(International Tables) Wyckoff relations for space group 15

C2/c

No. 15

C_2h⁶

C 1 2/c 1
UNIQUE AXIS b
CELL CHOICE 1
	Axes	Coordinates	Wyckoff positions
			4a	4b	4c	4d	4e	8f
*I Maximal translationengleiche* subgroups**
[2] C1c1 (9)			4a	4a	4a	4a	4a	2 × 4a
[2] C121 (5)		x, y, z + (1/4)	4c	4c	4c	4c	2a; 2b	2 × 4c
[2] P-1 (2)	(1/2)(a - b), b, c	2x, x + y, z	1a; 1b	1c; 1g	1e; 1f	1d; 1h	2i	2 × 2i
*II Maximal klassengleiche* subgroups**
Loss of centring translations
[2] P12₁/n1 (14)			2a; 2b	2c; 2d	4e	4e	4e	2 × 4e
[2] P12₁/c1 (14)		x + (1/4), y + (1/4), z	4e	4e	2a; 2d	2b; 2c	4e	2 × 4e
[2] P12/c1 (13)			2a; 2b	2c; 2d	4g	4g	2e; 2f	2 × 4g
[2] P12/n1 (13)		x + (1/4), y + (1/4), z	4g	4g	2a; 2b	2c; 2d	2e; 2f	2 × 4g
Enlarged unit cell, isomorphic
[3] C12/c1	a, 3b, c	x, (1/3)y, z; ±(0, (1/3), 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	3 × 4e	3 × 8f
[p] C12/c1	a, pb, c	x, (1/p)y, z; +(0, (u/p), 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	p × 4e	p × 8f
	p = prime > 2; u = 1, . . ., p - 1				((p - 1)/2) × 8f	((p - 1)/2) × 8f
[3] C12/c1	3a, b, c	(1/3)x, y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] C12/c1	3a, b, 2a + c	(1/3)(x - 2z), y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] C12/c1	3a, b, -2a + c	(1/3)(x + 2z), y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] C12/c1	a, b, 3c	x, y, (1/3)z; ±(0, 0, (1/3))	4a; 8f	4b; 8f	4c; 8f	4d; 8f	4e; 8f	3 × 8f
[p] C12/c1	a, b, pc	x, y, (1/p)z; +(0, 0, (u/p))	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c; ((p - 1)/2) × 8f	4d; ((p - 1)/2) × 8f	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;
[p] C12/c1	pa, b, 2qa + c	(1/p)(x - 2qz), y, z; +((u/p), 0, 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;				((p - 1)/2) × 8f	((p - 1)/2) × 8f
	-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* p = 4n - 1

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3

A12/n1
UNIQUE AXIS b
CELL CHOICE 2
	Axes	Coordinates	Wyckoff positions
			4a	4b	4c	4d	4e	8f
*I Maximal translationengleiche* subgroups**
[2] A1n1			4a	4a	4a	4a	4a	2 × 4a
[2] A121		x - (1/4), y, z - (1/4)	4c	4c	4c	4c	2a; 2b	2 × 4c
[2] P-1	a, b, (1/2)(-b + c)	x, y + z, 2z	1a; 1e	1c; 1d	1g; 1h	1b; 1f	2i	2 × 2i
*II Maximal klassengleiche* subgroups**
Loss of centring translations
[2] P12₁/a1			2a; 2b	2c; 2d	4e	4e	4e	2 × 4e
[2] P12₁/n1		x, y + (1/4), z + (1/4)	4e	4e	2a; 2d	2b; 2c	4e	2 × 4e
[2] P12/n1			2a; 2b	2c; 2d	4g	4g	2e; 2f	2 × 4g
[2] P12/a1		x, y + (1/4), z + (1/4)	4g	4g	2a; 2b	2c; 2d	2e; 2f	2 × 4g
Enlarged unit cell, isomorphic
[3] A12/n1	a, 3b, c	x, (1/3)y, z; ±(0, (1/3), 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	3 × 4e	3 × 8f
[p] A12/n1	a, pb, c	x, (1/p)y, z; +(0, (u/p), 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	p × 4e	p × 8f
	p = prime > 2; u = 1, . . ., p - 1				((p - 1)/2) × 8f	((p - 1)/2) × 8f
[3] A12/n1	a - 2c, b, 3c	x, y, (1/3)(2x + z); ±(0, 0, (1/3))	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] A12/n1	a + 2c, b, 3c	x, y, (1/3)(-2x + z); ±(0, 0, (1/3))	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] A12/n1	a, b, 3c	x, y, (1/3)z; ±(0, 0, (1/3))	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] A12/n1	3a, b, c	(1/3)x, y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4c; 8f	4d; 8f	4e; 8f	3 × 8f
[p] A12/n1	pa, b, c	(1/p)x, y, z; +((u/p), 0, 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c; ((p - 1)/2) × 8f	4d; ((p - 1)/2) × 8f	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;
[p] A12/n1	a + 2qc, b, pc	x, y, (1/p)(-2qx + z); +(0, 0, (u/p))	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;				((p - 1)/2) × 8f	((p - 1)/2) × 8f
	-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* p = 4n - 1

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3

I12/a1
UNIQUE AXIS b
CELL CHOICE 3
	Axes	Coordinates	Wyckoff positions
			4a	4b	4c	4d	4e	8f
*I Maximal translationengleiche* subgroups**
I1a1			4a	4a	4a	4a	4a	2 × 4a
I121		x + (1/4), y, z	4c	4c	4c	4c	2a; 2b	2 × 4c
P-1	a, (1/2)(-a + b - c), c	x + y, 2y, y + z	1a; 1d	1b; 1f	1c; 1g	1e; 1h	2i	2 × 2i
*II Maximal klassengleiche* subgroups**
Loss of centring translations
P12₁/c1			2a; 2b	2c; 2d	4e	4e	4e	2 × 4e
P12₁/a1		x - (1/4), y + (1/4), z - (1/4)	4e	4e	2a; 2d	2b; 2c	4e	2 × 4e
P12/a1			2a; 2b	2c; 2d	4g	4g	2e; 2f	2 × 4g
P12/c1		x - (1/4), y + (1/4), z - (1/4)	4g	4g	2a; 2b	2c; 2d	2e; 2f	2 × 4g
Enlarged unit cell, isomorphic
I12/a1	a, 3b, c	x, (1/3)y, z; ±(0, (1/3), 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	3 × 4e	3 × 8f
I12/a1	a, pb, c	x, (1/p)y, z; +(0, (u/p), 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	p × 4e	p × 8f
	p = prime > 2; u = 1, . . ., p - 1				((p - 1)/2) × 8f	((p - 1)/2) × 8f
I12/a1	a, b, 2a + 3c	x - (2/3)z, y, (1/3)z; ±(0, 0, (1/3))	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
I12/a1	3a, b, 2a + c	(1/3)(x - 2z), y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
I12/a1	3a, b, c	(1/3)x, y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
I12/a1	a - 2c, b, 3c	x, y, (1/3)(2x + z); ±(0, 0, (1/3))	4a; 8f	4b; 8f	4c; 8f	4d; 8f	4e; 8f	3 × 8f
I12/a1	pa, b, c	(1/p)x, y, z; +((u/p), 0, 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c; ((p - 1)/2) × 8f	4d; ((p - 1)/2) × 8f	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;
I12/a1	a + 2qc, b, pc	x, y, (1/p)(-2qx + z); +(0, 0, (u/p))	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;				((p - 1)/2) × 8f	((p - 1)/2) × 8f
	-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* p = 4n - 1

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3

A112/a
UNIQUE AXIS c
CELL CHOICE 1
	Axes	Coordinates	Wyckoff positions
			4a	4b	4c	4d	4e	8f
*I Maximal translationengleiche* subgroups**
[2] A11a (9)			4a	4a	4a	4a	4a	2 × 4a
[2] A112 (5)		x + (1/4), y, z	4c	4c	4c	4c	2a; 2b	2 × 4c
[2] P-1 (2)	a, (1/2)(b - c), c	x, 2y, y + z	1a; 1d	1b; 1f	1e; 1g	1c; 1h	2i	2 × 2i
*II Maximal klassengleiche* subgroups**
Loss of centring translations
[2] P112₁/n (14)			2a; 2b	2c; 2d	4e	4e	4e	2 × 4e
[2] P112₁/a (14)		x, y + (1/4), z + (1/4)	4e	4e	2a; 2d	2b; 2c	4e	2 × 4e
[2] P112/a (13)			2a; 2b	2c; 2d	4g	4g	2e; 2f	2 × 4g
[2] P112/n (13)		x, y + (1/4), z + (1/4)	4g	4g	2a; 2b	2c; 2d	2e; 2f	2 × 4g
Enlarged unit cell, isomorphic
[3] A112/a	a, b, 3c	x, y, (1/3)z; ±(0, 0, (1/3))	4a; 8f	4b; 8f	4d; 8f	4c; 8f	3 × 4e	3 × 8f
[p] A112/a	a, b, pc	x, y, (1/p)z; +(0, 0, (u/p))	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	p × 4e	p × 8f
	p = prime > 2; u = 1, . . ., p - 1				((p - 1)/2) × 8f	((p - 1)/2) × 8f
[3] A112/a	a, 3b, c	x, (1/3)y, z; ±(0, (1/3), 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] A112/a	a + 2b, 3b, c	x, (1/3)(-2x + y), z; ±(0, (1/3), 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] A112/a	a - 2b, 3b, c	x, (1/3)(2x + y), z; ±(0, (1/3), 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] A112/a	3a, b, c	(1/3)x, y, z,; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4c; 8f	4d; 8f	4e; 8f	3 × 8f
[p] A112/a	pa, b, c	(1/p)x, y, z; +((u/p), 0, 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c; ((p - 1)/2) × 8f	4d; ((p - 1)/2) × 8f	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;
[p] A112/a	a + 2qb, pb, c	x, (1/p)(-2qx + y), z; +(0, (u/p), 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;				((p - 1)/2) × 8f	((p - 1)/2) × 8f
	-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* p = 4n - 1

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3

B112/n
UNIQUE AXIS c
CELL CHOICE 2
	Axes	Coordinates	Wyckoff positions
			4a	4b	4c	4d	4e	8f
*I Maximal translationengleiche* subgroups**
[2] B11n			4a	4a	4a	4a	4a	2 × 4a
[2] B112		x - (1/4), y - (1/4), z	4c	4c	4c	4c	2a; 2b	2 × 4c
[2] P-1	(1/2)(a - c), b, c	2x, y, x + z	1a; 1g	1b; 1c	1f; 1h	1d; 1e	2i	2 × 2i
*II Maximal klassengleiche* subgroups**
Loss of centring translations
[2] P112₁/b			2a; 2b	2c; 2d	4e	4e	4e	2 × 4e
[2] P112₁/n		x + (1/4), y, z + (1/4)	4e	4e	2a; 2d	2b; 2c	4e	2 × 4e
[2] P112/n			2a; 2b	2c; 2d	4g	4g	2e; 2f	2 × 4g
[2] P112/b		x + (1/4), y, z + (1/4)	4g	4g	2a; 2b	2c; 2d	2e; 2f	2 × 4g
Enlarged unit cell, isomorphic
[3] B112/n	a, b, 3c	x, y, (1/3)z; ±(0, 0, (1/3))	4a; 8f	4b; 8f	4d; 8f	4c; 8f	3 × 4e	3 × 8f
[p] B112/n	a, b, pc	x, y, (1/p)z; +(0, 0, (u/p))	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	p × 4e	p × 8f
	p = prime > 2; u = 1, . . ., p - 1				((p - 1)/2) × 8f	((p - 1)/2) × 8f
[3] B112/n	3a, -2a + b, c	(1/3)(x + 2y), y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] B112/n	3a, 2a + b, c	(1/3)(x - 2y), y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] B112/n	3a, b, c	(1/3)z, y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
[3] B112/n	a, 3b, c	x, (1/3)y, z; ±(0, (1/3), 0)	4a; 8f	4b; 8f	4c; 8f	4d; 8f	4e; 8f	3 × 8f
[p] B112/n	a, pb, c	x, (1/p)y, z; +(0, (u/p), 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c; ((p - 1)/2) × 8f	4d; ((p - 1)/2) × 8f	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;
[p] B112/n	pa, 2qa + b, c	(1/p)(x - 2qy), y, z; +((u/p), 0, 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;				((p - 1)/2) × 8f	((p - 1)/2) × 8f
	-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* p = 4n - 1

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3

I112/b
UNIQUE AXIS c
CELL CHOICE 3
	Axes	Coordinates	Wyckoff positions
			4a	4b	4c	4d	4e	8f
*I Maximal translationengleiche* subgroups**
I11b			4a	4a	4a	4a	4a	2 × 4a
I112		x, y + (1/4), z	4c	4c	4c	4c	2a; 2b	2 × 4c
P-1	a, b, (1/2)(-a - b + c)	x + z, y + z, 2z	1a; 1c	1d; 1e	1b; 1f	1g; 1h	2i	2 × 2i
*II Maximal klassengleiche* subgroups**
Loss of centring translations
P112₁/a			2a; 2b	2c; 2d	4e	4e	4e	2 × 4e
P112₁/b		x - (1/4), y - (1/4), z + (1/4)	4e	4e	2a; 2d	2b; 2c	4e	2 × 4e
P112/b			2a; 2b	2c; 2d	4g	4g	2e; 2f	2 × 4g
P112/a		x - (1/4), y - (1/4), z + (1/4)	4g	4g	2a; 2b	2c; 2d	2e; 2f	2 × 4g
Enlarged unit cell, isomorphic
I112/b	a, b, 3c	x, y, (1/3)z; ±(0, 0, (1/3))	4a; 8f	4b; 8f	4d; 8f	4c; 8f	3 × 4e	3 × 8f
I112/b	a, b, pc	x, y, (1/p)z; +(0, 0, (u/p))	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	p × 4e	p × 8f
	p = prime > 2; u = 1, . . ., p - 1				((p - 1)/2) × 8f	((p - 1)/2) × 8f
I112/b	3a + 2b, b, c	(1/3)x, -(2/3)x + y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
I112/b	a + 2b, 3b, c	x, (1/3)(-2x + y), z; ±(0, (1/3), 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
I112/b	a, 3b, c	x, (1/3)y, z; ±(0, (1/3), 0)	4a; 8f	4b; 8f	4d; 8f	4c; 8f	4e; 8f	3 × 8f
I112/b	3a, -2a + b, c	(1/3)(x + 2y), y, z; ±((1/3), 0, 0)	4a; 8f	4b; 8f	4c; 8f	4d; 8f	4e; 8f	3 × 8f
I112/b	a, pb, c	x, (1/p)y, z; +(0, (u/p), 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c; ((p - 1)/2) × 8f	4d; ((p - 1)/2) × 8f	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;
I112/b	pa, 2qa + b, c	(1/p)(x - 2qy), y, z; +((u/p), 0, 0)	4a; ((p - 1)/2) × 8f	4b; ((p - 1)/2) × 8f	4c(d*);	4d(c*);	4e; ((p - 1)/2) × 8f	p × 8f
	p = prime > 2; u = 1, . . ., p - 1;				((p - 1)/2) × 8f	((p - 1)/2) × 8f
	-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* p = 4n - 1

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3