1. Species
2. List of 122 magnetic point group classes
3. Orientation of two-fold axes and mirror plane operations of F with respect to G
4. Internal symmetry of the tabulated macroscopic tensors
5. Layout of the tabulated arrays of the property-tensor matrices

1. Species

Two different symmetry-breaking phase transitions in a crystalline material are said to belong to the same species G > F if their high-symmetry phase belong to same macroscopic symmetry class G, their low-symmetry phase belong to same macroscopic symmetry class F and for a suitably chosen domain state they have the same correspondence between the symmetry elements of symmetry groups G and F. Species No.: serial number #... of a species from the list of all 212 species G … crystallographic point group or class expressing the symmetry of the high-symmetry (parent, prototypic) phase F … crystallographic point group of a representative domain state of the low-symmetry (descent, ferroic) phase or the associated oriented class. When necessary, the orientation of the symmetry elements in F with respect to G is indicated by extra subscripts |,/,_,+. Their meaning is given in Section 3.

2. List of 122 magnetic point group classes

All the magnetic point groups are listed here.

3. Orientation of two-fold axes and mirror plane operations of F with respect to G

Symmetry of point group G	Tetragonal and hexagonal				Cubic
Orientation of two-fold axes 2 and mirror planes m of subgroup F in rectangular coordinate system of point group G	[001]	(001)	<100>	{100}	<100>	{100}	<110>	{110)
Notation	2|	m|	2–	m–	2+	m+	2\	m\

4. Internal symmetry of the tabulated macroscopic tensors

Symbol	Matrix components		Tensor	Internal symmetry of a tensor	Physical property
	Symbol	Number
c	c	1	Scalar	c	Heat capacity
P	Pi	3	Polar vector	V	Spontaneous polarization, pyroelectricity, electrocaloric effect
M	Mi	3	Tensor of the 1st rank	aεV	Spontaneous magnetization, pyromagneticity, magnetocaloric effect
u ε	uμ εi,j	6	Tensor of the 2nd rank	[V2]	Strain*) Permittivity
α	αi,j	9	Tensor of the 2nd rank	aεV2	Magnetoelectric effect
d r	diμ riμ	18	Tensor of the 3rd rank	V[V2]	Piezoelectricity*) Electrooptics*)
Λ	Λiμ	18	Tensor of the 3rd rank	aεV[V2]	Piezomagnecity*)
s	sμν	21	Tensor of the 4th rank	[[V2]2]	Elastic compliance*)
Q π	Qμ,ν πμ,ν	36	Tensor of the 4th rank	[V2]2	Electrostriction*) Piezooptics*)

i, j = 1,2,3; μ,ν = 1,2,...,6.
^*) in contracted (matrix) notation

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