# Group 816293376.wj downloaded from the LMFDB on 11 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 := PcGroupCode(130514296904099625339102605947669284881541021344210961335439922807702001944992641115278799821120865973232985532569533400328411387424275168145270068212309581437118187206065291045951320797688951418476596407228501621014270082999769583061502775556756883627174695775995801810761860734015544437274207878997333049314714036484528519034048635784378122996616252658523299240765525377881941677527935139473290853178875105213858943969687633533914108066452730486799526349192267698745791815695820135567232067447296899423421376341355220044575391239459278584458970832799667556473530093640674003848365919252757242356466273464960445051304086511071320769736039665236019526314915218409276496873441076595576858913141414333506103516966827170058983152554502816159811965527727813167661274366158368658926347054544802654165395129261954811687945517525465456879531767032601633527158698417208206607766668300699888162082089518562177059354776431322178541186003887463493819516246523904616754545250548568181008053138894371696811593984175910290182847645866351744269170383784162048680040407029749180670115598351873187268917445564508530343016292842711059459344024899381797981761554532958321900794831853456678683233631892774655333473918111703657900992693702172311138225934075363316073946488583147711467845629279527070323047316094935368594998899056480538093175073131930117864903278554493995949975348112589235502077363253896916320842421583083507767774937955876550797512114521151876956227561297461682446492017084463061282935455899075500767995401663970042193492942078367231,816293376); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5; e := GPC.7; f := GPC.9; g := GPC.11; h := GPC.13; i := GPC.15; j := GPC.16; k := GPC.17; l := GPC.18; m := GPC.19; n := GPC.20; o := GPC.21; p := GPC.22;
GPerm := Group( (1,19,36,18,3,21,34,17,2,20,35,16)(4,14,23,29)(5,15,24,30)(6,13,22,28)(7,10,26,33)(8,11,27,32)(9,12,25,31), (1,14,3,15)(2,13)(7,8,9)(10,36)(11,34,12,35)(16,32,18,31)(17,33)(19,30,21,29)(20,28)(22,27)(23,25)(24,26), (1,35,2,34,3,36)(4,14,8,11,6,15,7,12,5,13,9,10)(22,29,27,31,23,28,25,32,24,30,26,33) );

 
# Booleans 
booleans_816293376_wj := rec( 
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);