/* Group 26400.h downloaded from the LMFDB on 21 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, -5, -2, -2, -2, -3, -11, 18, 389072, 324146, 74, 605523, 345972, 481504, 218263, 65272, 38056, 130, 1155605, 523814, 14063, 20012, 158, 1033206, 390615, 32784, 46653, 186, 460807, 892816, 74905, 11554, 286, 1555208, 874817, 38906, 38915]); a,b,c := Explode([GPC.1, GPC.3, GPC.5]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "c2", "c4", "c8", "c24"]);
GPerm := PermutationGroup< 27 | (12,13,14,16,15), (1,2)(3,5)(4,6)(7,8)(12,13,14,16,15), (1,2)(3,5)(4,6)(7,8)(9,10,11)(17,18,21,26,22,23,25,27,20,19), (1,3,2,5)(4,7,6,8)(12,14,15,13,16)(17,19,21,27,26)(18,23,25,22,24), (12,14,15,13,16)(17,19,25,18,24)(20,22,21,23,27), (12,14,15,13,16)(17,20,22,27,25,24,18,21,19,26,23), (12,15,16,14,13)(18,20,22,25,19,24,23,26,21,27), (1,4,5,8,2,6,3,7)(12,13,14,16,15)(17,21,23,24,18,19,20,26,27,22), (3,5)(4,8)(6,7)(9,10)(12,14,15,13,16)(17,22,21,27,25,20,23,24,26,19) >;
GLFp := MatrixGroup< 4, GF(11) | [[3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3], [7, 8, 8, 6, 5, 8, 4, 1, 5, 5, 0, 10, 6, 9, 5, 7], [5, 6, 8, 10, 5, 0, 9, 8, 7, 1, 7, 5, 3, 7, 6, 2], [5, 3, 8, 0, 0, 0, 1, 6, 5, 1, 4, 8, 8, 7, 5, 2], [8, 4, 4, 5, 1, 9, 0, 1, 5, 9, 4, 7, 7, 8, 3, 2], [8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8], [2, 5, 0, 4, 4, 5, 1, 0, 7, 2, 1, 6, 4, 7, 7, 4], [0, 3, 9, 0, 4, 10, 8, 9, 4, 1, 3, 8, 10, 4, 7, 2], [5, 2, 0, 8, 4, 1, 3, 3, 3, 10, 5, 5, 0, 8, 0, 6]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_26400_h := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>;