# Group 800000000.wi downloaded from the LMFDB on 10 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(53466101321923295439885344093821220941113462633235126373397251021897985434611327824228550886832805652604979250891995474395649401619211617510485693735241900692999244835219627203561623175918112294252220394197120800287225926021784287559161317550661995008647806861755635152805244031064055632847653615318351573837463092475808375026384372674877419723475496417011031720561357628743929403464102681362498990941751867095980778712167814288004549675980571682855539203290928205899157126034366909514666383505400558219597094969285789589593917428266749819132484852685368533142713555050236540984687225233803271560736695828722931205122911551332605095988437791045562077086703840803007493274295637104334690312421239147400140749089787794408111190388279072122481175668563291401887804932277427694559814004217069351490947801554378734828157563747833785141175060819246324172243774270690478317194058542586733099095871613441152045017880633330767419361255202946393186862326687752654032755014696590494633002620344594070968679492774993163377230856026469312697147602995933878679053325328819647367337753018095746153973907698263400484635675815296431272213631966471278772646741928606027063498676354223420602399319128626611870016961688402499349273723258200891429440454797804351070446538891687881510566809599,800000000); a := GPC.1; b := GPC.3; c := GPC.5; d := GPC.7; e := GPC.10; f := GPC.13; g := GPC.15; h := GPC.16; i := GPC.17; j := GPC.18; k := GPC.19;
GPerm := Group( (1,26,12,20,2,30,11,17,3,29,15,19,4,28,14,16,5,27,13,18)(6,35,39,25,9,32,37,22,7,34,40,24,10,31,38,21,8,33,36,23), (1,2,5,4)(6,10,9,8,7)(11,13,14,12)(16,19)(17,18)(21,22,25,24)(26,29,27,30,28)(32,34,35,33)(36,40)(37,39), (1,31,4,35,3,32,5,33)(2,34)(6,19,8,18)(7,16)(9,20,10,17)(11,25,12,22,15,23,14,21)(13,24)(26,38,27,40,28,37,29,39,30,36) );

 
# Booleans 
booleans_800000000_wi := 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);