#######################
##
##        slice group of megaminx
##
################################

f1:=(2,4,6,8,10)(14,23,20,17,11)(24,21,18,15,13)(25,22,19,16,12);

rf2:=(2,1,10,13,25)(17,29,20,19,18)(9,12,14,24,3)
(6,16,28,30,21)(23,4,7,15,27)(26,22,5,8,11);

f2:=(9,12,14,24,3)(6,16,28,30,21)(23,4,7,15,27)(26,22,5,8,11);
f3:=rf2*f1*rf2^-1;
f8:=rf2^2*f1*rf2^-2;
f7:=rf2^3*f1*rf2^-3;
f6:=rf2^4*f1*rf2^-4;

rf4:=(5,4,21,19,6)(11,12,13,14,27)(7,3,22,20,18)
(10,25,26,28,15)(16,9,2,23,29)(24,30,17,8,1);

f5:=rf4*f1*rf4^-1;
f10:=rf4^2*f1*rf4^-2;
f9:=rf4^3*f1*rf4^-3;

g:=[];
g[1]:=f1;
g[2]:=f2;
g[3]:=f3;
g[4]:=f6;
g[5]:=f7;
g[6]:=f8;
g[7]:=f5;
g[8]:=f10;
g[9]:=f9;

c:=[1];

for i in [1..6]  do
  for j in [1..6] do
    c[6*(i-1)+j]:=g[i]*g[j]^-1;
  od;
od;

C:=Group(c,c[1]);