# Group 492960.a downloaded from the LMFDB on 16 September 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 
GPerm := Group( (1,2)(3,7,11,23,37,18,36,73,128,72,127,154,104,153,116,61,115,85,131,76,69,108,57,107,82,136,158,140,160,123,67,100,51,34,16,33,42,21,10,5,9,17,35,26,12,25,49,96,46,95,145,133,155,138,84,117,62,102,53,91,135,80,111,59,110,152,119,156,143,89,129,74,44,22,43,32,15,8)(4,6)(13,27,54,103,122,66,31,50,99,141,87,41,20,40,83,114,65,121,68,124,106,56,75,130,150,147,159,149,137,92,63,118,94,45,93,55,105,81,39,19,38,77,132,98,48,24,47,97,120,64,30,14,29,60,112,88,142,90,144,134,79,52,101,146,151,148,157,113,70,86,139,126,71,125,78,109,58,28), (1,3,4)(2,5,6)(7,12,13)(8,14,16)(9,18,19)(10,20,22)(11,21,24)(15,31,17)(23,45,46)(25,50,51)(26,52,53)(27,55,56)(28,57,59)(29,61,62)(30,63,65)(32,67,68)(33,69,70)(34,49,48)(35,71,72)(36,47,74)(37,75,76)(38,78,79)(39,80,82)(40,84,85)(41,86,88)(42,89,90)(43,91,92)(44,73,66)(54,100,104)(58,105,101)(60,113,114)(64,119,96)(77,129,133)(81,109,130)(83,137,112)(87,140,128)(93,108,143)(95,131,142)(97,146,147)(98,148,149)(99,150,151)(102,121,127)(103,115,152)(106,154,116)(107,141,155)(110,156,118)(111,120,153)(117,158,132)(122,159,157)(123,125,135)(134,145,138)(136,160,139) );
GLFp := Group([[[ Z(79)^0, Z(79)^0 ], [ 0*Z(79), Z(79)^0 ]], [[ Z(79)^0, 0*Z(79) ], [ Z(79)^0, Z(79)^0 ]]]);

 
# Booleans 
booleans_492960_a := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := true,
quasisimple := true,
rational := false,
solvable := false,
supersolvable := false);