# Group 7550.a downloaded from the LMFDB on 17 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(15070744659543818099,7550); a := GPC.1;
GPerm := Group( (1,2)(3,15,27,10,22,5,17,24,12,19,7,14,26,9,21,4,16,23,11,18,6,13,25,8,20)(28,31,34,37,40,43,46,49,52,55,58,61,64,67,70,73,76,79,82,85,88,91,94,97,100,103,106,109,112,115,118,121,124,127,130,133,136,139,142,145,148,151,154,157,160,163,166,169,172,175,178,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,129,132,135,138,141,144,147,150,153,156,159,162,165,168,171,174,177,29,32,35,38,41,44,47,50,53,56,59,62,65,68,71,74,77,80,83,86,89,92,95,98,101,104,107,110,113,116,119,122,125,128,131,134,137,140,143,146,149,152,155,158,161,164,167,170,173,176), (3,27,22,17,12,7,26,21,16,11,6,25,20,15,10,5,24,19,14,9,4,23,18,13,8)(28,34,40,46,52,58,64,70,76,82,88,94,100,106,112,118,124,130,136,142,148,154,160,166,172,178,33,39,45,51,57,63,69,75,81,87,93,99,105,111,117,123,129,135,141,147,153,159,165,171,177,32,38,44,50,56,62,68,74,80,86,92,98,104,110,116,122,128,134,140,146,152,158,164,170,176,31,37,43,49,55,61,67,73,79,85,91,97,103,109,115,121,127,133,139,145,151,157,163,169,175,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,29,35,41,47,53,59,65,71,77,83,89,95,101,107,113,119,125,131,137,143,149,155,161,167,173), (3,7,6,5,4)(8,12,11,10,9)(13,17,16,15,14)(18,22,21,20,19)(23,27,26,25,24)(28,58,88,118,148,178,57,87,117,147,177,56,86,116,146,176,55,85,115,145,175,54,84,114,144,174,53,83,113,143,173,52,82,112,142,172,51,81,111,141,171,50,80,110,140,170,49,79,109,139,169,48,78,108,138,168,47,77,107,137,167,46,76,106,136,166,45,75,105,135,165,44,74,104,134,164,43,73,103,133,163,42,72,102,132,162,41,71,101,131,161,40,70,100,130,160,39,69,99,129,159,38,68,98,128,158,37,67,97,127,157,36,66,96,126,156,35,65,95,125,155,34,64,94,124,154,33,63,93,123,153,32,62,92,122,152,31,61,91,121,151,30,60,90,120,150,29,59,89,119,149), (28,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29) );
GLFp := Group([[[ Z(151)^0, Z(151)^0 ], [ 0*Z(151), Z(151)^0 ]], [[ Z(151)^3, 0*Z(151) ], [ 0*Z(151), Z(151)^3 ]], [[ Z(151)^75, 0*Z(151) ], [ 0*Z(151), Z(151)^75 ]]]);

 
# Booleans 
booleans_7550_a := 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);