Gallulin's Table of 219 (230) Space Groups

GALIULIN'S TABLE OF 219 (230) SPACE GROUPS

32 Crystal Classes

Systems	Merohedries
i	1
2/m	2	m
mmm	222	mm2
4/mmm	422	4mm	4i2m	4m	4		4i
6/mmm	622	6mm	6i2m	6m	6		6i
				3im	32	3m		3i	3
m3m	432		4i3m	m3	23

219 (230) SPACE GROUPS

P1+.

P2/m
P2/b
- - -
I2/m
I2/b

P2s/m
P2s/b
- - -

P2.
P2s+.
- - - -
I2.

Pm.
Pb+.
- - -
Im.
Ib+.

Pmmm" Pccm Pban Pnnn	Pmma Pmna Pbam Pmmn Pnnm Pcca Pnna Pbcm Pbcn Pccn Pnma Pbca
- - - Cmmm' Cccm Cmma Ccca	- - - Cmcm Cmca
- - - Immm' Ibam	- - - Imma Ibca
- - - Fmmm' Fddd	- - -

P222
P222s
P2s2s2
P2s2s2s+

- - - - -
C222
C222s

- - - - -
I222
I2s2s2s

- - - - -
F222

Pmm2. Pcc2. Pma2. Pnc2. Pnn2. Pba2.	Pmc2s. Pmn2s. Pca2s+. Pna2s+.
- - - Cmm2. Ccc2. ..... C2mm. C2mb. C2cm. C2cb.	- - - Cmc2s. .....
- - - Imm2. Ima2. Iba2.	- - -
- - - Fmm2. Fdd2	- - -

P4/mmm" P4/mcc P4/nbm P4/nnc	P4/mbm' P4/nmm P4/mnc P4s/mmc' P4s/mcm' P4s/nnm P4s/mnm' P4s/nmc P4/ncc P4s/nbc P4s/ncm P4s/mbc
- - - I4/mmm' I4/mcm'	- - - I4r/amd I4r/acd

P422
P422s
P4s22
P4s22s
P4r22*
P4r22s*

- - - - -
I422
I4r22

P4mm. P4cc. P4bm. P4nc.	P4smc. P4snm. P4scm. P4sbc.
- - - I4mm. I4cm.	- - - I4rmd I4rcd

P4i2m P4i2c ..... P4im2 P4ic2 P4ib2 P4in2	P4i2sm P4i2sc ......
- - - I4i2m ..... I4im2 I4ic2	- - - I4i2d .....

P4/m P4/n	P4s/m P4s/n
- - - I4/m	- - - I4r/a

P4.
P4s.
P4r+*

- - -
I4.
I4r

- - -

P4i

- -
I4i

P6/mmm"
P6/mcc

P6s/mcm'
P6s/mmc'

P622
P6s22
P6rr22*
P6r22*

P6mm.
P6cc.

P6smc.
P6scm.

P6i2m'
P6i2c
.....
P6i2m"
P6ic2

......

P6/m

P6s/m

P6.
P6s.
P6rr*
P6r*+

P6i

P3im1
P3ic1
.........
P3i1m
P3i1c

P321
P3r21*
......
P312
P3r12*

P3m1.
P3c1.
.....
P31m.
P31c.

P3i

P3.
P3r*+

R3im
R3ic

R32

R3m
R3c

R3i

Pm3m" Pn3n	Pm3n' Pn3m'
- - - Im3m'	- - - Ia3d
- - - Fm3m" Fm3c'	- - - Fd3m' Fd3c

P432
P4s32
P4r32*

- - -
I432
I4r32

- - -
F432
F4r32

- - - - - - -

P4i3m' P4i3n'
- - - I4i3m'	- - - I4i3d
- - - F4i3m" F4i3c	- - -

Pm3' Pn3	Pa3
- - - Im3'	- - - Ia3
- - - Fm3' Fd3	- - -

P23
P2s3

- - -
I23
I2s3

- - -
F23

* - enantiamorphous
+ - without special points
- - kaleidoscopics
' - Molnars
. - degenerations

by E.S.Fedorov - the groups of symmetry transformations of discrete regular objects;
by D.Hilbert - the discrete groups of moving with finite independent regions;
by H.Zassenhaus - such finite exension of free abelian group in which only identity of factor-group corresponds identity automorphism of normal divisor.

If you want to look at the same table in a compact form cleak here.