%id
U3A
%name
Dihedral U3A
%central_charge
58/35
%group
%%name
Sym(3)
%%order
6
%character
1, 0, 4
%mtc
lee_yang.3fieldsx-
%modules
%%number
6
%%weights
0, 1/7, 5/7, 2/5, 19/35, 4/35
%mtc
%properties
rational
unitary
C2
%subvoas
%%subvoa
%%%id
ising
%%%orbit
%%%%centralizer
2
%%%%length
3
%%%%coset
N1minimal3
%%subvoa
%%%id
minimal3
%%%orbit
%%%%centralizer
2
%%%%order
2
%%%%length
3
%%%%coset
minimal4
%%%%note
subVOA not extendable to minimal-ext3
%%subvoa
%%%id
minimal-ext3
%%%orbit
%%%%centralizer
Sym(3)
%%%%length
1
%%%%coset
minimal-ext4
%%note
There are 2^4-1=15 Virasoro vectors in V corresponding to the above subVOAs and the conformal vector
%griess_algebra
%%product
{2,0,0,0}, {0,0,0,0}, {0,0,2/3,0}, {0,0,0,2/3}
{0,0,0,0}, {0,2,0,0}, {0,0,4/3,0}, {0,0,0,4/3}
{0,0,2/3,0}, {0,0,4/3,0}, {0,0,0,20}, {135,252,0,0}
{0,0,0,2/3}, {0,0,0,4/3}, {135,252,0,0}, {0,0,20,0}
%%form
2/5, 0, 0, 0
0, 3/7, 0, 0
0, 0, 0, 81
0, 0, 81, 0
%references
%%ref
%%%author
J. Conway
%%%title
A simple construction for the Fischer-Griess monster group
%%ref
%%%author
S. Sakuma
H. Yamauchi
%%%title
Vertex operator algebra with two Miyamoto involutions generating S3
%%%classic
Journal of Algebra 267 (2003), 272-297
%source
G. H. and H. Y. by hand
%note
this is a small example in which there are two orbits of the same subVOA.