character_table = {
    'C1=1':
    { 'rotation_list':
      [ 'E' ],
      'character_table'
      { 'A1': [ 1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'Ci=S2=-1':
    { 'rotation_list':
      [ 'E', 'i' ],
      'character_table'
      { 'Ag': [ 1,1 ],
      { 'Au': [ 1,-1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'Cs=C1h':
    { 'rotation_list':
      [ 'E', 'sgh' ],
      'character_table'
      { 'A\'': [ 1,1 ],
      { 'A\'\'': [ 1,-1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'sgh'   : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'C2=2':
    { 'rotation_list':
      [ 'E', 'C2' ],
      'character_table'
      { 'A': [ 1,1 ],
      { 'B': [ 1,-1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'C2v=mm2':
    { 'rotation_list':
      [ 'E', 'C2', 'sgv', 'sgv\'' ],
      'character_table'
      { 'A1': [ 1,1,1,1 ],
      { 'A2': [ 1,1,-1,-1 ],
      { 'B1': [ 1,-1,1,-1 ],
      { 'B2': [ 1,-1,-1,1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            'sgv'   : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)) ) ],
            'sgv\'' : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'C2h=2/m':
    { 'rotation_list':
      [ 'E', 'C2', 'i', 'sgh' ],
      'character_table'
      { 'Ag': [ 1,1,1,1 ],
      { 'Bg': [ 1,-1,1,-1 ],
      { 'Au': [ 1,1,-1,-1 ],
      { 'Bu': [ 1,-1,-1,1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
            'sgh'   : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'D2=222':
    { 'rotation_list':
      [ 'E', 'C4', 'C2', 'C4^3' ],
      'character_table'
      { 'A': [ 1,1,1,1 ],
      { 'B1': [ 1,1,-1,-1 ],
      { 'B1': [ 1,-1,1,-1 ],
      { 'B2': [ 1,-1,-1,1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C4'    : [ ( ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            'C4^3'  : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)),
                          (-1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'D2h=2/mmm':
    { 'rotation_list':
      [ 'E', 'C2', 'C2\'', 'C2\'\'', 'i', 'sg(xy)', 'sg\'(yz)', 'sg\'\'(xz)' ],
      'character_table'
      { 'Ag': [ 1,1,1,1,1,1,1,1 ],
      { 'B1g': [ 1,1,-1,-1,1,1,-1,-1 ],
      { 'B2g': [ 1,-1,1,-1,1,-1,1,-1 ],
      { 'B3g': [ 1,-1,-1,1,1,-1,-1,1 ],
      { 'Au': [ 1,1,1,1,-1,-1,-1,-1 ],
      { 'B1u': [ 1,1,-1,-1,-1,-1,1,1 ],
      { 'B2u': [ 1,-1,1,-1,-1,1,-1,1 ],
      { 'B3u': [ 1,-1,-1,1,-1,1,1,-1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            'C2\''  : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            'C2\'\'': [ ( ( 0, 1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)),
                          ( 1,-1, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)),
                          (-1, 0, 0)
                          (-1, 1, 0)
                          ( 0, 0,-1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
            'sg(xy)': [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            'sg\'(yz)': [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            'sg\'\'(xz)': [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'D2d=-42m':
    { 'rotation_list':
      [ 'E', '2S4', 'C2', '2C2\'', '2sgd' ],
      'character_table'
      { 'A1': [ 1,1,1,1,1 ],
      { 'A2': [ 1,1,1,-1,-1 ],
      { 'B1': [ 1,-1,1,1,-1 ],
      { 'B2': [ 1,-1,1,-1,1 ],
      { 'E': [ 2,0,-2,0,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2S4'   : [ ( ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            '2C2\'' : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            '2sgd'  : [ ( ( 0, 1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 1,-1, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 0, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'C3=3':
    { 'rotation_list':
      [ 'E', 'C3', 'C3^2' ],
      'character_table'
      { 'A': [ 1,1,1 ],
      { 'E': [ {1,1},{e,e*},{e*,e} ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C3'    : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C3^2'  : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'C3v=3m':
    { 'rotation_list':
      [ 'E', '2C3', '3sgv' ],
      'character_table'
      { 'A1': [ 1,1,1 ],
      { 'A2': [ 1,1,-1 ],
      { 'E': [ 2,-1,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C3'   : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            '3sgv'  : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'C3h=-6':
    { 'rotation_list':
      [ 'E', 'C3', 'C3^2', 'sgh', 'S3', 'S3^5' ],
      'character_table'
      { 'A\'': [ 1,1,1,1,1,1 ],
      { 'E\'': [ {1,1},{e,e*},{e*,e},{1,1},{e,e*},{e*,e} ],
      { 'A\'\'': [ 1,1,1,-1,-1,-1 ],
      { 'E\'\'': [ {1,1},{e,e*},{e*,e},{-1,-1},{-e,-e*},{-e*,-e} ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C3'    : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C3^2'  : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'sgh'   : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            'S3'    : [ ( (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            'S3^5'  : [ ( (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'S6=-3':
    { 'rotation_list':
      [ 'E', 'C3', 'C3^2', 'i', 'S6^5', 'S6' ],
      'character_table'
      { 'Ag': [ 1,1,1,1,1,1 ],
      { 'Eg': [ {1,1},{e,e*},{e*,e},{1,1},{e,e*},{e*,e} ],
      { 'Au': [ 1,1,1,-1,-1,-1 ],
      { 'Eu': [ {1,1},{e,e*},{e*,e},{-1,-1},{-e,-e*},{-e*,-e} ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C3'    : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C3^2'  : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
            'S6^5'  : [ ( ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0,-1)),
                          ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            'S6'    : [ ( ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0,-1)),
                          ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'D3=32':
    { 'rotation_list':
      [ 'E', '2C3', '3C2' ],
      'character_table'
      { 'A1': [ 1,1,1 ],
      { 'A2': [ 1,1,-1 ],
      { 'E': [ 2,-1,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C3'   : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            '3C2'   : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'D3d=-3m':
    { 'rotation_list':
      [ 'E', '2C3', '3C2', 'i', '2S6', '3sgd' ],
      'character_table'
      { 'A1g': [ 1,1,1,1,1,1 ],
      { 'A2g': [ 1,1,-1,1,1,-1 ],
      { 'Eg': [ 2,-1,0,2,-1,0 ],
      { 'A1u': [ 1,1,1,-1,-1,-1 ],
      { 'A2u': [ 1,1,-1,-1,-1,1 ],
      { 'Eu': [ 2,-1,0,-2,1,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C3'   : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            '3C2'   : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
            '2S6'   : [ ( ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0,-1)),
                          ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            '3sgd'  : [ ( ( 0, 1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 1,-1, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 0, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'D3h=-6m2':
    { 'rotation_list':
      [ 'E', '2C3', '3C2', 'sgh', '2S3', '3sgv' ],
      'character_table'
      { 'A1\'': [ 1,1,1,1,1,1 ],
      { 'A2\'': [ 1,1,-1,1,1,-1 ],
      { 'E\'': [ 2,-1,0,2,-1,0 ],
      { 'A1\' \'': [ 1,1,1,-1,-1,-1 ],
      { 'A2\' \'': [ 1,1,-1,-1,-1,1 ],
      { 'E\' \'': [ 2,-1,0,-2,1,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C3'   : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            '3C2'   : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            'sgh'   : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            '2S3'   : [ ( (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            '3sgv'  : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'C4=4':
    { 'rotation_list':
      [ 'E', 'C4', 'C2', 'C4^3' ],
      'character_table'
      { 'A': [ 1,1,1,1 ],
      { 'B': [ 1,-1,1,-1 ],
      { 'E': [ {1,1},{i,-i},{-1,1},{-i,i} ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C4'    : [ ( ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            'C4^3'  : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)),
                          (-1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'C4h=4/m':
    { 'rotation_list':
      [ 'E', 'C4', 'C4^2', 'C4^3', 'i', 'S4^3', 'sgh', 'S4' ],
      'character_table'
      { 'Ag': [ 1,1,1,1,1,1,1,1 ],
      { 'Bg': [ 1,-1,1,-1,1,-1,1,-1 ],
      { 'Eg': [ {1,1},{i,-i},{-1,-1},{-i,i},{1,1},{i,-i},{-1,-1},{-I,i} ],
      { 'Au': [ 1,1,1,1,-1,-1,-1,-1 ],
      { 'Bu': [ 1,-1,1,-1,-1,1,-1,1 ],
      { 'Eu': [ {1,1},{i,-i},{-1,-1},{-i,i},{-1,-1},{-i,i},{1,1},{i,-i} ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C4'    : [ ( ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C4^2'  : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)),
                          (-1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            'C4^3'  : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)),
                          (-1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
            'S4^3'  : [ ( ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            'sgh'   : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            'S4'    : [ ( ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'C4v=4mm':
    { 'rotation_list':
      [ 'E', '2C4', 'C2', '2sgv', '2sgd' ],
      'character_table'
      { 'A1': [ 1,1,1,1,1 ],
      { 'A2': [ 1,1,1,-1,-1 ],
      { 'B1': [ 1,-1,1,1,-1 ],
      { 'B2': [ 1,-1,1,-1,1 ],
      { 'E': [ 2,0,-2,0,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C4'   : [ ( ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            '2sgv'  : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)) ) ],
            '2sgd'  : [ ( ( 0, 1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 1,-1, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 0, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'D4=422':
    { 'rotation_list':
      [ 'E', '2C4', 'C2', '2C2\'', '2C2^\'\'' ],
      'character_table'
      { 'A1': [ 1,1,1,1,1 ],
      { 'A2': [ 1,1,1,-1,-1 ],
      { 'B1': [ 1,-1,1,1,-1 ],
      { 'B2': [ 1,-1,1,-1,1 ],
      { 'E': [ 2,0,-2,0,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C4'   : [ ( ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            '2C2\'' : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            '2C2^\'\'': [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'D4h=4/mmm':
    { 'rotation_list':
      [ 'E', '2C4', 'C2', '2C2\'', '2C2\'\'', 'i', '2S4', 'sgh', '2sgv', '2sgd' ],
      'character_table'
      { 'A1g': [ 1,1,1,1,1,1,1,1,1,1 ],
      { 'A2g': [ 1,1,1,-1,-1,1,1,1,-1,-1 ],
      { 'B1g': [ 1,-1,1,1,-1,1,-1,1,1,-1 ],
      { 'B2g': [ 1,-1,1,-1,1,1,-1,1,-1,1 ],
      { 'Eg': [ 2,0,-2,0,0,2,0,-2,0,0 ],
      { 'A1u': [ 1,1,1,1,1,-1,-1,-1,-1,-1 ],
      { 'A2u': [ 1,1,1,-1,-1,-1,-1,-1,1,1 ],
      { 'B1u': [ 1,-1,1,1,-1,-1,1,-1,-1,1 ],
      { 'B2u': [ 1,-1,1,-1,1,-1,1,-1,1,-1 ],
      { 'Eu': [ 2,0,-2,0,0,-2,0,2,0,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C4'   : [ ( ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            '2C2\'' : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            '2C2\'\'': [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
            '2S4'   : [ ( ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            'sgh'   : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            '2sgv'  : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)) ) ],
            '2sgd'  : [ ( ( 0, 1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 1,-1, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 0, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'D4d':
    { 'rotation_list':
      [ 'E', '2S8', '2C4', '2S8^3', '2C2', '4C2\'', '4sgd' ],
      'character_table'
      { '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 ],
      { 'E1': [ 2,2,0,-2,-2,0,0 ],
      { 'E2': [ 2,0,-2,0,2,0,0 ],
      { 'E3': [ 2,-2,0,2,-2,0,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2S8'   : [ ( ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            '2C4'   : [ ( ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            '2S8^3' : [ ( ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            '2C2'   : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            '4C2\'' : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            '4sgd'  : [ ( ( 0, 1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 1,-1, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 0, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'S4=-4':
    { 'rotation_list':
      [ 'E', 'S4', 'C2', 'S4^3' ],
      'character_table'
      { 'A': [ 1,1,1,1 ],
      { 'B': [ 1,-1,1,-1 ],
      { 'E': [ {1,1},{i,-i},{-1,-1},{-i,i} ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'S4'    : [ ( ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            'S4^3'  : [ ( ( 0, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'C6=6':
    { 'rotation_list':
      [ 'E', 'C6', 'C6^2', 'C6^3', 'C6^4', 'C6^5' ],
      'character_table'
      { 'A': [ 1,1,1,1,1,1 ],
      { 'B': [ 1,-1,1,-1,1,-1 ],
      { 'E1': [ {1,1},{e, e*},{-e*, -e},{-1, -1},{-e, -e*},{e*,-e} ],
      { 'E2': [ {1,1},{-e*, -e},{-e, -e*},{1,1},{-e*, -e},{-e, -e*} ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6'    : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6^2'  : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6^3'  : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6^4'  : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6^5'  : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'C6h=6/m':
    { 'rotation_list':
      [ 'E', 'C6', 'C6^2', 'C6^3', 'C6^4', 'C6^5', 'i', 'S3^5', 'S6^5', 'sgh', 'S6', 'S3' ],
      'character_table'
      { 'Ag': [ 1,1,1,1,1,1,1,1,1,1,1,1 ],
      { 'Bg': [ 1,-1,1,-1,1,-1,1,-1,1,-1,1,-1 ],
      { 'E1g': [ {1,1},{e,e*},{-e*,-e},{-1,-1},{-e,-e*},{e*,e},{1,1},{e,e*},{-e*,-e},{-1,-1},{-e,-e*},{e*,e} ],
      { 'E2g': [ {1,1},{-e*,-e},{-e,-e*},{1,1},{-e*,-e},{-e,-e*},{1,1},{-e*,-e},{-e,-e*},{1,1},{-e*,-e},{-e,-e*} ],
      { 'Au': [ 1,1,1,1,1,1,-1,-1,-1,-1,-1,-1 ],
      { 'Bu': [ 1,-1,1,-1,1,-1,-1,1,-1,1,-1,1 ],
      { 'E1u': [ {1,1},{e,e*},{-e*,-e},{-1,-1},{-e,-e*},{e*,e},{-1,-1},{-e,-e*},{e*,e},{1,1},{e,e*},{-e*,-e} ],
      { 'E2u': [ v,{-e*,-e},{-e,-e*},{1,1},{-e*,-e},{-e,-e*},{-1,-1},{e*,e},{e,e*},{-1,-1},{e*,e},{e,e*} ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6'    : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6^2'  : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6^3'  : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6^4'  : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6^5'  : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
            'S3^5'  : [ ( (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            'S6^5'  : [ ( ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0,-1)),
                          ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            'sgh'   : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            'S6'    : [ ( ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0,-1)),
                          ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            'S3'    : [ ( (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'C6v=6mm':
    { 'rotation_list':
      [ 'E', '2C6', '2C3', 'C2', '3sgh', '3sgd' ],
      'character_table'
      { 'A1': [ 1,1,1,1,1,1 ],
      { 'A2': [ 1,1,1,1,-1,-1 ],
      { 'B1': [ 1,-1,1,-1,1,-1 ],
      { 'B2': [ 1,-1,1,-1,-1,1 ],
      { 'E1': [ 2,1,-1,-2,0,0 ],
      { 'E2': [ 2,-1,-1,2,0,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C6'   : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C3'   : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            '3sgh'  : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            '3sgd'  : [ ( ( 0, 1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 1,-1, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 0, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'D6=622':
    { 'rotation_list':
      [ 'E', '2C6', '2C6^2', 'C6^3', '3C2\'', '3C2\'\'' ],
      'character_table'
      { 'A1': [ 1,1,1,1,1,1 ],
      { 'A2': [ 1,1,1,1,-1,-1 ],
      { 'B1': [ 1,-1,1,-1,1,-1 ],
      { 'B2': [ 1,-1,1,-1,-1,1 ],
      { 'E1': [ 2,1,-1,-2,0,0 ],
      { 'E2': [ 2,-1,-1,2,0,0 ],
      { '': [ ,,,,, ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C6'   : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C6^2' : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            'C6^3'  : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            '3C2\'' : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            '3C2\'\'': [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
      ]
    },

    'D6h=6/mmm':
    { 'rotation_list':
      [ 'E', '2C6', '2C3', 'C2', '3C2\'', '2C2\'\'', 'i', '2S2', '2S6', 'sgh', '3sgd', '3sgv' ],
      'character_table'
      { 'A1g': [ 1,1,1,1,1,1,1,1,1,1,1,1 ],
      { 'A2g': [ 1,1,1,1,-1,-1,1,1,1,1,-1,-1 ],
      { 'B1g': [ 1,-1,1,-1,1,-1,1,-1,1,-1,1,-1 ],
      { 'B2g': [ 1,-1,1,-1,-1,1,1,-1,1,-1,-1,1 ],
      { 'E1g': [ 2,1,-1,-2,0,0,2,1,-1,-2,0,0 ],
      { 'E2g': [ 2,-1,-1,2,0,0,2,-1,-1,2,0,0 ],
      { 'A1u': [ 1,1,1,1,1,1,-1,-1,-1,-1,-1,-1 ],
      { 'A2u': [ 1,1,1,1,-1,-1,-1,-1,-1,-1,1,1 ],
      { 'B1u': [ 1,-1,1,-1,1,-1,-1,1,-1,1,1,-1 ],
      { 'B2u': [ 1,-1,1,-1,-1,1,-1,1,-1,1,1,-1 ],
      { 'E1u': [ 2,1,-1,-2,0,0,-2,-1,1,2,0,0 ],
      { 'E2u': [ 2,-1,-1,2,0,0,-2,1,1,-2,0,0 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C6'   : [ ( ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            '2C3'   : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            'C2'    : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            '3C2\'' : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            '2C2\'\'': [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
            '2S2'   : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0,-1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0,-1)) ) ],
            '2S6'   : [ ( ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0,-1)),
                          ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
            'sgh'   : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0,-1)) ) ],
            '3sgd'  : [ ( ( 0, 1, 0)
                          ( 1, 0, 0)
                          ( 0, 0, 1)),
                          ( 1,-1, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 0, 0)
                          (-1, 1, 0)
                          ( 0, 0, 1)) ) ],
            '3sgv'  : [ ( ( 0,-1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)),
                          ( 1, 0, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'T=23':
    { 'rotation_list':
      [ 'E', '4C3', '4C3^2', '3C2' ],
      'character_table'
      { 'A': [ 1,1,1,1 ],
      { 'E': [ {1,1},{e,e*},{e*,e},{1,1} ],
      { 'T': [ 3,0,0,-1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '4C3'   : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            '4C3^2' : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            '3C2'   : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
      ]
    },

    'Th=m3':
    { 'rotation_list':
      [ 'E', '4C3', '4C3^2', '3C2', 'i', '4S6', '4S6^5', 'sgh' ],
      'character_table'
      { 'Ag': [ 1,1,1,1,1,1,1,1 ],
      { 'Eg': [ {1,1},{e,e*},{e*,e},{1,1},{1,1},{e,e*},{e*,e},{1,1} ],
      { 'Tg': [ 3,0,0,1,0,0,0,-1 ],
      { 'Au': [ 1,1,1,1,-1,-1,-1,-1 ],
      { 'Eu': [ {1,1},{e,e*},{e*,e},{-e,-e*},{-1,-1},{-e,-e*},{-e*,-e},{-1,-1} ],
      { 'Tu': [ 3,0,0,0,-1,0,0,1 ] },
      'mapping_table': [
          { 'E'     : [ ( ( 1, 0, 0)
                          ( 0, 1, 0)
                          ( 0, 0, 1)) ) ],
            '4C3'   : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            '4C3^2' : [ ( ( 0,-1, 0)
                          ( 1,-1, 0)
                          ( 0, 0, 1)),
                          (-1, 1, 0)
                          (-1, 0, 0)
                          ( 0, 0, 1)) ) ],
            '3C2'   : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0, 1)) ) ],
            'i'     : [ ( (-1, 0, 0)
                          ( 0,-1, 0)
                          ( 0, 0,-1)) ) ],
            '4S6'   : [ ( ( 0, 1, 0)
                          (-1, 1, 0)
                          ( 0, 0,-1)),
                          ( 1,-1, 0)
                          ( 1, 0, 0)
                          ( 0, 0,-1)) ) ],
