/* Group 24900.c downloaded from the LMFDB on 26 June 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([6, -2, -2, -3, -83, -5, -5, 12, 31, 68, 717124, 178, 717125]); a,b := Explode([GPC.1, GPC.5]); AssignNames(~GPC, ["a", "a2", "a4", "a12", "b", "b5"]);
GPerm := PermutationGroup< 115 | (1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(84,85,86)(87,88,89,91,93,95,97,99,101,103,105,107,109,111,110,108,106,104,102,100,98,96,94,92,90)(112,113)(114,115), (1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6,4,2)(84,86,85)(88,90)(89,92)(91,94)(93,96)(95,98)(97,100)(99,102)(101,104)(103,106)(105,108)(107,110)(109,111)(112,114,113,115) >;
GLFp := MatrixGroup< 2, GF(499) | [[436, 74, 132, 63], [377, 182, 26, 377]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_24900_c := rec< RF |  
Agroup := true,
Zgroup := true,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>;