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Minimal supergroups (of index 23) isomorphic to the group 8 (Cm) of the group 8 (Cm)


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...
1Cm
(
   1   0   0   r
   0  23   0   0
   0   0   1   t
)


WP splitting


2Cm
(
   1   0   0   r
   0   1   0   0
   0   0  23   23t
)


WP splitting


3Cm
(
  23   0   0   23r
   0   1   0   0
   0   0   1   t
)


WP splitting


4Cm
(
   1   0  -1   r-t
   0   1   0   0
   0   0  23   23t
)


WP splitting


5Cm
(
  23   0   0   23r
   0   1   0   0
  -2   0   1   -2r+t
)


WP splitting


6Cm
(
   1   0  -3   r-3t
   0   1   0   0
   0   0  23   23t
)


WP splitting


7Cm
(
  23   0   0   23r
   0   1   0   0
  -4   0   1   -4r+t
)


WP splitting


8Cm
(
   1   0  -5   r-5t
   0   1   0   0
   0   0  23   23t
)


WP splitting


9Cm
(
  23   0   0   23r
   0   1   0   0
  -6   0   1   -6r+t
)


WP splitting


10Cm
(
   1   0  -7   r-7t
   0   1   0   0
   0   0  23   23t
)


WP splitting


11Cm
(
  23   0   0   23r
   0   1   0   0
  -8   0   1   -8r+t
)


WP splitting


12Cm
(
   1   0  -9   r-9t
   0   1   0   0
   0   0  23   23t
)


WP splitting


13Cm
(
  23   0   0   23r
   0   1   0   0
  -10   0   1   -10r+t
)


WP splitting


14Cm
(
   1   0  -11   r-11t
   0   1   0   0
   0   0  23   23t
)


WP splitting


15Cm
(
  23   0   0   23r
   0   1   0   0
  -12   0   1   -12r+t
)


WP splitting


16Cm
(
   1   0  -13   r-13t
   0   1   0   0
   0   0  23   23t
)


WP splitting


17Cm
(
  23   0   0   23r
   0   1   0   0
  -14   0   1   -14r+t
)


WP splitting


18Cm
(
   1   0  -15   r-15t
   0   1   0   0
   0   0  23   23t
)


WP splitting


19Cm
(
  23   0   0   23r
   0   1   0   0
  -16   0   1   -16r+t
)


WP splitting


20Cm
(
   1   0  -17   r-17t
   0   1   0   0
   0   0  23   23t
)


WP splitting


21Cm
(
  23   0   0   23r
   0   1   0   0
  -18   0   1   -18r+t
)


WP splitting


22Cm
(
   1   0  -19   r-19t
   0   1   0   0
   0   0  23   23t
)


WP splitting


23Cm
(
  23   0   0   23r
   0   1   0   0
  -20   0   1   -20r+t
)


WP splitting


24Cm
(
   1   0  -21   r-21t
   0   1   0   0
   0   0  23   23t
)


WP splitting


25Cm
(
  23   0   0   23r
   0   1   0   0
  -22   0   1   -22r+t
)


WP splitting








  

    
      
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