# Group 37056.v 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(1162807216188907072466679951664714799546112836890580916394525055,37056); a := GPC.1; b := GPC.8;
GPerm := Group( (2,4,3,6)(5,10,7,12)(8,9,14,13)(11,20,15,22)(16,19,26,23)(17,24,25,18)(21,34,27,36)(28,33,42,37)(29,38,41,32)(30,31,40,39)(35,52,43,54)(44,51,62,55)(45,56,61,50)(46,49,60,57)(47,58,59,48)(53,74,63,76)(64,73,86,77)(65,78,85,72)(66,71,84,79)(67,80,83,70)(68,69,82,81)(75,100,87,102)(88,99,114,103)(89,104,113,98)(90,97,112,105)(91,106,111,96)(92,95,110,107)(93,108,109,94)(101,130,115,132)(116,129,146,133)(117,134,145,128)(118,127,144,135)(119,136,143,126)(120,125,142,137)(121,138,141,124)(122,123,140,139)(131,156,147,166)(148,167,178,158)(149,169,176,159)(150,171,174,160)(151,173,172,161)(152,175,170,162)(153,177,168,163)(154,179,157,164)(155,180,185,165)(181,187,191,183)(182,188,186,184)(189,193,192,190)(194,195,197,199,201,203,205,207,209,211,213,215,217,219,221,223,225,227,229,231,233,235,237,239,241,243,245,247,249,251,253,255,196,198,200,202,204,206,208,210,212,214,216,218,220,222,224,226,228,230,232,234,236,238,240,242,244,246,248,250,252,254,256,257)(258,259,260), (1,2,5,11,21,35,53,75,101,131,157,134,102,133,159,173,125,97,73,52,72,96,124,152,176,144,112,84,60,40,24,12,23,39,59,83,111,143,164,183,190,192,186,166,177,121,93,69,49,33,20,32,48,68,92,120,150,172,140,108,80,56,36,55,79,107,139,162,167,130,155,181,188,180,117,89,65,45,29,17,9,4,8,16,28,44,64,88,116,148,168,136,104,76,103,135,160,171,127,99,74,98,126,153,178,146,114,86,62,42,26,14,6,13,25,41,61,85,113,145,165,184,191,185,132,158,175,123,95,71,51,34,50,70,94,122,151,174,142,110,82,58,38,22,37,57,81,109,141,163,156,182,189,193,187,179,119,91,67,47,31,19,10,18,30,46,66,90,118,149,170,138,106,78,54,77,105,137,161,169,129,100,128,154,147,115,87,63,43,27,15,7,3), (194,196)(195,198)(197,200)(199,202)(201,204)(203,206)(205,208)(207,210)(209,212)(211,214)(213,216)(215,218)(217,220)(219,222)(221,224)(223,226)(225,228)(227,230)(229,232)(231,234)(233,236)(235,238)(237,240)(239,242)(241,244)(243,246)(245,248)(247,250)(249,252)(251,254)(253,256)(255,257) );
GLFp := Group([[[ Z(193)^0, Z(193)^0 ], [ 0*Z(193), Z(193)^0 ]], [[ Z(193)^96, 0*Z(193) ], [ 0*Z(193), Z(193)^96 ]], [[ Z(193)^73, 0*Z(193) ], [ 0*Z(193), Z(193)^121 ]]]);

 
# Booleans 
booleans_37056_v := 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);