# Group 6144.bkl downloaded from the LMFDB on 24 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(10209857721010475538240284544467219478682935812995323397516990247210363779843941117108736,6144); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.6; e := GPC.8; f := GPC.9; g := GPC.11; h := GPC.12;
GPerm := Group( (1,19)(3,9)(5,60)(6,12)(8,61)(11,58)(13,59)(15,21)(17,64)(18,24)(23,62)(25,63)(26,42)(27,45)(28,36)(29,39)(30,54)(31,57)(32,48)(33,51)(35,41)(38,44)(47,53)(50,56), (1,57)(3,35)(5,26)(6,38)(8,27)(9,41)(11,28)(12,44)(13,29)(15,47)(17,30)(18,50)(19,31)(21,53)(23,32)(24,56)(25,33)(36,58)(39,59)(42,60)(45,61)(48,62)(51,63)(54,64), (1,25)(2,7)(4,10)(5,58)(8,59)(11,60)(13,61)(14,20)(16,22)(17,62)(19,63)(23,64)(26,36)(27,39)(28,42)(29,45)(30,48)(31,51)(32,54)(33,57)(34,40)(37,43)(46,52)(49,55), (1,23,61,11)(3,6,15,18)(5,63,17,59)(8,58,19,62)(9,12,21,24)(13,60,25,64)(26,39,30,51)(27,48,31,36)(28,45,32,57)(29,54,33,42)(34,46)(35,50,47,38)(37,49)(40,52)(41,56,53,44)(43,55), (1,13)(2,14)(3,15)(4,16)(5,62)(6,18)(7,20)(8,63)(9,21)(10,22)(11,64)(12,24)(17,58)(19,59)(23,60)(25,61)(26,48)(27,51)(28,54)(29,57)(30,36)(31,39)(32,42)(33,45)(34,46)(35,47)(37,49)(38,50)(40,52)(41,53)(43,55)(44,56), (1,57)(2,34)(3,35)(4,37)(5,26)(6,38)(7,40)(8,27)(9,41)(10,43)(11,28)(12,44)(13,29)(14,46)(15,47)(16,49)(17,30)(18,50)(19,31)(20,52)(21,53)(22,55)(23,32)(24,56)(25,33)(36,58)(39,59)(42,60)(45,61)(48,62)(51,63)(54,64), (1,13)(5,58)(7,20)(8,59)(9,21)(10,22)(11,64)(12,24)(17,62)(19,63)(23,60)(25,61)(26,36)(27,39)(28,54)(29,57)(30,48)(31,51)(32,42)(33,45)(40,52)(41,53)(43,55)(44,56), (1,25,56)(3,26,36)(5,35,58)(6,27,39)(8,38,59)(9,28,42)(11,41,60)(12,29,45)(13,44,61)(15,30,48)(17,47,62)(18,31,51)(19,50,63)(21,32,54)(23,53,64)(24,33,57), (1,25)(5,58)(8,59)(11,60)(13,61)(17,62)(19,63)(23,64)(26,36)(27,39)(28,42)(29,45)(30,48)(31,51)(32,54)(33,57), (1,57)(5,58)(7,40)(8,59)(9,41)(10,43)(11,28)(12,44)(13,29)(17,62)(19,63)(20,52)(21,53)(22,55)(23,32)(24,56)(25,33)(26,36)(27,39)(30,48)(31,51)(42,60)(45,61)(54,64), (1,13)(3,15)(5,62)(6,18)(8,63)(9,21)(11,64)(12,24)(17,58)(19,59)(23,60)(25,61)(26,48)(27,51)(28,54)(29,57)(30,36)(31,39)(32,42)(33,45)(35,47)(38,50)(41,53)(44,56), (1,23)(2,4)(3,6)(5,59)(7,10)(8,58)(9,12)(11,61)(13,60)(14,16)(15,18)(17,63)(19,62)(20,22)(21,24)(25,64)(26,39)(27,36)(28,45)(29,42)(30,51)(31,48)(32,57)(33,54)(34,37)(35,38)(40,43)(41,44)(46,49)(47,50)(52,55)(53,56) );

 
# Booleans 
booleans_6144_bkl := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := true,
solvable := true,
supersolvable := true);