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In the title isoquinoline­dione derivative, C16H16N2O3S, the piperidine ring in the tetra­hydro­isoquinoline ring system adopts a distorted envelope conformation. The thia­zole ring is essentially planar [maximum deviation = 0.004 (1) Å] and is inclined at a dihedral angle of 31.08 (3)° with respect to the mean plane through the tetra­hydro­isoquinoline ring system. In the crystal structure, inter­molecular O—H...O and C—H...O inter­actions link adjacent mol­ecules into a three-dimensional extended network. The crystal structure is further stabilized by weak C—H...π inter­actions.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536810010469/is2531sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536810010469/is2531Isup2.hkl
Contains datablock I

CCDC reference: 774357

Key indicators

  • Single-crystal X-ray study
  • T = 100 K
  • Mean [sigma](C-C) = 0.001 Å
  • R factor = 0.031
  • wR factor = 0.108
  • Data-to-parameter ratio = 20.0

checkCIF/PLATON results

No syntax errors found



Alert level C PLAT910_ALERT_3_C Missing # of FCF Reflections Below Th(Min) ..... 3 PLAT911_ALERT_3_C Missing # FCF Refl Between THmin & STh/L= 0.600 28 PLAT913_ALERT_3_C Missing # of Very Strong Reflections in FCF .... 10
Alert level G PLAT720_ALERT_4_G Number of Unusual/Non-Standard Labels .......... 1 PLAT793_ALERT_4_G The Model has Chirality at C9 (Verify) .... S
0 ALERT level A = In general: serious problem 0 ALERT level B = Potentially serious problem 3 ALERT level C = Check and explain 2 ALERT level G = General alerts; check 0 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 0 ALERT type 2 Indicator that the structure model may be wrong or deficient 3 ALERT type 3 Indicator that the structure quality may be low 2 ALERT type 4 Improvement, methodology, query or suggestion 0 ALERT type 5 Informative message, check

Comment top

1,3,4(2H)-Isoquinolinetrione derivatives have a variety of biological activities and are synthetic precursors for many naturally occurring alkaloids (Hall et al., 1994; Malamas & Hohman, 1994). The carbonyl group on C4 of isoquinoline-1,3,4-trione is an active site for photo-induced reactions with alkenes or other hydrogen donors to give photoaddition products such as oxetanes (Suau & Villatoro, 1994). Oxazole derivatives have been used as electron donor species in the Paternò-Büchi photocycloaddition with carbonyl groups (Griesbeck et al., 2003). Other interesting photo-reactions such as the [4+4] photocycloadditions have also been reported on substituted oxazole with 9,10-phenanthraquinone and 1-acetylisatin (Zhang et al., 2004). The crystal structure of Z-2-methyl-3'-phenyl-spiro[isoquinoline-4,2'-oxirane]-1,3-dione has been reported (Wang et al., 2000). In view of the importance of the title compound as a typical H-abstracted product in photoreaction between carbonyl and thiazoles, the paper reports its crystal structure.

In the title isoquinolinedione derivative (Fig. 1), atom C9 is the chiral center. The piperidine ring (C1/N1/C2/C3/C8/C9) of the tetrahydroisoquinoline ring system adopts a distorted envelope conformation with atom C9 as the flap; the puckering amplitude Q = 0.2512 (9) Å, θ = 113.8 (2)° and ϕ = 291.0 (2)° (Cremer & Pople, 1975). The thiazol ring (C11/C12/N2/C13/S1) is essentially planar, with maximum deviation of 0.004 (1) Å at atom C11, and it inclines at a dihedral angle of 31.08 (3)° with the tetrahydroisoquinoline ring system. Bond lengths and angles are consistent to those observed in related isoquinoline-1,3-dione structures (Fun et al. 2010a,b; Zhang et al., 2004).

In the crystal packing (Fig. 2), intermolecular O3—H1O3···O2, C4—H4A···O1, C10—H10A···O3 and C16—H16B···O1 hydrogen bonds (Table 1) link neighbouring molecules into a three-dimensional extended network. The crystal structure is further stabilized by intermolecular C15—H15B···Cg1 interactions (Table 1) involving the centroid of the C3–C8 benzene ring.

Related literature top

For general background to and applications of isoquinolinedione derivatives, see: Griesbeck et al. (2003); Hall et al. (1994); Malamas & Hohman (1994); Suau & Villatoro (1994); Zhang et al. (2004). For ring conformations, see: Cremer & Pople (1975). For related structures, see: Fun et al. (2010a,b); Wang et al. (2000). For the stability of the temperature controller used for the data collection, see: Cosier & Glazer (1986).

Experimental top

The title compound was obtained in the reaction between 1,3,4(2H)-isoquinolinetrione and 1,4,5-trimethyl thiazoles under photo-irradiation with light of wavelength > 400 nm. The compound was purified by flash column chromatography with ethyl acetate and petroleum ether as eluents. X-ray quality single crystals of the title compound were obtained by slow evaporation of solvents from the solution of the title compound in acetone and petroleum ether.

Refinement top

All the H atoms were located in a difference Fourier map and allowed to refine freely. Refined distances: C—H = 0.917 (16)–0.994 (15) Å.

Computing details top

Data collection: APEX2 (Bruker, 2009); cell refinement: SAINT (Bruker, 2009); data reduction: SAINT (Bruker, 2009); program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2009).

Figures top
[Figure 1] Fig. 1. The asymmetric unit of the title compound, showing the atomic numbering scheme. Displacement ellipsoids are drawn at the 50% probability level.
[Figure 2] Fig. 2. The crystal packing of the title compound, viewed along the a axis, showing the three-dimensional extended network. H atoms not involved in intermolecular interactions have been omitted for clarity.
4-[(2,4-Dimethylthiazol-5-yl)methyl]-4-hydroxy-2-methylisoquinoline- 1,3(2H,4H)-dione top
Crystal data top
C16H16N2O3SF(000) = 664
Mr = 316.37Dx = 1.441 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 9887 reflections
a = 10.2424 (8) Åθ = 2.5–35.1°
b = 15.0438 (13) ŵ = 0.24 mm1
c = 9.4786 (8) ÅT = 100 K
β = 92.839 (2)°Block, colourless
V = 1458.7 (2) Å30.52 × 0.26 × 0.09 mm
Z = 4
Data collection top
Bruker SMART APEX DUO CCD area-detector
diffractometer
5260 independent reflections
Radiation source: fine-focus sealed tube4752 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.024
ϕ and ω scansθmax = 32.5°, θmin = 2.7°
Absorption correction: multi-scan
(SADABS; Bruker, 2009)
h = 1515
Tmin = 0.887, Tmax = 0.979k = 2122
20742 measured reflectionsl = 1413
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.031Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.108All H-atom parameters refined
S = 1.14 w = 1/[σ2(Fo2) + (0.0649P)2 + 0.2915P]
where P = (Fo2 + 2Fc2)/3
5260 reflections(Δ/σ)max = 0.001
263 parametersΔρmax = 0.69 e Å3
0 restraintsΔρmin = 0.47 e Å3
Crystal data top
C16H16N2O3SV = 1458.7 (2) Å3
Mr = 316.37Z = 4
Monoclinic, P21/cMo Kα radiation
a = 10.2424 (8) ŵ = 0.24 mm1
b = 15.0438 (13) ÅT = 100 K
c = 9.4786 (8) Å0.52 × 0.26 × 0.09 mm
β = 92.839 (2)°
Data collection top
Bruker SMART APEX DUO CCD area-detector
diffractometer
5260 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2009)
4752 reflections with I > 2σ(I)
Tmin = 0.887, Tmax = 0.979Rint = 0.024
20742 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0310 restraints
wR(F2) = 0.108All H-atom parameters refined
S = 1.14Δρmax = 0.69 e Å3
5260 reflectionsΔρmin = 0.47 e Å3
263 parameters
Special details top

Experimental. The crystal was placed in the cold stream of an Oxford Cryosystems Cobra open-flow nitrogen cryostat (Cosier & Glazer, 1986) operating at 100.0 (1)K.

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > 2sigma(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
S10.86697 (2)0.201051 (14)0.69225 (2)0.01443 (7)
O10.38478 (7)0.29484 (4)0.78648 (8)0.01610 (14)
O20.46407 (7)0.59074 (5)0.82383 (8)0.01766 (14)
O30.57054 (7)0.27421 (4)0.59312 (7)0.01403 (13)
N10.42666 (7)0.44221 (5)0.81117 (8)0.01168 (13)
N21.03523 (7)0.32678 (5)0.71641 (8)0.01323 (14)
C10.45580 (8)0.35744 (5)0.76386 (9)0.01077 (14)
C20.49293 (8)0.51881 (6)0.77347 (9)0.01180 (14)
C30.59432 (8)0.50884 (5)0.66814 (9)0.01079 (14)
C40.64725 (9)0.58622 (6)0.61172 (10)0.01449 (16)
C50.73988 (9)0.57934 (6)0.51012 (10)0.01681 (17)
C60.77833 (9)0.49566 (6)0.46357 (10)0.01545 (16)
C70.72519 (9)0.41869 (6)0.51860 (9)0.01266 (15)
C80.63326 (8)0.42498 (5)0.62248 (8)0.01004 (14)
C90.58517 (8)0.34274 (5)0.69351 (8)0.00987 (14)
C100.68361 (8)0.31399 (6)0.81709 (9)0.01249 (15)
C110.81935 (8)0.29894 (5)0.77079 (9)0.01180 (15)
C120.92179 (8)0.35759 (6)0.77307 (9)0.01249 (15)
C131.02070 (8)0.24530 (6)0.66982 (9)0.01282 (15)
C140.31069 (9)0.45045 (6)0.89534 (10)0.01658 (17)
C150.92066 (10)0.45085 (7)0.82696 (11)0.01856 (18)
C161.12481 (9)0.19431 (6)0.59986 (11)0.01685 (17)
H4A0.6166 (16)0.6451 (12)0.6429 (18)0.032 (4)*
H5A0.7767 (17)0.6330 (12)0.4682 (18)0.032 (4)*
H6A0.8450 (15)0.4910 (11)0.3912 (16)0.022 (4)*
H7A0.7529 (14)0.3644 (11)0.4837 (16)0.022 (4)*
H10A0.6458 (14)0.2612 (11)0.8585 (15)0.020 (3)*
H10B0.6861 (14)0.3595 (10)0.8887 (15)0.018 (3)*
H14A0.2427 (16)0.4203 (11)0.8507 (16)0.023 (4)*
H14B0.2864 (18)0.5111 (13)0.8938 (19)0.038 (5)*
H14C0.3297 (17)0.4255 (12)0.9861 (18)0.032 (4)*
H15A1.0023 (19)0.4647 (13)0.870 (2)0.040 (5)*
H15B0.9089 (19)0.4918 (15)0.751 (2)0.048 (5)*
H15C0.8533 (19)0.4625 (13)0.886 (2)0.041 (5)*
H16A1.1181 (16)0.2067 (11)0.5008 (17)0.027 (4)*
H16B1.2092 (17)0.2095 (11)0.6394 (18)0.030 (4)*
H16C1.1129 (18)0.1315 (14)0.6097 (19)0.037 (5)*
H1O30.544 (2)0.2340 (15)0.629 (2)0.043 (5)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.01309 (11)0.00929 (11)0.02129 (12)0.00031 (6)0.00483 (8)0.00026 (7)
O10.0134 (3)0.0105 (3)0.0246 (3)0.0022 (2)0.0038 (2)0.0018 (2)
O20.0202 (3)0.0099 (3)0.0233 (3)0.0007 (2)0.0050 (3)0.0041 (2)
O30.0196 (3)0.0086 (3)0.0142 (3)0.0027 (2)0.0042 (2)0.0027 (2)
N10.0116 (3)0.0093 (3)0.0144 (3)0.0001 (2)0.0033 (2)0.0007 (2)
N20.0117 (3)0.0124 (3)0.0156 (3)0.0014 (2)0.0013 (2)0.0018 (2)
C10.0104 (3)0.0092 (3)0.0127 (3)0.0004 (2)0.0007 (2)0.0003 (3)
C20.0123 (3)0.0093 (3)0.0138 (3)0.0000 (3)0.0000 (3)0.0005 (3)
C30.0114 (3)0.0088 (3)0.0121 (3)0.0007 (3)0.0004 (3)0.0008 (2)
C40.0160 (4)0.0091 (3)0.0184 (4)0.0016 (3)0.0006 (3)0.0020 (3)
C50.0181 (4)0.0135 (4)0.0189 (4)0.0033 (3)0.0023 (3)0.0048 (3)
C60.0163 (4)0.0160 (4)0.0143 (3)0.0022 (3)0.0032 (3)0.0034 (3)
C70.0141 (3)0.0124 (3)0.0116 (3)0.0008 (3)0.0020 (3)0.0007 (3)
C80.0110 (3)0.0091 (3)0.0101 (3)0.0009 (2)0.0002 (2)0.0009 (2)
C90.0111 (3)0.0074 (3)0.0111 (3)0.0002 (2)0.0018 (2)0.0001 (2)
C100.0119 (3)0.0139 (3)0.0118 (3)0.0028 (3)0.0030 (3)0.0027 (3)
C110.0119 (3)0.0115 (3)0.0121 (3)0.0021 (3)0.0020 (3)0.0014 (2)
C120.0117 (3)0.0128 (3)0.0129 (3)0.0020 (3)0.0003 (3)0.0022 (3)
C130.0120 (3)0.0113 (3)0.0154 (3)0.0010 (3)0.0027 (3)0.0005 (3)
C140.0144 (4)0.0163 (4)0.0197 (4)0.0002 (3)0.0075 (3)0.0016 (3)
C150.0156 (4)0.0162 (4)0.0237 (4)0.0015 (3)0.0007 (3)0.0087 (3)
C160.0150 (4)0.0126 (4)0.0234 (4)0.0022 (3)0.0060 (3)0.0022 (3)
Geometric parameters (Å, º) top
S1—C111.7311 (9)C6—H6A0.994 (15)
S1—C131.7323 (9)C7—C81.3988 (11)
O1—C11.2155 (10)C7—H7A0.931 (16)
O2—C21.2248 (10)C8—C91.5031 (11)
O3—C91.4059 (10)C9—C101.5681 (12)
O3—H1O30.75 (2)C10—C111.4957 (12)
N1—C11.3891 (11)C10—H10A0.974 (16)
N1—C21.3930 (11)C10—H10B0.964 (15)
N1—C141.4685 (11)C11—C121.3703 (12)
N2—C131.3089 (11)C12—C151.4933 (13)
N2—C121.3839 (11)C13—C161.4951 (12)
C1—C91.5287 (11)C14—H14A0.917 (16)
C2—C31.4834 (12)C14—H14B0.95 (2)
C3—C81.3984 (11)C14—H14C0.950 (17)
C3—C41.4012 (12)C15—H15A0.94 (2)
C4—C51.3888 (13)C15—H15B0.95 (2)
C4—H4A0.990 (18)C15—H15C0.928 (19)
C5—C61.3970 (14)C16—H16A0.957 (16)
C5—H5A0.983 (18)C16—H16B0.953 (18)
C6—C71.3919 (12)C16—H16C0.96 (2)
C11—S1—C1390.17 (4)C1—C9—C10104.67 (6)
C9—O3—H1O3108.5 (16)C11—C10—C9113.28 (7)
C1—N1—C2124.16 (7)C11—C10—H10A112.9 (9)
C1—N1—C14116.45 (7)C9—C10—H10A105.8 (9)
C2—N1—C14119.14 (7)C11—C10—H10B108.8 (9)
C13—N2—C12111.16 (7)C9—C10—H10B108.9 (9)
O1—C1—N1120.95 (8)H10A—C10—H10B107.0 (13)
O1—C1—C9120.27 (8)C12—C11—C10128.32 (8)
N1—C1—C9118.58 (7)C12—C11—S1108.83 (6)
O2—C2—N1120.06 (8)C10—C11—S1122.73 (7)
O2—C2—C3122.83 (8)C11—C12—N2115.80 (8)
N1—C2—C3117.08 (7)C11—C12—C15126.26 (8)
C8—C3—C4120.65 (8)N2—C12—C15117.92 (8)
C8—C3—C2121.30 (7)N2—C13—C16123.95 (8)
C4—C3—C2118.02 (7)N2—C13—S1114.04 (6)
C5—C4—C3119.55 (8)C16—C13—S1122.00 (7)
C5—C4—H4A120.7 (10)N1—C14—H14A108.9 (10)
C3—C4—H4A119.7 (10)N1—C14—H14B107.0 (11)
C4—C5—C6119.94 (8)H14A—C14—H14B106.1 (15)
C4—C5—H5A120.5 (10)N1—C14—H14C108.9 (10)
C6—C5—H5A119.5 (10)H14A—C14—H14C109.9 (14)
C7—C6—C5120.65 (8)H14B—C14—H14C115.9 (16)
C7—C6—H6A119.7 (9)C12—C15—H15A109.7 (12)
C5—C6—H6A119.7 (9)C12—C15—H15B110.7 (13)
C6—C7—C8119.79 (8)H15A—C15—H15B105.4 (17)
C6—C7—H7A117.7 (9)C12—C15—H15C113.7 (12)
C8—C7—H7A122.5 (9)H15A—C15—H15C111.5 (16)
C3—C8—C7119.41 (7)H15B—C15—H15C105.4 (16)
C3—C8—C9119.94 (7)C13—C16—H16A108.5 (10)
C7—C8—C9120.44 (7)C13—C16—H16B110.9 (10)
O3—C9—C8109.07 (7)H16A—C16—H16B111.1 (14)
O3—C9—C1109.61 (7)C13—C16—H16C111.4 (11)
C8—C9—C1112.75 (7)H16A—C16—H16C106.5 (14)
O3—C9—C10110.26 (7)H16B—C16—H16C108.4 (15)
C8—C9—C10110.41 (7)
C2—N1—C1—O1170.99 (8)C7—C8—C9—C1160.42 (7)
C14—N1—C1—O13.16 (12)C3—C8—C9—C1091.86 (9)
C2—N1—C1—C914.15 (12)C7—C8—C9—C1082.90 (9)
C14—N1—C1—C9171.71 (7)O1—C1—C9—O335.47 (11)
C1—N1—C2—O2177.44 (8)N1—C1—C9—O3149.63 (7)
C14—N1—C2—O28.56 (13)O1—C1—C9—C8157.17 (8)
C1—N1—C2—C34.55 (12)N1—C1—C9—C827.93 (10)
C14—N1—C2—C3169.45 (8)O1—C1—C9—C1082.79 (9)
O2—C2—C3—C8174.08 (8)N1—C1—C9—C1092.12 (9)
N1—C2—C3—C87.97 (12)O3—C9—C10—C1164.06 (9)
O2—C2—C3—C48.02 (13)C8—C9—C10—C1156.54 (9)
N1—C2—C3—C4169.93 (8)C1—C9—C10—C11178.13 (7)
C8—C3—C4—C50.41 (13)C9—C10—C11—C1294.19 (11)
C2—C3—C4—C5178.32 (8)C9—C10—C11—S181.38 (9)
C3—C4—C5—C60.84 (14)C13—S1—C11—C120.55 (7)
C4—C5—C6—C70.35 (14)C13—S1—C11—C10176.87 (7)
C5—C6—C7—C80.59 (13)C10—C11—C12—N2176.72 (8)
C4—C3—C8—C70.53 (12)S1—C11—C12—N20.66 (10)
C2—C3—C8—C7177.31 (7)C10—C11—C12—C151.63 (15)
C4—C3—C8—C9174.28 (8)S1—C11—C12—C15177.69 (8)
C2—C3—C8—C97.87 (12)C13—N2—C12—C110.41 (11)
C6—C7—C8—C31.02 (13)C13—N2—C12—C15178.08 (8)
C6—C7—C8—C9173.77 (8)C12—N2—C13—C16178.59 (8)
C3—C8—C9—O3146.83 (8)C12—N2—C13—S10.04 (10)
C7—C8—C9—O338.41 (10)C11—S1—C13—N20.35 (7)
C3—C8—C9—C124.83 (10)C11—S1—C13—C16178.93 (8)
Hydrogen-bond geometry (Å, º) top
Cg1 is the centroid of C3–C8 benzene ring.
D—H···AD—HH···AD···AD—H···A
O3—H1O3···O2i0.75 (2)2.20 (2)2.8967 (10)154 (2)
C4—H4A···O1ii0.990 (18)2.350 (18)3.3045 (11)161.7 (13)
C10—H10A···O3iii0.975 (16)2.448 (14)3.2012 (11)133.8 (12)
C16—H16B···O1iv0.953 (17)2.565 (17)3.4698 (12)158.7 (13)
C15—H15B···Cg10.95 (2)2.812 (19)3.4494 (11)125.3 (15)
Symmetry codes: (i) x+1, y1/2, z+3/2; (ii) x+1, y+1/2, z+3/2; (iii) x, y+1/2, z+1/2; (iv) x+1, y, z.

Experimental details

Crystal data
Chemical formulaC16H16N2O3S
Mr316.37
Crystal system, space groupMonoclinic, P21/c
Temperature (K)100
a, b, c (Å)10.2424 (8), 15.0438 (13), 9.4786 (8)
β (°) 92.839 (2)
V3)1458.7 (2)
Z4
Radiation typeMo Kα
µ (mm1)0.24
Crystal size (mm)0.52 × 0.26 × 0.09
Data collection
DiffractometerBruker SMART APEX DUO CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Bruker, 2009)
Tmin, Tmax0.887, 0.979
No. of measured, independent and
observed [I > 2σ(I)] reflections
20742, 5260, 4752
Rint0.024
(sin θ/λ)max1)0.756
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.031, 0.108, 1.14
No. of reflections5260
No. of parameters263
H-atom treatmentAll H-atom parameters refined
Δρmax, Δρmin (e Å3)0.69, 0.47

Computer programs: APEX2 (Bruker, 2009), SAINT (Bruker, 2009), SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top
Cg1 is the centroid of C3–C8 benzene ring.
D—H···AD—HH···AD···AD—H···A
O3—H1O3···O2i0.75 (2)2.20 (2)2.8967 (10)154 (2)
C4—H4A···O1ii0.990 (18)2.350 (18)3.3045 (11)161.7 (13)
C10—H10A···O3iii0.975 (16)2.448 (14)3.2012 (11)133.8 (12)
C16—H16B···O1iv0.953 (17)2.565 (17)3.4698 (12)158.7 (13)
C15—H15B···Cg10.95 (2)2.812 (19)3.4494 (11)125.3 (15)
Symmetry codes: (i) x+1, y1/2, z+3/2; (ii) x+1, y+1/2, z+3/2; (iii) x, y+1/2, z+1/2; (iv) x+1, y, z.
 

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