Corepresentations PG

Irreducible corepresentations of the Projective Magnetic Point Group 4mm1'

Table of characters of the unitary symmetry operations

	1	4⁺ 4^-	2 ^d2	m₁₀ m₀₁ ^dm₁₀ ^dm₀₁	m_1-1 m₁₁ ^dm_1-1 ^dm₁₁	^d1	^d4⁺ ^d4^-
A₁	1	1	1	1	1	1	1
A₂	1	1	1	-1	-1	1	1
B₁	1	-1	1	1	-1	1	-1
B₂	1	-1	1	-1	1	1	-1
E	2	0	-2	0	0	2	0

E₂	2	-√2	0	0	0	-2	√2
E₁	2	√2	0	0	0	-2	-√2

Multiplication table of the symmetry operations

4⁺

4^-

m₁₀

m_1-1

m₀₁

m₁₁

^d1

^d4⁺

^d2

^d4^-

^dm₁₀

^dm_1-1

^dm₀₁

^dm₁₁

4⁺'

4^-'

m'₁₀

m'_1-1

m'₀₁

m'₁₁

^d1'

^d4⁺'

^d2'

^d4^-'

^dm'₁₀

^dm'_1-1

^dm'₀₁

^dm'₁₁

4⁺

4^-

m₁₀

m_1-1

m₀₁

m₁₁

^d1

^d4⁺

^d2

^d4^-

^dm₁₀

^dm_1-1

^dm₀₁

^dm₁₁

4⁺'

4^-'

m'₁₀

m'_1-1

m'₀₁

m'₁₁

^d1'

^d4⁺'

^d2'

^d4^-'

^dm'₁₀

^dm'_1-1

^dm'₀₁

^dm'₁₁

4⁺

^d4^-

m₁₁

^dm₁₀

m_1-1

m₀₁

^d4⁺

^d2

4^-

^d1

^dm₁₁

m₁₀

^dm_1-1

^dm₀₁

4⁺'

^d4^-'

m'₁₁

^dm'₁₀

m'_1-1

m'₀₁

^d4⁺'

^d2'

4^-'

^d1'

^dm'₁₁

m'₁₀

^dm'_1-1

^dm'₀₁

^d4^-

^d1

4⁺

m₀₁

^dm₁₁

^dm₁₀

m_1-1

^d2

4^-

^d4⁺

^dm₀₁

m₁₁

m₁₀

^dm_1-1

^d4^-'

^d1'

4⁺'

m'₀₁

^dm'₁₁

^dm'₁₀

m'_1-1

^d2'

4^-'

^d4⁺'

^dm'₀₁

m'₁₁

m'₁₀

^dm'_1-1

4^-

4⁺

^d2

^dm_1-1

m₀₁

m₁₁

m₁₀

^d4^-

^d1

^d4⁺

m_1-1

^dm₀₁

^dm₁₁

^dm₁₀

4^-'

4⁺'

^d2'

^dm'_1-1

m'₀₁

m'₁₁

m'₁₀

^d4^-'

^d1'

^d4⁺'

m'_1-1

^dm'₀₁

^dm'₁₁

^dm'₁₀

m₁₀

^dm_1-1

^dm₀₁

m₁₁

^d1

4⁺

^d4^-

^dm₁₀

m_1-1

m₀₁

^dm₁₁

^d4⁺

^d2

4^-

m'₁₀

^dm'_1-1

^dm'₀₁

m'₁₁

^d1'

4⁺'

^d4^-'

^dm'₁₀

m'_1-1

m'₀₁

^dm'₁₁

^d4⁺'

^d2'

4^-'

m_1-1

m₀₁

m₁₁

^dm₁₀

4^-

^d1

^d4⁺

^d2

^dm_1-1

^dm₀₁

^dm₁₁

m₁₀

^d4^-

4⁺

m'_1-1

m'₀₁

m'₁₁

^dm'₁₀

4^-'

^d1'

^d4⁺'

^d2'

^dm'_1-1

^dm'₀₁

^dm'₁₁

m'₁₀

^d4^-'

4⁺'

m₀₁

m₁₁

m₁₀

m_1-1

^d2

^d4^-

^d1

^d4⁺

^dm₀₁

^dm₁₁

^dm₁₀

^dm_1-1

4^-

4⁺

m'₀₁

m'₁₁

m'₁₀

m'_1-1

^d2'

^d4^-'

^d1'

^d4⁺'

^dm'₀₁

^dm'₁₁

^dm'₁₀

^dm'_1-1

4^-'

4⁺'

m₁₁

m₁₀

^dm_1-1

m₀₁

^d4⁺

^d4^-

^d1

^dm₁₁

^dm₁₀

m_1-1

^dm₀₁

4⁺

^d2

4^-

m'₁₁

m'₁₀

^dm'_1-1

m'₀₁

^d4⁺'

^d4^-'

^d1'

^dm'₁₁

^dm'₁₀

m'_1-1

^dm'₀₁

4⁺'

^d2'

4^-'

^d1

^d4⁺

^d2

^d4^-

^dm₁₀

^dm_1-1

^dm₀₁

^dm₁₁

4⁺

4^-

m₁₀

m_1-1

m₀₁

m₁₁

^d1'

^d4⁺'

^d2'

^d4^-'

^dm'₁₀

^dm'_1-1

^dm'₀₁

^dm'₁₁

4⁺'

4^-'

m'₁₀

m'_1-1

m'₀₁

m'₁₁

^d4⁺

^d2

4^-

^d1

^dm₁₁

m₁₀

^dm_1-1

^dm₀₁

4⁺

^d4^-

m₁₁

^dm₁₀

m_1-1

m₀₁

^d4⁺'

^d2'

4^-'

^d1'

^dm'₁₁

m'₁₀

^dm'_1-1

^dm'₀₁

4⁺'

^d4^-'

m'₁₁

^dm'₁₀

m'_1-1

m'₀₁

^d2

4^-

^d4⁺

^dm₀₁

m₁₁

m₁₀

^dm_1-1

^d4^-

^d1

4⁺

m₀₁

^dm₁₁

^dm₁₀

m_1-1

^d2'

4^-'

^d4⁺'

^dm'₀₁

m'₁₁

m'₁₀

^dm'_1-1

^d4^-'

^d1'

4⁺'

m'₀₁

^dm'₁₁

^dm'₁₀

m'_1-1

^d4^-

^d1

^d4⁺

m_1-1

^dm₀₁

^dm₁₁

^dm₁₀

4^-

4⁺

^d2

^dm_1-1

m₀₁

m₁₁

m₁₀

^d4^-'

^d1'

^d4⁺'

m'_1-1

^dm'₀₁

^dm'₁₁

^dm'₁₀

4^-'

4⁺'

^d2'

^dm'_1-1

m'₀₁

m'₁₁

m'₁₀

^dm₁₀

m_1-1

m₀₁

^dm₁₁

^d4⁺

^d2

4^-

m₁₀

^dm_1-1

^dm₀₁

m₁₁

^d1

4⁺

^d4^-

^dm'₁₀

m'_1-1

m'₀₁

^dm'₁₁

^d4⁺'

^d2'

4^-'

m'₁₀

^dm'_1-1

^dm'₀₁

m'₁₁

^d1'

4⁺'

^d4^-'

^dm_1-1

^dm₀₁

^dm₁₁

m₁₀

^d4^-

4⁺

m_1-1

m₀₁

m₁₁

^dm₁₀

4^-

^d1

^d4⁺

^d2

^dm'_1-1

^dm'₀₁

^dm'₁₁

m'₁₀

^d4^-'

4⁺'

m'_1-1

m'₀₁

m'₁₁

^dm'₁₀

4^-'

^d1'

^d4⁺'

^d2'

^dm₀₁

^dm₁₁

^dm₁₀

^dm_1-1

4^-

4⁺

m₀₁

m₁₁

m₁₀

m_1-1

^d2

^d4^-

^d1

^d4⁺

^dm'₀₁

^dm'₁₁

^dm'₁₀

^dm'_1-1

4^-'

4⁺'

m'₀₁

m'₁₁

m'₁₀

m'_1-1

^d2'

^d4^-'

^d1'

^d4⁺'

^dm₁₁

^dm₁₀

m_1-1

^dm₀₁

4⁺

^d2

4^-

m₁₁

m₁₀

^dm_1-1

m₀₁

^d4⁺

^d4^-

^d1

^dm'₁₁

^dm'₁₀

m'_1-1

^dm'₀₁

4⁺'

^d2'

4^-'

m'₁₁

m'₁₀

^dm'_1-1

m'₀₁

^d4⁺'

^d4^-'

^d1'

4⁺'

4^-'

m'₁₀

m'_1-1

m'₀₁

m'₁₁

^d1'

^d4⁺'

^d2'

^d4^-'

^dm'₁₀

^dm'_1-1

^dm'₀₁

^dm'₁₁

^d1

^d4⁺

^d2

^d4^-

^dm₁₀

^dm_1-1

^dm₀₁

^dm₁₁

4⁺

4^-

m₁₀

m_1-1

m₀₁

m₁₁

4⁺'

^d4^-'

m'₁₁

^dm'₁₀

m'_1-1

m'₀₁

^d4⁺'

^d2'

4^-'

^d1'

^dm'₁₁

m'₁₀

^dm'_1-1

^dm'₀₁

^d4⁺

^d2

4^-

^d1

^dm₁₁

m₁₀

^dm_1-1

^dm₀₁

4⁺

^d4^-

m₁₁

^dm₁₀

m_1-1

m₀₁

^d4^-'

^d1'

4⁺'

m'₀₁

^dm'₁₁

^dm'₁₀

m'_1-1

^d2'

4^-'

^d4⁺'

^dm'₀₁

m'₁₁

m'₁₀

^dm'_1-1

^d2

4^-

^d4⁺

^dm₀₁

m₁₁

m₁₀

^dm_1-1

^d4^-

^d1

4⁺

m₀₁

^dm₁₁

^dm₁₀

m_1-1

4^-'

4⁺'

^d2'

^dm'_1-1

m'₀₁

m'₁₁

m'₁₀

^d4^-'

^d1'

^d4⁺'

m'_1-1

^dm'₀₁

^dm'₁₁

^dm'₁₀

^d4^-

^d1

^d4⁺

m_1-1

^dm₀₁

^dm₁₁

^dm₁₀

4^-

4⁺

^d2

^dm_1-1

m₀₁

m₁₁

m₁₀

m'₁₀

^dm'_1-1

^dm'₀₁

m'₁₁

^d1'

4⁺'

^d4^-'

^dm'₁₀

m'_1-1

m'₀₁

^dm'₁₁

^d4⁺'

^d2'

4^-'

^dm₁₀

m_1-1

m₀₁

^dm₁₁

^d4⁺

^d2

4^-

m₁₀

^dm_1-1

^dm₀₁

m₁₁

^d1

4⁺

^d4^-

m'_1-1

m'₀₁

m'₁₁

^dm'₁₀

4^-'

^d1'

^d4⁺'

^d2'

^dm'_1-1

^dm'₀₁

^dm'₁₁

m'₁₀

^d4^-'

4⁺'

^dm_1-1

^dm₀₁

^dm₁₁

m₁₀

^d4^-

4⁺

m_1-1

m₀₁

m₁₁

^dm₁₀

4^-

^d1

^d4⁺

^d2

m'₀₁

m'₁₁

m'₁₀

m'_1-1

^d2'

^d4^-'

^d1'

^d4⁺'

^dm'₀₁

^dm'₁₁

^dm'₁₀

^dm'_1-1

4^-'

4⁺'

^dm₀₁

^dm₁₁

^dm₁₀

^dm_1-1

4^-

4⁺

m₀₁

m₁₁

m₁₀

m_1-1

^d2

^d4^-

^d1

^d4⁺

m'₁₁

m'₁₀

^dm'_1-1

m'₀₁

^d4⁺'

^d4^-'

^d1'

^dm'₁₁

^dm'₁₀

m'_1-1

^dm'₀₁

4⁺'

^d2'

4^-'

^dm₁₁

^dm₁₀

m_1-1

^dm₀₁

4⁺

^d2

4^-

m₁₁

m₁₀

^dm_1-1

m₀₁

^d4⁺

^d4^-

^d1

^d1'

^d4⁺'

^d2'

^d4^-'

^dm'₁₀

^dm'_1-1

^dm'₀₁

^dm'₁₁

4⁺'

4^-'

m'₁₀

m'_1-1

m'₀₁

m'₁₁

4⁺

4^-

m₁₀

m_1-1

m₀₁

m₁₁

^d1

^d4⁺

^d2

^d4^-

^dm₁₀

^dm_1-1

^dm₀₁

^dm₁₁

^d4⁺'

^d2'

4^-'

^d1'

^dm'₁₁

m'₁₀

^dm'_1-1

^dm'₀₁

4⁺'

^d4^-'

m'₁₁

^dm'₁₀

m'_1-1

m'₀₁

4⁺

^d4^-

m₁₁

^dm₁₀

m_1-1

m₀₁

^d4⁺

^d2

4^-

^d1

^dm₁₁

m₁₀

^dm_1-1

^dm₀₁

^d2'

4^-'

^d4⁺'

^dm'₀₁

m'₁₁

m'₁₀

^dm'_1-1

^d4^-'

^d1'

4⁺'

m'₀₁

^dm'₁₁

^dm'₁₀

m'_1-1

^d4^-

^d1

4⁺

m₀₁

^dm₁₁

^dm₁₀

m_1-1

^d2

4^-

^d4⁺

^dm₀₁

m₁₁

m₁₀

^dm_1-1

^d4^-'

^d1'

^d4⁺'

m'_1-1

^dm'₀₁

^dm'₁₁

^dm'₁₀

4^-'

4⁺'

^d2'

^dm'_1-1

m'₀₁

m'₁₁

m'₁₀

4^-

4⁺

^d2

^dm_1-1

m₀₁

m₁₁

m₁₀

^d4^-

^d1

^d4⁺

m_1-1

^dm₀₁

^dm₁₁

^dm₁₀

^dm'₁₀

m'_1-1

m'₀₁

^dm'₁₁

^d4⁺'

^d2'

4^-'

m'₁₀

^dm'_1-1

^dm'₀₁

m'₁₁

^d1'

4⁺'

^d4^-'

m₁₀

^dm_1-1

^dm₀₁

m₁₁

^d1

4⁺

^d4^-

^dm₁₀

m_1-1

m₀₁

^dm₁₁

^d4⁺

^d2

4^-

^dm'_1-1

^dm'₀₁

^dm'₁₁

m'₁₀

^d4^-'

4⁺'

m'_1-1

m'₀₁

m'₁₁

^dm'₁₀

4^-'

^d1'

^d4⁺'

^d2'

m_1-1

m₀₁

m₁₁

^dm₁₀

4^-

^d1

^d4⁺

^d2

^dm_1-1

^dm₀₁

^dm₁₁

m₁₀

^d4^-

4⁺

^dm'₀₁

^dm'₁₁

^dm'₁₀

^dm'_1-1

4^-'

4⁺'

m'₀₁

m'₁₁

m'₁₀

m'_1-1

^d2'

^d4^-'

^d1'

^d4⁺'

m₀₁

m₁₁

m₁₀

m_1-1

^d2

^d4^-

^d1

^d4⁺

^dm₀₁

^dm₁₁

^dm₁₀

^dm_1-1

4^-

4⁺

^dm'₁₁

^dm'₁₀

m'_1-1

^dm'₀₁

4⁺'

^d2'

4^-'

m'₁₁

m'₁₀

^dm'_1-1

m'₀₁

^d4⁺'

^d4^-'

^d1'

m₁₁

m₁₀

^dm_1-1

m₀₁

^d4⁺

^d4^-

^d1

^dm₁₁

^dm₁₀

m_1-1

^dm₀₁

4⁺

^d2

4^-

Table of projective phases in group multiplication

	1	4⁺	2	4^-	m₁₀	m_1-1	m₀₁	m₁₁	^d1	^d4⁺	^d2	^d4^-	^dm₁₀	^dm_1-1	^dm₀₁	^dm₁₁	1'	4⁺'	2'	4^-'	m'₁₀	m'_1-1	m'₀₁	m'₁₁	^d1'	^d4⁺'	^d2'	^d4^-'	^dm'₁₀	^dm'_1-1	^dm'₀₁	^dm'₁₁
1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
4⁺	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
2	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
4^-	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
m₁₀	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
m_1-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
m₀₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
m₁₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^d1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^d4⁺	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^d2	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^d4^-	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^dm₁₀	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^dm_1-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^dm₀₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^dm₁₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
1'	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
4⁺'	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
2'	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
4^-'	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
m'₁₀	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
m'_1-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
m'₀₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
m'₁₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^d1'	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^d4⁺'	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^d2'	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^d4^-'	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^dm'₁₀	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^dm'_1-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^dm'₀₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
^dm'₁₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1

Matrices of the representations of the group

The antiunitary operations are written in red color

Matrix presentation

Seitz symbol

A₁

A₂

B₁

B₂

E₂

E₁

 1  0
 0  1

 1  0
 0  1

 1  0
 0  1

 1  0
 0  1

 1  0
 0  1

  0  -1
  1   0

 e^-iπ/4   0
  0   e^iπ/4

4⁺

-1

 -i   0
  0   i

  e^3iπ/4   0
  0  e^-3iπ/4

 e^-iπ/4   0
  0   e^iπ/4

 -1   0
  0  -1

 -i   0
  0   i

 -1   0
  0  -1

 -i   0
  0   i

 -i   0
  0   i

  0   1
 -1   0

  e^iπ/4   0
  0  e^-iπ/4

4^-

-1

  i   0
  0  -i

 e^-3iπ/4   0
  0   e^3iπ/4

  e^iπ/4   0
  0  e^-iπ/4

 -1   0
  0   1

  0  -i
 -i   0

m₁₀

-1

 0  1
 1  0

  0  -1
  1   0

  0  -1
  1   0

 0  1
 1  0

  0  e^3iπ/4
  e^iπ/4   0

m_1-1

-1

  0   i
 -i   0

  0  e^-3iπ/4
  e^-iπ/4   0

  0   e^iπ/4
 e^3iπ/4   0

  1   0
  0  -1

  0  -1
  1   0

m₀₁

-1

  0  -1
 -1   0

 0  i
 i  0

 0  i
 i  0

  0  -1
 -1   0

  0  e^-3iπ/4
  e^-iπ/4   0

m₁₁

-1

  0  -i
  i   0

  0   e^-iπ/4
 e^-3iπ/4   0

  0  e^3iπ/4
  e^iπ/4   0

 1  0
 0  1

 -1   0
  0  -1

^d1

 1  0
 0  1

 -1   0
  0  -1

 -1   0
  0  -1

  0  -1
  1   0

  e^3iπ/4   0
  0  e^-3iπ/4

^d4⁺

-1

 -i   0
  0   i

 e^-iπ/4   0
  0   e^iπ/4

  e^3iπ/4   0
  0  e^-3iπ/4

 -1   0
  0  -1

  i   0
  0  -i

^d2

 -1   0
  0  -1

  i   0
  0  -i

  i   0
  0  -i

  0   1
 -1   0

 e^-3iπ/4   0
  0   e^3iπ/4

^d4^-

-1

  i   0
  0  -i

  e^iπ/4   0
  0  e^-iπ/4

 e^-3iπ/4   0
  0   e^3iπ/4

 -1   0
  0   1

 0  i
 i  0

^dm₁₀

-1

 0  1
 1  0

  0   1
 -1   0

  0   1
 -1   0

 0  1
 1  0

  0   e^-iπ/4
 e^-3iπ/4   0

^dm_1-1

-1

  0   i
 -i   0

  0   e^iπ/4
 e^3iπ/4   0

  0  e^-3iπ/4
  e^-iπ/4   0

  1   0
  0  -1

  0   1
 -1   0

^dm₀₁

-1

  0  -1
 -1   0

  0  -i
 -i   0

  0  -i
 -i   0

  0  -1
 -1   0

  0   e^iπ/4
 e^3iπ/4   0

^dm₁₁

-1

  0  -i
  i   0

  0  e^3iπ/4
  e^iπ/4   0

  0   e^-iπ/4
 e^-3iπ/4   0

 1  0
 0  1

 1  0
 0  1

-1

  0  -1
 -1   0

  0   1
 -1   0

  0   1
 -1   0

  0  -1
  1   0

 e^-iπ/4   0
  0   e^iπ/4

4⁺'

-1

  0   i
 -i   0

  0  e^3iπ/4
  e^iπ/4   0

  0   e^-iπ/4
 e^-3iπ/4   0

 -1   0
  0  -1

 -i   0
  0   i

-1

 0  1
 1  0

  0  -i
 -i   0

  0  -i
 -i   0

  0   1
 -1   0

  e^iπ/4   0
  0  e^-iπ/4

4^-'

-1

  0  -i
  i   0

  0  e^-3iπ/4
  e^-iπ/4   0

  0   e^iπ/4
 e^3iπ/4   0

 -1   0
  0   1

  0  -i
 -i   0

m'₁₀

-1

 -1   0
  0  -1

 1  0
 0  1

 1  0
 0  1

 0  1
 1  0

  0  e^3iπ/4
  e^iπ/4   0

m'_1-1

-1

 -i   0
  0   i

  e^iπ/4   0
  0  e^-iπ/4

 e^-3iπ/4   0
  0   e^3iπ/4

  1   0
  0  -1

  0  -1
  1   0

m'₀₁

-1

 1  0
 0  1

 -i   0
  0   i

 -i   0
  0   i

  0  -1
 -1   0

  0  e^-3iπ/4
  e^-iπ/4   0

m'₁₁

-1

  i   0
  0  -i

  e^3iπ/4   0
  0  e^-3iπ/4

 e^-iπ/4   0
  0   e^iπ/4

 1  0
 0  1

 -1   0
  0  -1

^d1'

-1

  0  -1
 -1   0

  0  -1
  1   0

  0  -1
  1   0

  0  -1
  1   0

  e^3iπ/4   0
  0  e^-3iπ/4

^d4⁺'

-1

  0   i
 -i   0

  0   e^-iπ/4
 e^-3iπ/4   0

  0  e^3iπ/4
  e^iπ/4   0

 -1   0
  0  -1

  i   0
  0  -i

^d2'

-1

 0  1
 1  0

 0  i
 i  0

 0  i
 i  0

  0   1
 -1   0

 e^-3iπ/4   0
  0   e^3iπ/4

^d4^-'

-1

  0  -i
  i   0

  0   e^iπ/4
 e^3iπ/4   0

  0  e^-3iπ/4
  e^-iπ/4   0

 -1   0
  0   1

 0  i
 i  0

^dm'₁₀

-1

 -1   0
  0  -1

 -1   0
  0  -1

 -1   0
  0  -1

 0  1
 1  0

  0   e^-iπ/4
 e^-3iπ/4   0

^dm'_1-1

-1

 -i   0
  0   i

 e^-3iπ/4   0
  0   e^3iπ/4

  e^iπ/4   0
  0  e^-iπ/4

  1   0
  0  -1

  0   1
 -1   0

^dm'₀₁

-1

 1  0
 0  1

  i   0
  0  -i

  i   0
  0  -i

  0  -1
 -1   0

  0   e^iπ/4
 e^3iπ/4   0

^dm'₁₁

-1

  i   0
  0  -i

 e^-iπ/4   0
  0   e^iπ/4

  e^3iπ/4   0
  0  e^-3iπ/4

k-Subgroupsmag

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