/* Group 393216.ks downloaded from the LMFDB on 14 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([18, -2, -2, -3, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2622672, 5245705, 91, 489026, 10491555, 325317, 2622927, 201, 8899656, 4446834, 15520903, 7746649, 3880267, 2610818, 1289888, 6542, 26071209, 2458107, 1194525, 13023, 52367050, 28053460, 14102794, 26992, 77360843, 29541053, 19293599, 85964124, 28838190, 14779956, 121746, 64012045, 34264975, 17903641, 2706547, 94420094, 35672432, 19491890, 2623388, 94652943, 47464737, 24325107, 4570053, 19810474, 9023992, 2509270, 107759825, 30827987, 26689229, 5311079]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.7, GPC.8, GPC.9, GPC.10, GPC.11, GPC.12, GPC.13, GPC.14, GPC.15, GPC.16, GPC.17, GPC.18]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p"]);
GPerm := PermutationGroup< 40 | (2,7)(4,40)(5,11)(8,14)(20,24)(22,28)(25,31)(27,34), (2,7)(4,40)(5,11)(8,14)(9,16)(12,17)(13,18)(15,19)(20,24)(22,28)(25,31)(27,34)(29,36)(32,37)(33,38)(35,39), (1,21)(2,28)(3,23)(4,20)(5,31)(6,26)(7,22)(8,34)(9,36)(10,30)(11,25)(12,37)(13,38)(14,27)(15,39)(16,29)(17,32)(18,33)(19,35)(24,40), (1,6)(2,7)(3,10)(4,40)(5,11)(8,14)(12,17)(15,19)(20,24)(21,26)(22,28)(23,30)(25,31)(27,34)(32,37)(35,39), (2,22)(4,24)(5,25)(7,28)(8,27)(11,31)(14,34)(20,40), (1,10)(2,4)(3,6)(5,14)(7,40)(8,11)(9,13)(12,19)(15,17)(16,18)(20,28)(21,30)(22,24)(23,26)(25,34)(27,31)(29,33)(32,39)(35,37)(36,38), (1,9)(3,13)(6,16)(10,18)(12,17)(15,19)(21,29)(23,33)(26,36)(30,38)(32,37)(35,39), (9,29)(12,32)(13,33)(15,35)(16,36)(17,37)(18,38)(19,39), (2,7)(4,40)(12,17)(15,19)(20,24)(22,28)(32,37)(35,39), (1,3)(5,8)(6,10)(11,14)(21,23)(25,27)(26,30)(31,34), (1,6)(2,7)(3,10)(4,40)(5,11)(8,14)(9,16)(12,17)(13,18)(15,19)(20,24)(21,26)(22,28)(23,30)(25,31)(27,34)(29,36)(32,37)(33,38)(35,39), (1,21)(3,23)(5,25)(6,26)(8,27)(10,30)(11,31)(14,34), (2,40)(4,7)(5,8)(11,14)(20,22)(24,28)(25,27)(31,34), (1,23)(2,7)(4,22)(5,39,11,35)(6,30)(8,19,14,15)(9,33)(12,27,17,34)(16,38)(20,24)(25,37,31,32)(28,40), (2,20)(4,28)(5,8)(7,24)(11,14)(12,32)(15,35)(17,37)(19,39)(22,40)(25,27)(31,34), (2,15)(4,17)(7,19)(12,40)(20,35)(21,23)(22,32)(24,39)(25,27)(26,30)(28,37)(29,33)(31,34)(36,38), (9,13)(12,15)(16,18)(17,19)(29,33)(32,35)(36,38)(37,39), (2,40)(4,7)(12,15)(17,19)(20,22)(24,28)(32,35)(37,39) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_393216_ks := 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>;