# Group 1530.2 downloaded from the LMFDB on 25 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 
GPC := PcGroupCode(9220974514328978579475403071,1530); a := GPC.1; b := GPC.2;
GPerm := Group( (2,3)(4,5), (6,7,9,8,10,12,11,13,14), (15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31), (6,8,11)(7,10,13)(9,12,14), (1,2,4,5,3) );
GLFp := Group([[[ Z(919)^111, Z(919)^394 ], [ Z(919)^393, Z(919)^111 ]], [[ Z(919)^0, 0*Z(919) ], [ 0*Z(919), Z(919)^459 ]]]);

 
# Booleans 
booleans_1530_2 := rec( 
Agroup := true,
Zgroup := true,
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);