# Group 169869312.nb downloaded from the LMFDB on 03 February 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(13998772360176394161602463604573558246262003350231178383569037078618652977696340311985268073098495453583934616920917249642863426214911875260805548416887889937075533307413919432694557846503269269195147205180780543146211378174848911291173797543537681182620236682783989704024908830749789211923105190234670821925846044659929935236727053710664234069389763953439295202728406360846308811726639830255499725980373391458948974854190673086718788973621124628777463966941990747685603071172677954187652297666791569144240335385157770987434839156460056877085815180507661125111385426930821278137406229014148690109920969564455688255328765856111354513819013773011336338756536276125203120370400418333961948055586213313619046607722851743236196674546385048958842948359767427641443945023052397955886882077965889474350147611311610773067388202243101026912189892340424892623671626245651065171797261334942511211563075285248481019286231193716187008661644957739402429001833867496990209112842488594845874723504086628743263013995388082204550459834172485271927543724604662446651354515672374531866217204737054789756789934443993494932687498569920955232941984074818557148610361372484728959264278132022889592727398953296189312957663151982905507924790176276997235294800614537315570241360538591126203844409151993267470951353098211145241522974703555517114145346908644623065046646011589278246232758479166460256316526625188692358349900417657389043218718643894430823806098463858611235235382031932322135384854212501199743346251746217645567578133177263602720701030773262048318581125183603804544830715628550404931381525495346612549428143417620910683156189211124368494876404289453976966735948922113248088335807711749740469128211665101791892098517721466658651612406691857570698419603687646280431011264196724515184844261707048797433671272774384873205261947011382714368,169869312); a := GPC.1; b := GPC.2; c := GPC.5; d := GPC.6; e := GPC.8; f := GPC.10; g := GPC.13; 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;
GPerm := Group( (1,36,20,4,34,17)(2,35,19,3,33,18)(5,32,22,7,30,24)(6,31,21,8,29,23)(9,28,16,11,26,14,10,27,15,12,25,13), (3,4)(7,8)(9,10)(13,35)(14,36)(15,33,16,34)(17,31,21,28,18,32,22,27)(19,29,23,25)(20,30,24,26) );

 
# Booleans 
booleans_169869312_nb := 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);