/* Group 1889568.ij downloaded from the LMFDB on 03 February 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([15, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 30, 807032, 10736972, 122, 71073363, 43081218, 89678254, 52969519, 15649684, 5346274, 214, 12138125, 40986560, 16563995, 127372776, 56553546, 14035176, 1542936, 2132316, 306, 97044487, 36858262, 33765157, 2852707, 181908998, 3513398, 20674478, 9637433, 4962128, 2743553, 277928, 527828, 398, 185860809, 39864624, 283623130, 37208185, 9409000, 1568230, 11980, 2110, 75738251, 46189466, 16796201, 3110471, 38981, 5531, 169996332, 47048067, 42709722, 3580272, 1649802, 21192, 315161293, 121746268, 22589323, 7393753, 627583, 78253, 38588414, 160137029, 20703644, 826274, 235004, 224234]); a,b,c,d,e,f,g,h,i,j := Explode([GPC.1, GPC.3, GPC.5, GPC.7, GPC.9, GPC.11, GPC.12, GPC.13, GPC.14, GPC.15]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "c2", "d", "d2", "e", "e2", "f", "g", "h", "i", "j"]);
GPerm := PermutationGroup< 27 | (1,3,2)(4,6,5,8,13,14,17,7,11)(9,15,18,10,16,12)(19,21,23)(20,22,25,24,27,26), (1,2,4)(3,5,7,10,11,13)(6,9,14)(8,12,16)(15,17,18)(19,20,21)(22,24,26,27,23,25) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1889568_ij := 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>;