# Group 331776.br downloaded from the LMFDB on 13 October 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(12122764109785332372757445430219730340368223077988914864143827901137421544205382906107602233111151728497800423333699192175652918396305584054587818092337809425088669443389053797970815490914757114916954293686448068037108640934789992898526718499935807301936515146557766906986942422345079987249589316749695199382146711517018040347271087211814016848545052987741982584730868036379600408088657347141018039922640282461772557903070908789178749492098745055068903747575652160698934484064819894121939585477809971595936,331776); a := GPC.1; b := GPC.3; c := GPC.5; d := GPC.6; e := GPC.8; f := GPC.10; g := GPC.12; h := GPC.13; i := GPC.14; j := GPC.15; k := GPC.16;
GPerm := Group( (1,2,4,7)(3,5,9,14)(6,11)(8,12)(10,13)(15,16), (1,3,6,9,4,8,13,16)(2,5,10,14,7,12,11,15)(17,18,19,20) );

 
# Booleans 
booleans_331776_br := 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);