# Group 18632.h downloaded from the LMFDB on 29 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(4966808997440717052587247743,18632); a := GPC.1;
GPerm := Group( (1,2,4,6,3,5,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25), (26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162), (1,3)(2,5)(4,7)(6,8) );
GLFp := Group([[[ Z(137)^0, Z(137)^0 ], [ 0*Z(137), Z(137)^0 ]], [[ Z(137)^68, 0*Z(137) ], [ 0*Z(137), Z(137)^68 ]], [[ Z(137), 0*Z(137) ], [ 0*Z(137), Z(137) ]]]);

 
# Booleans 
booleans_18632_h := rec( 
Agroup := true,
Zgroup := true,
abelian := true,
almost_simple := false,
cyclic := true,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true);