# Group 78400.a 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(1805331933456576500903170370978159770016109520127815267398835216589368901582581255706782151351,78400); a := GPC.1; b := GPC.2; c := GPC.6;
GPerm := Group( (1,2,4,8,13,16,15,11)(3,6,10,14,12,9,7,5)(24,25,27,29,32)(26,30,33,31,28)(34,35,37,39,40,38,36), (1,3)(2,5)(4,7)(6,11)(8,9)(10,15)(12,13)(14,16)(24,26)(25,28)(27,31)(29,33)(30,32)(35,36)(37,38)(39,40), (3,7,12,10)(5,9,14,6)(17,18,19,20,21,22,23)(24,27,32,25,29)(26,30,33,31,28)(34,36,38,40,39,37,35) );
GLFp := Group([[[ Z(281)^0, 0*Z(281) ], [ 0*Z(281), Z(281)^2 ]], [[ Z(281), 0*Z(281) ], [ 0*Z(281), Z(281)^279 ]], [[ 0*Z(281), Z(281)^0 ], [ Z(281)^0, 0*Z(281) ]]]);

 
# Booleans 
booleans_78400_a := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true);