/* Group 13134.f downloaded from the LMFDB on 30 September 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([4, -2, -11, -3, -199, 8, 124610, 13602, 46, 78147, 54391]); a,b := Explode([GPC.1, GPC.3]); AssignNames(~GPC, ["a", "a2", "b", "b3"]);
GPerm := PermutationGroup< 202 | (2,3)(4,7)(5,9)(6,8)(10,19)(11,21)(12,20)(13,25)(14,27)(15,26)(16,24)(17,23)(18,22)(28,49)(29,51)(30,50)(31,54)(32,55)(33,52)(34,53)(35,47)(36,62)(37,61)(38,65)(39,67)(40,66)(41,64)(42,63)(43,60)(44,59)(45,58)(46,57)(48,56)(68,107)(69,108)(70,100)(71,111)(72,113)(73,112)(74,109)(75,110)(76,116)(77,115)(78,92)(79,105)(80,114)(81,104)(82,103)(83,123)(84,124)(85,106)(86,93)(87,127)(88,128)(89,131)(90,130)(91,129)(94,126)(95,125)(96,122)(97,121)(98,120)(99,119)(101,118)(102,117)(132,177)(133,169)(134,162)(135,174)(136,156)(137,153)(138,179)(139,146)(140,167)(141,149)(142,178)(143,160)(144,147)(145,172)(148,154)(150,175)(151,171)(152,176)(155,182)(157,184)(158,185)(159,187)(161,188)(163,191)(164,190)(165,189)(166,180)(168,186)(170,181)(173,183)(192,198)(193,197)(194,196)(195,199), (200,201,202), (2,4,10,28,68,132,174,100,45,17,6)(3,7,19,49,107,177,135,70,58,23,8)(5,13,35,22,12,33,43,16,11,31,15)(9,25,47,18,20,52,60,24,21,54,26)(14,38,87,159,178,163,158,173,165,91,40)(27,65,127,187,142,191,185,183,189,129,66)(29,71,90,79,56,37,85,88,98,44,73)(30,74,125,86,64,55,92,84,118,57,39)(32,78,124,101,46,67,50,109,95,93,41)(34,36,83,155,99,170,134,69,133,126,63)(42,53,62,123,182,119,181,162,108,169,94)(48,61,106,128,120,59,112,51,111,130,105)(72,137,193,184,166,199,172,96,140,76,139)(75,143,190,161,179,121,148,104,131,115,144)(77,147,110,160,164,188,138,97,154,81,89)(80,151,192,136,186,196,176,102,175,103,141)(82,149,114,171,198,156,168,194,152,117,150)(113,153,197,157,180,195,145,122,167,116,146), (1,2,5,14,39,89,82,35,81,153,189,177,169,142,74,120,183,182,174,159,176,114,52,65,128,134,192,148,77,31,76,146,196,191,130,66,43,96,171,199,170,95,42,15,41,92,141,73,140,86,37,13,36,84,158,190,129,180,118,108,49,100,68,45,99,71,136,123,184,193,175,105,55,21,7,20,53,24,8,22,56,85,144,121,59,23,57,117,143,127,188,186,126,179,113,51,19,50,110,172,145,75,30,10,29,72,138,94,168,161,87,160,102,46,17,44,97,147,106,48,18,6,16,34,12,4,11,32,79,150,197,157,83,156,111,119,58,107,70,28,69,101,166,91,164,185,124,62,25,61,93,167,112,149,78,64,26,63,125,181,195,151,122,60,40,90,163,194,139,116,54,115,154,198,162,88,38,33,80,152,187,135,155,173,98,109,178,133,132,165,137,104,47,103,131,67,27,9,3) >;
GLFp := MatrixGroup< 2, GF(199) | [[1, 1, 0, 1], [59, 0, 0, 132]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_13134_f := 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>;