# Group 62750.f downloaded from the LMFDB on 26 June 2026. 
 
## 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(4713870823472255048160198253953312749,62750); a := GPC.1; b := GPC.4;
GPerm := Group( (1,2,4,10,28,70,160,174,80,173,108,44,53,127,223,187,241,200,99,40,14,39,95,196,150,63,149,237,163,130,54,21,7,19,49,118,65,152,177,82,32,81,175,227,129,87,35,12,34,85,181,103,41,101,143,60,142,229,204,165,74,164,135,57,22,55,110,210,246,202,100,179,83,178,219,248,184,88,183,188,161,96,159,203,104,176,224,172,78,171,240,154,166,102,72,138,58,136,226,153,66,26,9,25,64,151,123,220,244,238,213,116,48,18,47,113,197,97,128,225,245,214,117,71,86,182,217,148,139,157,243,251,194,93,126,215,158,69,27,68,156,242,190,249,198,98,109,45,17,6,16,43,106,167,75,29,73,141,112,206,107,205,235,144,234,195,216,119,209,114,124,221,201,236,146,192,250,199,185,131,211,115,207,247,180,84,33,11,31,79,170,137,232,239,169,77,30,76,121,50,120,162,147,62,24,61,145,92,193,230,133,56,132,212,111,46,105,42,15,5,13,37,91,191,189,90,36,89,186,125,52,20,51,122,218,208,222,168,94,38,67,155,231,134,228,233,140,59,23,8,3), (2,5,14,18,6)(3,7,20,27,9)(4,11,32,36,12)(8,22,56,63,24)(10,29,74,78,30)(13,38,93,44,16)(15,41,102,65,25)(17,19,50,112,46)(21,53,128,67,26)(23,58,137,144,60)(28,71,161,162,72)(31,80,140,107,43)(33,83,145,84,64)(34,37,92,167,86)(35,49,119,185,88)(39,96,114,47,97)(40,98,157,68,100)(42,104,178,146,61)(45,55,131,87,110)(48,115,51,123,117)(52,124,159,69,126)(54,129,226,148,62)(57,134,70,154,66)(59,139,221,181,141)(73,163,244,204,106)(75,166,246,203,151)(76,91,192,236,168)(77,118,215,121,170)(79,89,187,95,85)(81,169,210,113,176)(82,174,237,156,177)(90,188,122,219,190)(94,195,231,152,179)(99,199,238,149,201)(101,164,142,105,197)(103,182,241,155,202)(108,207,120,217,208)(109,136,206,247,209)(111,211,127,224,173)(116,212,132,228,189)(125,147,135,150,222)(130,184,183,223,143)(133,229,180,158,216)(138,191,249,239,153)(160,165,245,250,242)(171,234,196,200,230)(172,186,218,175,235)(193,214,198,205,225)(194,227,243,220,240)(213,233,232,251,248)(252,253,255,257,259,261,263,265,267,269,288,308,321,335,351,368,376,359,342,356,373,362,343,334,333,332,331,330,329,313,290,287,285,283,281,279,277,275,273,271,272,274,276,278,280,282,284,286,289,309,322,336,352,369,375,358,341,326,339,355,372,361,350,349,348,347,346,345,328,312,307,305,303,301,299,297,295,293,291,292,294,296,298,300,302,304,306,311,324,338,354,371,374,357,340,325,310,323,337,353,370,367,366,365,360,364,363,344,327,320,319,318,317,316,315,314,270,268,266,264,262,260,258,256,254)(377,378), (377,378) );
GLFp := Group([[[ Z(251)^0, Z(251)^0 ], [ 0*Z(251), Z(251)^0 ]], [[ Z(251)^26, 0*Z(251) ], [ 0*Z(251), Z(251)^226 ]], [[ Z(251)^125, 0*Z(251) ], [ 0*Z(251), Z(251)^125 ]]]);

 
# Booleans 
booleans_62750_f := 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);