# Group 366912.a downloaded from the LMFDB on 01 May 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 
GPerm := Group( (1,2,8,24,56,79,89,103,84,111,107,108,77,106,112,95,53,22,49,62,33,12,3,5)(4,9,26,58,100,109,105,92,57,101,76,86,55,69,94,51,21,6,20,47,72,32,11,15)(7,10,28,60,59,38,65,97,52,96,70,78,36,68,104,74,98,54,63,25,61,34,13,19)(14,29,64,102,73,99,91,48,90,75,35,46,23,30,67,50,41,16,27,66,93,71,31,37)(17,42,85,87,110,88,80,39)(18,43,81,45,83,40,82,44)(113,114,115,116,117,118,119), (1,4,14,36,77,55,23,7)(2,9,29,68,106,69,30,10)(3,11,31,70,107,76,35,13)(5,15,37,78,108,86,46,19)(6,16,38,79,109,99,54,22)(8,26,64,104,112,94,67,28)(12,32,71,96,111,101,75,34)(17,39,80,88,110,87,85,42)(18,40,81,44,83,43,82,45)(20,27,65,89,105,91,63,49)(21,41,59,56,100,73,98,53)(24,58,102,74,95,51,50,60)(25,62,47,66,97,103,92,48)(33,72,93,52,84,57,90,61)(113,114,115,116,117,118,119)(120,121,122), (1,3,6)(4,11,16)(5,17,18)(7,13,22)(8,25,27)(14,31,38)(15,39,40)(19,42,45)(20,28,48)(21,50,52)(23,35,54)(24,57,59)(26,62,65)(33,73,74)(36,70,79)(37,80,81)(41,60,84)(43,86,87)(44,78,88)(46,85,82)(47,89,64)(49,67,92)(51,93,53)(55,76,99)(56,58,90)(61,100,102)(63,94,103)(66,105,104)(72,98,95)(77,107,109)(83,108,110)(91,112,97) );
GLFq := Group([[[Z(169)^68, Z(169)^106], [Z(169)^164, Z(169)^25]],[[Z(169)^132, 0*Z(169)], [0*Z(169), Z(169)^132]],[[Z(169)^121, Z(169)^110], [Z(169)^0, Z(169)^110]],[[Z(169)^150, 0*Z(169)], [0*Z(169), Z(169)^150]],[[Z(169)^32, 0*Z(169)], [0*Z(169), Z(169)^32]],[[Z(169)^120, 0*Z(169)], [0*Z(169), Z(169)^120]],[[Z(169)^36, Z(169)^158], [Z(169)^72, Z(169)^12]],[[Z(169)^159, 0*Z(169)], [0*Z(169), Z(169)^159]]]);

 
# Booleans 
booleans_366912_a := 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 := false,
supersolvable := false);