/* Group 236196.lh downloaded from the LMFDB on 19 July 2026. */
 
/* 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([12, -2, -3, -2, -3, -3, -3, -3, 3, 3, 3, 3, 3, 24, 209965, 2021546, 1198274, 98, 8290371, 4051599, 553431, 12262324, 2664376, 1730908, 630400, 8530277, 6080849, 1794989, 270485, 281, 54438, 9102, 14681095, 8973523, 155551, 1547467, 540055, 125347, 2134520, 10357652, 3365096, 1758392, 613388, 142952, 3674193, 21939994, 1582450, 866098, 114106, 256678, 8817995, 1516355, 2519471, 334427, 35063]); a,b,c,d,e,f,g,h,i := Explode([GPC.1, GPC.3, GPC.5, GPC.6, GPC.8, GPC.9, GPC.10, GPC.11, GPC.12]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "d", "d3", "e", "f", "g", "h", "i"]);
GPerm := PermutationGroup< 36 | (1,34,3,35,2,36)(4,9,17,21,29,33)(5,7,18,19,30,31)(6,8,16,20,28,32)(10,14,12,15,11,13)(22,26,24,27,23,25), (1,16,25,6,13,28,3,18,27,5,15,30,2,17,26,4,14,29)(7,35)(8,34)(9,36)(10,21)(11,20)(12,19)(22,33)(23,32)(24,31) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_236196_lh := rec< RF |  
Agroup := false,
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 := true>;