# Group 1092.25 downloaded from the LMFDB on 08 October 2026. 
 
## Various presentations of this group are stored in this file: 
#	 GPC is polycyclic presentation, GPerm is permutation group 
#	 GLZ, GLFp, GLZN, 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( (2,3,5,9,6,11,8,13,10,7,12,14,4), (3,6,9,4,7,12)(5,10,8,14,11,13), (1,2)(3,4)(5,8)(6,9)(7,12)(13,14) );
GLFp := Group([[[ Z(13)^7, Z(13)^9, Z(13)^3 ], [ 0*Z(13), Z(13)^3, Z(13)^7 ], [ Z(13)^0, Z(13)^4, Z(13)^10 ]], [[ Z(13)^2, 0*Z(13), Z(13)^8 ], [ Z(13)^5, Z(13)^6, Z(13)^4 ], [ Z(13)^11, 0*Z(13), Z(13)^8 ]]]);

 
# Booleans 
booleans_1092_25 := rec( 
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := true,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := true,
quasisimple := true,
rational := false,
solvable := false,
supersolvable := false);