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Minimal supergroups (of index 19) isomorphic to the group 6 (Pm) of the group 6 (Pm)


Minimal Supergroups
Each supergroup is determined by:
  • The transformation matrix relating the basis of the supergroup with of the subgroup - given in the column Transformation matrix.
  • The coset representatives in the decomposition of the supergroup with respect to the subgroup G = H + Hg + ... one representative from each coset of the decomposition is given in the column Coset representative. To see all the representatives click over [Full cosets].
There are group-supergroup pairs for which there are parameter/s in the translational part of the transformation matrix.
In this case if there are the same parameters in the cosets representatives for each value of the parameters different supergroup of the same type will be obtained. 
NNon-conventional HM symbol Transformation matrixCoset RepresentativesWyckoff SplittingMore...
1Pm
(
   1   0   0   r
   0  19   0   0
   0   0   1   t
)


WP splitting


2Pm
(
   1   0   0   r
   0   1   0   0
   0   0  19   19t
)


WP splitting


3Pm
(
  19   0   0   19r
   0   1   0   0
   0   0   1   t
)


WP splitting


4Pm
(
  19   0   0   19r
   0   1   0   0
  -1   0   1   -r+t
)


WP splitting


5Pm
(
  19   0   0   19r
   0   1   0   0
  -2   0   1   -2r+t
)


WP splitting


6Pm
(
  19   0   0   19r
   0   1   0   0
  -3   0   1   -3r+t
)


WP splitting


7Pm
(
  19   0   0   19r
   0   1   0   0
  -4   0   1   -4r+t
)


WP splitting


8Pm
(
  19   0   0   19r
   0   1   0   0
  -5   0   1   -5r+t
)


WP splitting


9Pm
(
  19   0   0   19r
   0   1   0   0
  -6   0   1   -6r+t
)


WP splitting


10Pm
(
  19   0   0   19r
   0   1   0   0
  -7   0   1   -7r+t
)


WP splitting


11Pm
(
  19   0   0   19r
   0   1   0   0
  -8   0   1   -8r+t
)


WP splitting


12Pm
(
  19   0   0   19r
   0   1   0   0
  -9   0   1   -9r+t
)


WP splitting


13Pm
(
  19   0   0   19r
   0   1   0   0
  -10   0   1   -10r+t
)


WP splitting


14Pm
(
  19   0   0   19r
   0   1   0   0
  -11   0   1   -11r+t
)


WP splitting


15Pm
(
  19   0   0   19r
   0   1   0   0
  -12   0   1   -12r+t
)


WP splitting


16Pm
(
  19   0   0   19r
   0   1   0   0
  -13   0   1   -13r+t
)


WP splitting


17Pm
(
  19   0   0   19r
   0   1   0   0
  -14   0   1   -14r+t
)


WP splitting


18Pm
(
  19   0   0   19r
   0   1   0   0
  -15   0   1   -15r+t
)


WP splitting


19Pm
(
  19   0   0   19r
   0   1   0   0
  -16   0   1   -16r+t
)


WP splitting


20Pm
(
  19   0   0   19r
   0   1   0   0
  -17   0   1   -17r+t
)


WP splitting


21Pm
(
  19   0   0   19r
   0   1   0   0
  -18   0   1   -18r+t
)


WP splitting








  

    
      
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