# Group 222336.c downloaded from the LMFDB on 02 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(37097160007589559346172724542001354389676430342183986399777974480803442486150841531632832745206017722015451442986660349127785311380706657670001179302965305932348977757744294053613713787736577559968912679074423684202879,222336); a := GPC.1; b := GPC.6;
GPerm := Group( (2,4,14,50,42,11,3,9,34,87,28,7)(5,19,59,144,120,45,12,43,76,157,69,22)(6,16,17,56,83,40,10,29,35,98,82,26)(8,18,15,52,64,20,13,37,36,100,88,30)(21,61,116,169,80,110,44,55,62,148,108,66)(23,63,123,166,131,122,46,118,72,162,96,71)(24,75,127,47,125,114,41,112,93,32,92,78)(25,33,57,54,135,109,39,49,99,102,168,79)(27,84,172,113,185,107,38,104,141,77,151,73)(31,89,134,128,159,70,48,129,177,95,175,90)(51,132,145,183,115,124,97,163,158,150,65,74)(53,136,143,147,176,121,101,167,182,187,156,68)(58,60,146,186,133,181,103,117,171,155,138,140)(67,152,192,188,180,189,119,165,190,154,139,153)(81,142,126,184,191,164,111,178,94,174,193,170)(85,173,161,160,130,86,106,179,149,137,91,105)(226,227,228), (1,2,5,20,64,149,122,49,131,79,167,192,168,129,124,84,102,181,150,86,27,6,24,76,158,69,146,83,26,81,139,144,163,174,85,114,56,141,176,91,154,67,21,57,94,32,8,31,17,4,15,53,137,128,80,25,66,151,177,100,93,103,37,11,16,55,70,22,68,63,142,179,169,193,189,166,77,155,187,152,112,87,92,115,42,14,51,133,159,143,164,73,23,72,117,43,116,62,19,60,123,46,107,170,182,175,138,97,34,28,65,125,50,75,165,147,186,113,162,153,191,148,173,178,118,121,45,90,61,29,7,18,58,127,52,134,185,110,39,108,95,160,101,36,9,35,48,13,47,126,99,44,119,188,130,156,172,98,78,106,184,132,157,180,111,40,82,171,120,145,59,41,10,38,105,183,140,54,104,74,89,135,190,136,109,96,33,71,161,88,30,12,3), (2,6,25,30,7,26,79,88,28,82,168,100,87,98,102,36,34,35,99,37,9,29,49,13,3,10,39,20,11,40,109,64,42,83,135,52,50,56,54,15,14,17,57,18,4,16,33,8)(5,21,65,71,22,66,150,96,69,108,158,162,157,148,163,72,76,62,97,118,43,55,124,46,12,44,115,122,45,110,183,131,120,80,145,166,144,169,132,123,59,116,51,63,19,61,74,23)(24,77,137,90,78,141,149,175,92,104,179,95,32,38,106,177,93,107,86,129,112,185,130,48,41,113,160,70,114,172,161,159,125,84,173,128,47,27,85,134,127,73,105,89,75,151,91,31)(53,138,170,154,68,155,193,190,156,171,174,165,187,117,94,119,182,103,178,189,167,181,111,180,101,133,164,188,121,186,191,192,176,146,184,152,147,60,126,67,143,58,142,153,136,140,81,139)(194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225)(226,227,228) );
GLFp := Group([[[ Z(193)^0, Z(193)^0 ], [ 0*Z(193), Z(193)^0 ]], [[ Z(193)^4, 0*Z(193) ], [ 0*Z(193), Z(193)^188 ]], [[ Z(193)^2, 0*Z(193) ], [ 0*Z(193), Z(193)^6 ]]]);

 
# Booleans 
booleans_222336_c := rec( 
Agroup := true,
Zgroup := false,
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);