/* Group 40960.yn downloaded from the LMFDB on 25 October 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([14, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 512960, 495181, 172943, 1699742, 173476, 3390, 698043, 7409, 172175, 59181, 1364654, 143938, 216472, 38266, 1460, 845, 517459, 222465, 110591, 33829, 243, 78406, 4520887, 713237, 405027, 149681, 17087, 43533, 329, 645128, 4483509, 609303, 304677, 225171, 40945, 29199, 11867, 6193120, 872280, 364710, 182388, 130658, 16096, 6268, 1060, 458, 3548171, 2009292, 31373]); a,b,c,d,e,f,g,h,i,j,k := Explode([GPC.1, GPC.2, GPC.3, GPC.4, GPC.5, GPC.6, GPC.8, GPC.10, GPC.11, GPC.13, GPC.14]); AssignNames(~GPC, ["a", "b", "c", "d", "e", "f", "f2", "g", "g2", "h", "i", "i2", "j", "k"]);
GPerm := PermutationGroup< 40 | (1,28,40,20,15,2,27,39,19,16)(3,26,37,18,13,4,25,38,17,14)(5,30,34,24,10,6,29,33,23,9)(7,32,35,22,12,8,31,36,21,11), (1,16,23,38,29)(2,15,24,37,30)(3,13,21,39,32)(4,14,22,40,31)(5,10,20,35,27)(6,9,19,36,28)(7,11,18,34,26)(8,12,17,33,25), (1,18,28,13,35,2,17,27,14,36)(3,20,25,16,33,4,19,26,15,34)(5,21,29,11,38,6,22,30,12,37)(7,23,32,10,40,8,24,31,9,39) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_40960_yn := 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>;