# Group 93312.cl downloaded from the LMFDB on 06 November 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(83653592321549767217687766029954780498622756788208068263977960468513988549848473933830876895436732623347663956887209204277029447594655438756280309755196383027615385412072308749731573636208644453173650773,93312); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.6; e := GPC.8; f := GPC.10; g := GPC.12;
GPerm := Group( (1,3,6)(2,4,8)(9,10,13)(12,17,15)(18,19,22,26,24,20,25,23,21)(27,29)(28,30), (1,4)(2,3)(5,7)(6,8)(9,11,13,16,10,14)(12,15,17)(18,20,26,22,25,21)(23,24)(27,30), (1,2)(3,5)(4,7)(6,8)(9,10,13)(11,12,16,17,14,15)(19,22,23,20,24,21)(25,26)(27,28,30,29), (1,4,3,2)(5,6,8,7)(9,12)(10,15)(13,17)(18,21,26,20,25,22)(19,23)(27,29,30,28) );

 
# Booleans 
booleans_93312_cl := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false);