Bilbao Crystallographic Server contains two programs related with
The information you can obtain using the program MINSUP
is as follows: for a given space group the program shows a table with all of
the minimal supergroups of index 2, 3, and 4.
- MINSUP which gives all of the minimal supergroups of
index 2, 3, and 4 of a given group.
- SUPERGROUPS, which calculates all of the
different supergroups of a given type.
To specify the group for which you want to see the minimal supergroups, you should
give its number in the International Tables for Crystallography, Vol.A
or you can select it from the table with the space group numbers and symbols, which is
accessible through the link ``choose''.
The list with the minimal supergroups is represented as a table which contains:
- The number of the supergroup in the International Tables for
Crystallography, Vol. A, and its Hermann-Mauguin symbol.
- The index of the group in the supergroup and the supergroup type are
- A link to the list with the transformation matrices that related the
basis of the supergroup with that of the subgroup.
The table described above contains only the types of the minimal supergroups.
If you are interested in all of the supergroups of a given type, then you should
select the type of the supergroup, marking the corresponding checkbox and click on
the button [Show].
For a given supergroup-group pair with specified index the program
SUPERGROUPS gives all of the different
supergroups of the given type. The result contains:
- The transformation matrices that relate the basis of the supergroup
with that of the subgroup.
- One representative from each coset in the decomposition of the
supergroup with respect to the group and a link to the full cosets
in this decomposition
If you click oh the button [Full Cosets] you can see the
the coset decomposition of the supergroup with respect
to the group.
NOTE, that the coset representatives are given with respect to the basis of the
For some group-supergroup pairs there is a
parameter r,s, or/and t in the transformation matrix and in the
translational part of the coset representatives. This parameter can have any
value and each one of this values will give different supergroup of the same
The result from the calculation of all of the different supergroups contains:
- the transformation matrices and
- one representative from each coset in the
left cosets decomposition of the supergroup with respect to the group.
The button [Full Cosets] is provided to access the full cosets in
this decomposition. The page obtained using this button contains the correspondent
transformation matrix and the elements of the supergroup, given with respect to the
group and distributed into left cosets.
The program SUPERGROUPS gives the possibility to
obtain all of the different supergroups of the same type even if the supergroups
are not minimal. To do that you should give the supergroup and the group number
as given in the International Tables for Crystallography, vol.A, and
the index of the group in the supergroup. All of this data is
obligatory.. If you do not know the group number you can select it from the
table with the space group numbers and symbols.
When all of the data is given, click on [Find the Supergroups] to
obtain all of the different supergroups of the given
More about the program SUPERGROUPS