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File Name	Spin Space Group	G0 Symbol	L0 Symbol	it	ik
$0.200 / M n 3 S n$	$P^{3_{001}^{1}} {6_{3} /}^{1} m^{m_{\frac{π}{3}}} m^{m_{\frac{2 π}{3}}} c^{m} 1$	$P 6_{3} / m m c (194)$	$P 2_{1} / m (11)$	$6$	$1$

Space Group	Magnetic Space Group	Spin Part PG	Configuration	Magnetic Phase
$P 6_{3} / m m c (194)$	$\begin{aligned} C m^{'} c m^{'} (63.464) \\ T y p e I I I \end{aligned}$	$\begin{aligned} C 3 v \times C s & = D 3 h \\ 3 m \times m & = - 6 m 2 \end{aligned}$	$C o p l a n a r$	$C a n t i n g A F M$

Little Cogroup at General Position		Spin Splitting
without SOC	with SOC	without SOC	with SOC
$^{m_{001}} - 1$	$1$	$k - d e p e n d e n t$	$Y e s$

Effective Magnetic Point Group	Anomalous Hall Effect
$6 / m m m 1^{'}$	without SOC	with SOC
$6 / m m m 1^{'}$	$N o$	$Y e s$

Effective MPG Constraint on Order-3 Tensor
T-odd	Quantum metric dipole	$O n l y z e r o s$
T-odd	Inversed mass dipole	$O n l y z e r o s$
T-even	Berry curvature dipole	$O n l y z e r o s$

G0-std Unit Magnetic Cell:

a	b	c	alpha	beta	gamma
5.665	5.665	4.531	90.0	90.0	120.0

Fractional Coordinates & Moments (in G0-std Unit Magnetic Cell)

No.	Atom	Site	Moment (in lattice)
1	Mn	[0.3224, 0.1612, 0.75]	[2.595, 1.4982, 0.0]
2	Mn	[0.6776, 0.8388, 0.25]	[2.595, 1.4982, 0.0]
3	Mn	[0.8388, 0.6776, 0.75]	[-2.595, 1.4982, 0.0]
4	Mn	[0.1612, 0.3224, 0.25]	[-2.595, 1.4982, 0.0]
5	Mn	[0.8388, 0.1612, 0.75]	[0.0, -2.9964, 0.0]
6	Mn	[0.1612, 0.8388, 0.25]	[0.0, -2.9964, 0.0]
7	Sn	[0.3333, 0.6667, 0.75]	[0.0, 0.0, 0.0]
8	Sn	[0.6667, 0.3333, 0.25]	[0.0, 0.0, 0.0]

Elements of the Spin Space Group (G0-std-setting):

Real Space Elements are under the basis of the lattice given above.

Spin Part Elements are represented corresponding to the SpinPartPG.

No.	Spin Rotation	Space Rotation	Space Translation	Seitz Symbol
1	$[\begin{matrix} 0.5 & 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 1.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${m_{\frac{5 π}{6}} \| \| m_{010} \| τ_{(0.0, 0.0, 0.0)}}$
2	$[\begin{matrix} 0.5 & 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 1.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${2_{\frac{π}{3}} \| \| m_{010} \| τ_{(0.0, 0.0, 0.0)}}$
3	$[\begin{matrix} 0.5 & 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 1.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${m_{\frac{5 π}{6}} \| \| 2_{210} \| τ_{(0.0, 0.0, 0.5)}}$
4	$[\begin{matrix} 0.5 & 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 1.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${2_{\frac{π}{3}} \| \| 2_{210} \| τ_{(0.0, 0.0, 0.5)}}$
5	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${1 \| \| 1 \| τ_{(0.0, 0.0, 0.0)}}$
6	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${m_{001} \| \| 1 \| τ_{(0.0, 0.0, 0.0)}}$
7	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${1 \| \| m_{001} \| τ_{(0.0, 0.0, 0.5)}}$
8	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${m_{001} \| \| m_{001} \| τ_{(0.0, 0.0, 0.5)}}$
9	$[\begin{matrix} - 0.5 & - 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & - 1.0 & 0.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${3_{001}^{1} \| \| 6_{001}^{1} \| τ_{(0.0, 0.0, 0.5)}}$
10	$[\begin{matrix} - 0.5 & - 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & - 1.0 & 0.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${- 6_{001}^{5} \| \| 6_{001}^{1} \| τ_{(0.0, 0.0, 0.5)}}$
11	$[\begin{matrix} - 0.5 & - 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & - 1.0 & 0.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${3_{001}^{1} \| \| - 3_{001}^{2} \| τ_{(0.0, 0.0, 0.0)}}$
12	$[\begin{matrix} - 0.5 & - 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & - 1.0 & 0.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${- 6_{001}^{5} \| \| - 3_{001}^{2} \| τ_{(0.0, 0.0, 0.0)}}$
13	$[\begin{matrix} 0.5 & - 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & - 1.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${m_{010} \| \| m_{120} \| τ_{(0.0, 0.0, 0.5)}}$
14	$[\begin{matrix} 0.5 & - 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & - 1.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${2_{100} \| \| m_{120} \| τ_{(0.0, 0.0, 0.5)}}$
15	$[\begin{matrix} 0.5 & - 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & - 1.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${m_{010} \| \| 2_{100} \| τ_{(0.0, 0.0, 0.0)}}$
16	$[\begin{matrix} 0.5 & - 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & - 1.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${2_{100} \| \| 2_{100} \| τ_{(0.0, 0.0, 0.0)}}$
17	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${m_{\frac{π}{6}} \| \| m_{1 - 10} \| τ_{(0.0, 0.0, 0.5)}}$
18	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${2_{\frac{2 π}{3}} \| \| m_{1 - 10} \| τ_{(0.0, 0.0, 0.5)}}$
19	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${m_{\frac{π}{6}} \| \| 2_{110} \| τ_{(0.0, 0.0, 0.0)}}$
20	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${2_{\frac{2 π}{3}} \| \| 2_{110} \| τ_{(0.0, 0.0, 0.0)}}$
21	$[\begin{matrix} - 0.5 & 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ - 1.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${3_{001}^{2} \| \| 6_{001}^{5} \| τ_{(0.0, 0.0, 0.5)}}$
22	$[\begin{matrix} - 0.5 & 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ - 1.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${- 6_{001}^{1} \| \| 6_{001}^{5} \| τ_{(0.0, 0.0, 0.5)}}$
23	$[\begin{matrix} - 0.5 & 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ - 1.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${3_{001}^{2} \| \| - 3_{001}^{1} \| τ_{(0.0, 0.0, 0.0)}}$
24	$[\begin{matrix} - 0.5 & 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ - 1.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${- 6_{001}^{1} \| \| - 3_{001}^{1} \| τ_{(0.0, 0.0, 0.0)}}$
25	$[\begin{matrix} - 0.5 & 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 1.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${3_{001}^{2} \| \| 3_{001}^{1} \| τ_{(0.0, 0.0, 0.0)}}$
26	$[\begin{matrix} - 0.5 & 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 1.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${- 6_{001}^{1} \| \| 3_{001}^{1} \| τ_{(0.0, 0.0, 0.0)}}$
27	$[\begin{matrix} - 0.5 & 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 1.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${3_{001}^{2} \| \| - 6_{001}^{5} \| τ_{(0.0, 0.0, 0.5)}}$
28	$[\begin{matrix} - 0.5 & 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 1.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${- 6_{001}^{1} \| \| - 6_{001}^{5} \| τ_{(0.0, 0.0, 0.5)}}$
29	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${m_{\frac{π}{6}} \| \| m_{110} \| τ_{(0.0, 0.0, 0.0)}}$
30	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${2_{\frac{2 π}{3}} \| \| m_{110} \| τ_{(0.0, 0.0, 0.0)}}$
31	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${m_{\frac{π}{6}} \| \| 2_{1 - 10} \| τ_{(0.0, 0.0, 0.5)}}$
32	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${2_{\frac{2 π}{3}} \| \| 2_{1 - 10} \| τ_{(0.0, 0.0, 0.5)}}$
33	$[\begin{matrix} 0.5 & - 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 1.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${m_{010} \| \| m_{100} \| τ_{(0.0, 0.0, 0.0)}}$
34	$[\begin{matrix} 0.5 & - 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 1.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${2_{100} \| \| m_{100} \| τ_{(0.0, 0.0, 0.0)}}$
35	$[\begin{matrix} 0.5 & - 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 1.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${m_{010} \| \| 2_{120} \| τ_{(0.0, 0.0, 0.5)}}$
36	$[\begin{matrix} 0.5 & - 0.866 & 0.0 \\ - 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 1.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${2_{100} \| \| 2_{120} \| τ_{(0.0, 0.0, 0.5)}}$
37	$[\begin{matrix} - 0.5 & - 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 1.0 & 0.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${3_{001}^{1} \| \| 3_{001}^{2} \| τ_{(0.0, 0.0, 0.0)}}$
38	$[\begin{matrix} - 0.5 & - 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 1.0 & 0.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${- 6_{001}^{5} \| \| 3_{001}^{2} \| τ_{(0.0, 0.0, 0.0)}}$
39	$[\begin{matrix} - 0.5 & - 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 1.0 & 0.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${3_{001}^{1} \| \| - 6_{001}^{1} \| τ_{(0.0, 0.0, 0.5)}}$
40	$[\begin{matrix} - 0.5 & - 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 1.0 & 0.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${- 6_{001}^{5} \| \| - 6_{001}^{1} \| τ_{(0.0, 0.0, 0.5)}}$
41	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${1 \| \| 2_{001} \| τ_{(0.0, 0.0, 0.5)}}$
42	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${m_{001} \| \| 2_{001} \| τ_{(0.0, 0.0, 0.5)}}$
43	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${1 \| \| - 1 \| τ_{(0.0, 0.0, 0.0)}}$
44	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${m_{001} \| \| - 1 \| τ_{(0.0, 0.0, 0.0)}}$
45	$[\begin{matrix} 0.5 & 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ - 1.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${m_{\frac{5 π}{6}} \| \| m_{210} \| τ_{(0.0, 0.0, 0.5)}}$
46	$[\begin{matrix} 0.5 & 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ - 1.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.5 \end{matrix}]$	${2_{\frac{π}{3}} \| \| m_{210} \| τ_{(0.0, 0.0, 0.5)}}$
47	$[\begin{matrix} 0.5 & 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ - 1.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${m_{\frac{5 π}{6}} \| \| 2_{010} \| τ_{(0.0, 0.0, 0.0)}}$
48	$[\begin{matrix} 0.5 & 0.866 & 0.0 \\ 0.866 & - 0.5 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ - 1.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${2_{\frac{π}{3}} \| \| 2_{010} \| τ_{(0.0, 0.0, 0.0)}}$

FINDSPINGROUP: Identify Spin Group and Related Properties