# Group 1856.54 downloaded from the LMFDB on 14 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(20378595078084293859208837788287050062900087635995,1856); a := GPC.1; b := GPC.2;
GPerm := Group( (1,34,2,33)(3,36,4,35)(5,38,6,37)(7,40,8,39)(9,42,10,41)(11,44,12,43)(13,46,14,45)(15,48,16,47)(17,50,18,49)(19,52,20,51)(21,54,22,53)(23,56,24,55)(25,58,26,57)(27,60,28,59)(29,62,30,61)(31,64,32,63), (1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)(33,58,34,57)(35,60,36,59)(37,62,38,61)(39,64,40,63)(41,56,42,55)(43,53,44,54)(45,50,46,49)(47,52,48,51), (1,13,5,12,4,16,8,10,2,14,6,11,3,15,7,9)(17,25,23,31,19,27,22,30,18,26,24,32,20,28,21,29)(33,41,39,47,35,43,38,46,34,42,40,48,36,44,37,45)(49,61,53,60,52,64,56,58,50,62,54,59,51,63,55,57), (1,7,3,6,2,8,4,5)(9,15,11,14,10,16,12,13)(17,21,20,24,18,22,19,23)(25,29,28,32,26,30,27,31)(33,37,36,40,34,38,35,39)(41,45,44,48,42,46,43,47)(49,55,51,54,50,56,52,53)(57,63,59,62,58,64,60,61), (1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15)(17,19,18,20)(21,23,22,24)(25,27,26,28)(29,31,30,32)(33,35,34,36)(37,39,38,40)(41,43,42,44)(45,47,46,48)(49,52,50,51)(53,56,54,55)(57,60,58,59)(61,64,62,63), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64), (65,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66) );
GLFp := Group([[[ Z(929)^16, 0*Z(929) ], [ 0*Z(929), Z(929)^16 ]], [[ Z(929)^29, 0*Z(929) ], [ 0*Z(929), Z(929)^899 ]], [[ 0*Z(929), Z(929)^16 ], [ Z(929)^0, 0*Z(929) ]]]);

 
# Booleans 
booleans_1856_54 := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true);