# Group 39402.n downloaded from the LMFDB on 06 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(43092145454621101664685501479509780233047,39402); a := GPC.1; b := GPC.5;
GPerm := Group( (1,2,4,10,26,56,106,160,196,182,199,175,121,64,119,101,90,44,20,7,18,9,24,52,83,140,163,153,126,181,193,179,122,177,143,85,42,19,21,45,86,50,23,17,39,78,133,185,132,77,124,108,162,190,146,88,43,47,81,138,187,141,97,49,38,68,125,180,129,73,98,79,134,92,46,89,94,116,170,137,149,183,128,152,96,70,32,69,59,112,136,80,40,41,82,139,188,195,157,191,167,135,186,161,107,76,36,55,105,158,150,93,84,51,100,58,110,144,168,113,159,164,109,57,65,29,63,117,104,62,87,142,172,154,99,53,28,61,115,169,114,60,27,34,66,123,176,192,151,145,102,120,173,156,103,54,25,12,31,67,30,11,14,35,74,130,184,147,189,166,174,155,111,165,131,75,37,16,6,15,5,13,33,72,71,127,91,148,178,198,194,197,171,118,95,48,22,8,3), (2,5,14,36,75,81,40,17,6)(3,7,19,41,83,60,55,25,9)(4,11,29,64,120,110,71,32,12)(8,21,46,91,132,152,101,51,23)(10,27,59,113,117,131,116,62,28)(13,34,73,128,143,102,53,24,15)(16,18,20,43,87,144,130,77,38)(22,47,93,149,134,140,109,98,49)(26,57,108,163,161,177,166,111,58)(30,66,124,78,114,63,118,100,52)(31,33,65,122,178,199,182,126,68)(35,69,115,74,129,135,79,39,67)(37,45,88,145,103,138,92,106,70)(42,84,141,85,142,157,104,54,86)(44,89,147,175,198,194,155,99,50)(48,94,151,165,188,184,193,153,96)(56,107,119,172,137,80,97,90,82)(61,72,76,95,139,127,180,159,105)(112,167,136,183,190,148,181,133,164)(121,174,156,170,150,191,158,168,176)(123,179,196,185,186,162,160,125,169)(146,189,197,173,195,192,171,154,187)(200,201,202,203,204,205,206,207,208,209,210)(211,212), (211,212) );
GLFp := Group([[[ Z(199)^33, 0*Z(199) ], [ 0*Z(199), Z(199)^165 ]], [[ Z(199)^0, Z(199)^0 ], [ 0*Z(199), Z(199)^0 ]], [[ Z(199)^25, 0*Z(199) ], [ 0*Z(199), Z(199)^179 ]]]);

 
# Booleans 
booleans_39402_n := rec( 
Agroup := true,
Zgroup := true,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true);