# Group 4608.z downloaded from the LMFDB on 13 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(24332391999871329910193348589163172818755088408618698105209212784130056231643704146946107988595850702167355440586504680838287851517969,4608); a := GPC.1; b := GPC.2; c := GPC.8; d := GPC.9;
GPerm := Group( (1,2,6,10,30,13,14,4)(3,7,18,24,54,33,34,12)(5,9,20,29,60,36,37,15)(8,25,48,21,16,19,44,26)(11,22,41,51,86,63,64,32)(17,28,46,59,92,66,67,38)(23,52,75,43,35,42,74,53)(27,55,80,47,39,45,76,56)(31,49,71,83,118,95,96,62)(40,58,78,91,124,98,99,68)(50,84,107,73,65,72,106,85)(57,87,112,79,69,77,108,88)(61,81,103,115,150,127,128,94)(70,90,110,123,156,130,131,100)(82,116,139,105,97,104,138,117)(89,119,144,111,101,109,140,120)(93,113,135,147,182,159,160,126)(102,122,142,155,188,162,163,132)(114,148,171,137,129,136,170,149)(121,151,176,143,133,141,172,152)(125,145,167,179,214,191,192,158)(134,154,174,187,220,194,195,164)(146,180,203,169,161,168,202,181)(153,183,208,175,165,173,204,184)(157,177,199,211,241,223,224,190)(166,186,206,219,247,226,227,196)(178,212,235,201,193,200,233,213)(185,215,244,207,197,205,236,216)(189,209,231,242,255,248,246,222)(198,218,239,254,256,250,249,228)(210,240,251,234,225,232,230,243)(217,245,221,238,229,237,252,253), (1,3,11,31,61,93,125,157,189,221,244,208,176,144,112,80,48,75,107,139,171,203,235,251,256,247,220,188,156,124,92,60,30,54,86,118,150,182,214,241,255,252,236,204,172,140,108,76,44,74,106,138,170,202,233,230,198,166,134,102,70,40,17,5)(2,7,22,49,81,113,145,177,209,238,207,175,143,111,79,47,21,43,73,105,137,169,201,234,250,226,194,162,130,98,66,36,13,33,63,95,127,159,191,223,248,253,216,184,152,120,88,56,26,53,85,117,149,181,213,243,218,186,154,122,90,58,28,9)(4,12,32,62,94,126,158,190,222,245,215,183,151,119,87,55,25,52,84,116,148,180,212,240,254,219,187,155,123,91,59,29,10,24,51,83,115,147,179,211,242,237,205,173,141,109,77,45,19,42,72,104,136,168,200,232,228,196,164,132,100,68,38,15)(6,18,41,71,103,135,167,199,231,229,197,165,133,101,69,39,16,35,65,97,129,161,193,225,249,227,195,163,131,99,67,37,14,34,64,96,128,160,192,224,246,217,185,153,121,89,57,27,8,23,50,82,114,146,178,210,239,206,174,142,110,78,46,20)(257,258,259), (2,8,10)(4,13,16)(6,19,21)(7,23,24)(9,27,29)(12,33,35)(14,25,26)(15,36,39)(18,42,43)(20,45,47)(22,50,51)(28,57,59)(32,63,65)(34,52,53)(37,55,56)(38,66,69)(41,72,73)(46,77,79)(49,82,83)(58,89,91)(62,95,97)(64,84,85)(67,87,88)(68,98,101)(71,104,105)(78,109,111)(81,114,115)(90,121,123)(94,127,129)(96,116,117)(99,119,120)(100,130,133)(103,136,137)(110,141,143)(113,146,147)(122,153,155)(126,159,161)(128,148,149)(131,151,152)(132,162,165)(135,168,169)(142,173,175)(145,178,179)(154,185,187)(158,191,193)(160,180,181)(163,183,184)(164,194,197)(167,200,201)(174,205,207)(177,210,211)(186,217,219)(190,223,225)(192,212,213)(195,215,216)(196,226,229)(199,232,234)(206,237,238)(209,239,242)(218,246,254)(222,248,249)(224,240,243)(227,245,253)(228,250,231) );
GLFp := Group([[[ Z(193)^142, Z(193)^140 ], [ Z(193)^187, Z(193)^45 ]], [[ Z(193), 0*Z(193) ], [ 0*Z(193), Z(193) ]], [[ Z(193)^167, Z(193)^13 ], [ Z(193)^15, Z(193)^41 ]]]);

 
# Booleans 
booleans_4608_z := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false);