GPC.9]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "c2", "c4", "d", "e"]);
GPerm := PermutationGroup< 53 | (1,2,8,12,23,32)(3,9,21)(4,14,22,6,11,26)(5,15,28,17,10,25)(7,19,20,18,27,31)(13,24,30,16,29,33)(38,39,40,42,41)(43,44)(45,49)(46,53)(48,52)(50,51), (38,40,41,39,42), (1,3,12,4,5,16,18,7,13,17,6)(2,9,23,14,15,29,27,19,24,10,11)(38,41,42,40,39)(43,45,48,46,50,47,51,53,52,49,44), (1,4)(2,8,9,21,23,32,14,22,15,28,29,33,27,31,19,20,24,30,10,25,11,26)(3,12)(5,6)(13,18)(16,17)(36,37)(38,41,42,40,39)(43,46)(44,50)(45,48)(47,49)(51,52), (34,35)(36,37)(38,40,41,39,42), (1,5)(2,10)(3,4)(6,16)(7,13)(8,20)(9,24)(14,27)(15,29)(17,18)(19,23)(21,31)(22,28)(26,30)(32,33)(34,36,35,37)(38,39,40,42,41)(43,47,44,50,49,46,52,48,53,45,51), (1,6,17,13,7,18,16,5,4,12,3)(8,21,32,22,28,33,31,20,30,25,26)(38,42,39,41,40)(43,48,50,51,52,44,45,46,47,53,49), (2,9)(3,6)(4,13)(5,7)(8,22)(10,14)(11,23)(12,17)(15,24)(16,18)(19,29)(21,32)(25,33)(26,28)(30,31)(38,40,41,39,42)(43,49)(45,52)(46,51)(47,50)(48,53), (1,7,4,6,18,12,17,16,3,13,5)(2,11,10,24,19,27,29,15,14,23,9)(8,22,31,25,21,28,20,26,32,33,30)(34,35)(36,37)(38,39,40,42,41)(43,48,50,51,52,44,45,46,47,53,49) >;
GLFp := MatrixGroup< 4, GF(11) | [[3, 0, 0, 0, 5, 8, 4, 0, 0, 0, 3, 0, 6, 0, 6, 8], [4, 0, 0, 0, 5, 9, 4, 0, 2, 2, 10, 0, 2, 2, 6, 4], [8, 2, 4, 4, 7, 2, 10, 2, 5, 2, 1, 6, 10, 2, 9, 0], [3, 2, 9, 8, 10, 6, 4, 9, 6, 4, 1, 9, 0, 6, 1, 4], [10, 2, 2, 0, 8, 3, 7, 8, 9, 1, 10, 7, 9, 7, 10, 10], [3, 1, 0, 9, 9, 2, 4, 0, 9, 10, 8, 6, 2, 6, 10, 9], [3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3], [8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8], [0, 10, 3, 5, 10, 8, 3, 3, 6, 7, 4, 1, 0, 6, 1, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_319440_x := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>;