Space group decoding - instructions

Rules for the input of a Hermann Mauguin space group symbol :

First letter is the Bravais symbol describing translational symmetry of the unit cell (P,A,B,C,R,I,F) followed by a blank (space).
The symmetry operator symbols generating the equipoints in the unit cell follow. They are all separated by a blank - except if a slash combines them (denoting that the symmetry plane is perpendicular to the corresponding symmetry axis). Example : I 4/m m m (not case sensitive)
A screw axis (usually denoted by a subscript following the axis) is entered as two adjacent numbers :
P 63/M M C, P 21 21 21
An inversion (shown by the bar above the axis) is entered as a minus sign. Example : R -3 C. The exception is the triade in the cubic systems, which is automatically recognized as an inversion in the centrosymmetric groups and thus can be omitted: F D 3 M is ok, and so is F d -3 m.
Settings with origin at center must be used.
Use monoclinic setting with b as unique axis (alpha, gamma = 90.0°).
Use obverse hexagonal setting for rhobohedral space groups.

List of recognized Hermann Mauguin Space Group Symbols

Enantiomorphic (chiral) space groups in green, chiral space groups with multiple indexing possibilities in red, polar space groups with undefined origin in bold red

 TRICLINIC
 P 1          P -1

 MONOCLINIC
 P 2         P 21        C 2         P M         P C
 C M         C C         P 2/M       P 21/M      C 2/M
 P 2/C       P 21/C      C 2/C

 ORTHORHOMBIC
 P 2 2 2     P 2 2 21    P 21 21 2   P 21 21 21  C 2 2 21
 C 2 2 2     F 2 2 2     I 2 2 2     I 21 21 21  P M M 2
 P M C 21    P C C 2     P M A 2     P C A 21    P N C 2
 P M N 21    P B A 2     P N A 21    P N N 2     C M M 2
 C M C 21    C C C 2     A M M 2     A B M 2     A M A 2
 A B A 2     F M M 2     F D D 2     I M M 2     I B A 2
 I M A 2     P M M M     P N N N     P C C M     P B A N
 P M M A     P N N A     P M N A     P C C A     P B A M
 P C C N     P B C M     P N N M     P M M N     P B C N
 P B C A     P N M A     C M C M     C M C A     C M M M
 C C C M     C M M A     C C C A     F M M M     F D D D
 I M M M     I B A M     I B C A     I M M A

 TETRAGONAL
 P 4         P 41        P 42        P 43        I 4
 I 41        P -4        I -4        P 4/M       P 42/M
 P 4/N       P 42/N      I 4/M       I 41/A      P 4 2 2
 P 4 21 2    P 41 2 2    P 41 21 2   P 42 2 2    P 42 21 2
 P 43 2 2    P 43 21 2   I 4 2 2     I 41 2 2    P 4 M M
 P 4 B M     P 42 C M    P 42 N M    P 4 C C     P 4 N C
 P 42 M C    P 42 B C    I 4 M M     I 4 C M     I 41 M D
 I 41 C D    P -4 2 M    P -4 2 C    P -4 21 M   P -4 21 C
 I -4 M 2    P -4 C 2    P -4 B 2    P -4 N 2    P -4 M 2
 I -4 C 2    I -4 2 M    I -4 2 D    P 4/M M M   P 4/M C C
 P 4/N B M   P 4/N N C   P 4/M B M   P 4/M N C   P 4/N M M
 P 4/N C C   P 42/M M C  P 42/M C M  P 42/N B C  P 42/N N M
 P 42/M B C  P 42/M N M  P 42/N M C  P 42/N C M  I 4/M M M
 I 4/M C M   I 41/A M D  I 41/A C D

 TRIGONAL
 P 3         P 31        P 32        R 3         P -3
 R -3        P 3 1 2     P 3 2 1     P 31 1 2   P 31 2 1
 P 32 1 2    P 32 2 1    R 3 2       P 3 M 1     P 3 1 M
 P 3 C 1     P 3 1 C     R 3 M       R 3 C       P -3 1 M
 P -3 1 C    P -3 M 1    P -3 C 1    R -3 M      R -3 C

 HEXAGONAL
 P 6         P 61        P 65        P 62        P 64
 P 63        P -6        P 6/M       P 63/M      P 6 2 2
 P 61 2 2    P 65 2 2    P 62 2 2    P 64 2 2    P 63 2 2
 P 6 M M     P 6 C C     P 63 C M    P 63 M C    P -6 M 2
 P -6 C 2    P -6 2 M    P -6 2 C    P 6/M M M   P 6/M C C
 P 63/M C M  P 63/M M C

 CUBIC (minus sign in front of triade optional)
 P 2 3       F 2 3       I 2 3       P 21 3      I 21 3
 P M 3       P N 3       F M 3       F D 3       I M 3
 P A 3       I A 3       P 4 3 2     P 42 3 2    F 4 3 2
 F 41 3 2    I 4 3 2     P 43 3 2    P 41 3 2    I 41 3 2
 P -4 3 M    F -4 3 M    I -4 3 M    P -4 3 N    F -4 3 C
 I -4 3 D    P M 3 M     P N 3 N     P M 3 N     P N 3 M
 F M 3 M     F M 3 C     F D 3 M     F D 3 C     I M 3 M
 I A 3 D

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