# Group 16600.a 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(29352362844077965155704141963180938019494125467539,16600); a := GPC.1; b := GPC.2;
GPerm := Group( (2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27), (1,2,4,6,8,10,12,14,16,18,20,22,24,25,23,21,19,17,15,13,11,9,7,5,3)(26,28,27,29)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112) );
GLFp := Group([[[ Z(499)^69, Z(499)^35 ], [ Z(499)^34, Z(499)^69 ]], [[ Z(499)^0, 0*Z(499) ], [ 0*Z(499), Z(499)^249 ]]]);

 
# Booleans 
booleans_16600_a := rec( 
Agroup := false,
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);