/* Group 113764.b downloaded from the LMFDB on 03 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([5, -2, -7, -17, -2, -239, 10, 76, 2032523, 502188, 94873, 58, 2237204, 1255459, 34014]); a,b := Explode([GPC.1, GPC.4]); AssignNames(~GPC, ["a", "a2", "a14", "b", "b2"]);
GPerm := PermutationGroup< 248 | (1,2,4,14,48,115,37,114,206,239,180,179,121,148,52,147,55,15,53,149,170,66,84,82,93,54,134,44,12,43,131,167,218,221,113,74,81,152,150,89,34,109,216,223,199,90,198,196,166,112,36,10,35,78,187,127,41,126,220,169,192,189,162,177,210,209,95,28,94,204,211,96,164,103,47,13,46,137,219,111,119,226,229,207,124,143,50,142,64,18,63,165,168,151,122,92,201,159,171,203,176,105,39,120,227,128,104,32,102,107,33,9,31,67,172,108,215,205,193,141,230,222,237,174,68,173,73,21,5,19,65,71,20,69,62,156,58,16,57,155,153,214,228,232,133,49,139,191,175,130,42,129,231,123,145,51,144,140,154,56,79,188,97,30,8,29,70,178,87,197,236,136,45,135,200,235,161,186,138,181,213,163,61,17,60,160,83,24,6,23,77,185,183,234,132,233,195,182,76,22,75,146,212,99,101,80,190,184,202,91,27,7,26,88,117,72,98,110,106,208,225,118,38,116,224,125,158,59,157,217,238,194,86,25,85,100,40,11,3), (2,5,20,70,98,30,96,37,10,13,34,105,84,24,81,28,7)(3,9,32,103,82,46,87,25,6,8,22,57,110,35,99,45,12)(4,15,54,151,234,142,228,121,39,42,119,212,199,156,164,62,17)(11,38,117,139,198,231,159,59,16,18,56,152,233,227,178,128,41)(14,49,140,170,236,179,88,53,123,125,230,210,95,207,102,146,51)(19,66,169,232,153,85,137,126,73,108,214,174,91,116,120,89,26)(21,48,113,36,83,191,200,90,93,101,189,79,29,64,167,133,43)(23,78,168,209,132,72,74,138,111,47,129,202,92,27,31,100,80)(33,106,213,201,203,115,97,61,67,68,171,215,131,55,58,75,44)(40,122,229,208,204,157,134,118,50,52,141,235,135,144,71,150,124)(60,65,130,185,211,205,154,175,177,186,77,163,224,194,136,155,104)(63,166,197,237,226,165,161,162,112,220,147,206,94,176,69,127,107)(76,180,143,173,158,239,195,86,192,218,221,188,187,225,182,222,183)(109,217,145,172,148,238,223,114,181,184,190,219,160,149,216,193,196)(247,248), (2,6,7,25,28,87,81,46,24,82,84,103,105,32,34,9,13,3,10,12,37,45,96,99,30,35,98,110,70,57,20,22,5,8)(4,16,17,59,62,159,164,231,156,198,199,139,212,117,119,38,42,11,39,41,121,128,228,178,142,227,234,233,151,152,54,56,15,18)(14,50,51,118,146,134,102,157,207,204,95,208,210,229,230,122,125,40,123,124,53,150,88,71,179,144,236,135,170,235,140,141,49,52)(19,67,26,61,89,97,120,115,116,203,91,201,174,213,214,106,108,33,73,44,126,75,137,58,85,55,153,131,232,215,169,171,66,68)(21,72,43,132,133,209,167,168,64,78,29,23,79,80,189,100,101,31,93,27,90,92,200,202,191,129,83,47,36,111,113,138,48,74)(60,161,104,165,155,226,136,237,194,197,224,166,163,63,77,107,186,127,177,69,175,176,154,94,205,206,211,147,185,220,130,112,65,162)(76,181,183,114,222,223,182,238,225,148,187,172,188,145,221,217,218,109,192,196,86,193,195,216,239,149,158,160,173,219,143,190,180,184)(240,241,242,243,244,245,246)(247,248) >;
GLFp := MatrixGroup< 2, GF(239) | [[1, 1, 0, 1], [26, 0, 0, 83], [238, 0, 0, 238]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_113764_b := rec< RF |  
Agroup := true,
Zgroup := false,
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>;