# Group 4586471424.x 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(124781365472887005677636376493420499059196328941600099513616526987038183643777139100974768531346599292619750319889712096034013421265755224681841726877291527617085467436604419265394075425004269559617353887205368146751663860214857268295434621803026502732358458698477223999196866428934251392612639777052883911970797273785062231959805199755384097313308576756506181536212817100783088270452076763196165357459843510839315516898767977603338135564026836054848927625963486884596405755888953651448213727292551674237932510636790125482170557696872302982745769991123487157224476015298010473866832903294833703385823005674284657867401783766471069935783186647394960316062720894053646303893955434135834310961706235440757508891395957087144492066595390035132345207827722556848902364029558619084729542116314639060648828249143507222128096913324961871870380277958216484080123702684009675079902044345240860543084250710376714007998723277083067238639193203283498168529419823005855833697707026411762412377718101272162556170359540609424887878032797379289707918289040846568609988321647504783104350823206491126860111868632794900410372560084606962707227239261694979137050804767991937470889153909645046096002260421385847244259212524577661277666200324962699147539016713976634947529912262579365041779439452459040950355653760999503623783316271179707692778821391663098442350755849107115834663209768616174645338135328412294616117736025683298177191805346395575820821342478576459816366583690104581971455510343568858924616159076989466722185471335281223500149616562411976426700720434758510524528419223646353669160047407391129117715738784526144990582054017119759907446120742876241595413197901609562082134095431803728904779106254267960376258881915655543468553262548973094636917619610832009757643195665671973392024307555742606284677905831370701144491870992408127355227194215845008525555223075568173893826425378032011141654848033803356596477526584843041735850624214871327775057061971686214392534186981333978013803950793800226170720761454597698442676475607187729529807436814912720961948137908381518705308399380674271776688860102842544360811271595236023266236329649400262813789822344352916231961314965147225068593016164953059574085457287681660096782244654337761555399989120049450988371586574476326074766437510015413815607505459184129419303499212484472325720256959478888998876823941973727086118380563681594714526319733604837269668361756791087684208016594273473637147912814435285180543679851725148292204590557264978042965626641089121129074428270643170790556863902092602641454437606446224881323231672823052524463175580790237440919405729878366508657525671252915832853383027392127842498073568648108310344553037819052037264062282159725322266580927751429151984574807475639332586334586000787126886509959361933740636082313816811154608214541133623903144012073928783310106366811839207640133753915286963451040965498782072599587072898023204666699889799016632708316524598569325099908291493792573762025488267157663608828016539128013613968657129472,4586471424); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.6; e := GPC.8; f := GPC.10; g := GPC.12; h := GPC.14; i := GPC.16; j := GPC.17; k := GPC.18; l := GPC.19; m := GPC.20; n := GPC.21; o := GPC.22; p := GPC.23; q := GPC.24; r := GPC.25; s := GPC.26; t := GPC.27; u := GPC.28;
GPerm := Group( (1,9,29,23,6,8,26,21,3,12,28,19,2,10,30,24,5,7,25,22,4,11,27,20)(13,33,15,35,17,32)(14,34,16,36,18,31), (1,32,15,22,27,9,2,31,16,21,28,10)(3,34,18,23,26,11,4,33,17,24,25,12)(5,35,14,19,30,7,6,36,13,20,29,8), (1,33,5,31,3,36,2,34,6,32,4,35)(7,14,23,27,10,16,19,26,11,17,22,29,8,13,24,28,9,15,20,25,12,18,21,30) );

 
# Booleans 
booleans_4586471424_x := 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);