# Group 612220032.kc downloaded from the LMFDB on 24 July 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 := PcGroupCode(1891391124510140205471544988652447905018080117607166594817931914365720678441745308340306782567885423495395749363920281999345048896998159274116769052379077557801434710466264044751305810437144529990941259833138981691296918153941849888728235770390890006605816956891900797780950903685953906271592138706453431051474578475477419349788240513163084504984084444650692481966523722869556755245228818711705500289091594624939818004113233524758906940929886908113552360933670375091515028143649971964171408060982704665334396232904114871470119626007610667649120631472432784729798403512590215597100115325141973728896268854246839558938654467111099256880039013211153530885519555419289161041920265866254236149087798112159392684715997719589668436047999919911747200068157182480575638100741787467989374972705200987079695433184759324669940451665709808679993599708904810744970543419053697982085440676791254052242691982622259509563862357544359204787943968590841576483364222419645168106420462885474610882862524552242104618831405199466490341228703625372908335659152052461091552623005976594316359627032595152743857491482879547162526359235559599397856273081518152930036560995078867134109123564083674862674338157480300195987743424963134270742490222324535004318571440205689726379623231454926250954278775583172907078484703789660605101234627627499350185356752060709083137424478490366817746105499570084698999790038949544365360792770373558085615507440494362742705633262337054865215860174143939242651998417999506968125219268702938710859491275315840772495672665257595143388821574660535012572414858915899001850581587944987192082700326943050963244551112525462126006098046366804574305247731743829422140707923777054093578445666983463327683935173198129050278871502532565636862598555937330829819837271724382635642195967,612220032); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5; e := GPC.6; f := GPC.7; g := GPC.9; h := GPC.11; i := GPC.12; j := GPC.13; k := GPC.14; l := GPC.15; m := GPC.16; n := GPC.17; o := GPC.18; p := GPC.19; q := GPC.20; r := GPC.21;
GPerm := Group( (1,24,2,23,3,22)(4,29)(5,28)(6,30)(7,21,9,19,8,20)(10,15,36,27,11,14,35,26,12,13,34,25)(16,17,18)(31,33,32), (1,8,6,36,14,20,29,22)(2,7,4,34,13,21,28,23)(3,9,5,35,15,19,30,24)(10,26,33,16)(11,27,31,18)(12,25,32,17) );

 
# Booleans 
booleans_612220032_kc := 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);