%id
U3C
%name
Dihedral U3C
%central_charge
16/11
%group
%%name
Sym(3)
%%order
6
%character
1, 0, 3, 4, 10, 16, 29, 44, 77, 112, 178
%modules
%%number
5
%%weights
0, 2/11, 6/11, 1/11, 9/11
%mtc
%properties
rational
unitary
C2
%subvoas
%%subvoa
%%%id
minimal1
%%%orbit
%%%%centralizer
2
%%%%order
2
%%%%length
3
%%%%coset
minimal-except9
%%%%
%%note
there are 2^3-1=7 Virasoro vectors in V: 3 times L(1/2,0) and 3 times L(21/22,0) and the conformal vector.
%%subvoa
%%%id
coset-kmA8_1-1
%%%note
V decomposes into 3 irreducible modules of conformal weight 0, 2, 2 under this subalgebra
%references
%%ref
%%%author
J. Conway
%%%title
A simple construction for the Fischer-Griess monster group
%%ref
%%%author
C. H. Lam
H. Yamada
H. Yamauchi
%%%title
McKay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2
%source
G. H. by hand
%note
V is the extension  L(1/2,0) x (L(21/22,0) + L(21/22,8)) + L(1/2,1/2) x (L(21/22,7/2) + L(21/22,45/2) +  L(1/2,1/16) x (L(21/22,31/16) + L(21/22,175/16))  