Abstract group data - 576.7437

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• gps_groups •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  abelian_quotient	text
  all_subgroups_known	boolean
  almost_simple	boolean
  aut_abelian	boolean
  aut_cyclic	boolean
  aut_derived_length	smallint
  aut_exponent	numeric
  aut_gen_orders	numeric[]
  aut_gens	numeric[]
  aut_group	text
  aut_hash	bigint
  aut_nilpotency_class	smallint
  aut_nilpotent	boolean
  aut_order	numeric
  aut_permdeg	integer
  aut_perms	numeric[]
  aut_phi_ratio	double precision
  aut_solvable	boolean
  aut_stats	numeric[]
  aut_supersolvable	boolean
  aut_tex	text
  autcent_abelian	boolean
  autcent_cyclic	boolean
  autcent_exponent	numeric
  autcent_group	text
  autcent_hash	bigint
  autcent_nilpotent	boolean
  autcent_order	numeric
  autcent_solvable	boolean
  autcent_split	boolean
  autcent_supersolvable	boolean
  autcent_tex	text
  autcentquo_abelian	boolean
  autcentquo_cyclic	boolean
  autcentquo_exponent	numeric
  autcentquo_group	text
  autcentquo_hash	bigint
  autcentquo_nilpotent	boolean
  autcentquo_order	numeric
  autcentquo_solvable	boolean
  autcentquo_supersolvable	boolean
  autcentquo_tex	text
  cc_stats	numeric[]
  center_label	text
  center_order	numeric
  central_product	boolean
  central_quotient	text
  commutator_count	integer
  commutator_label	text
  complements_known	boolean
  complete	boolean
  complex_characters_known	boolean
  composition_factors	text[]
  composition_length	smallint
  conjugacy_classes_known	boolean
  counter	integer
  cyclic	boolean
  derived_length	smallint
  dihedral	boolean
  direct_factorization	jsonb
  direct_product	boolean
  div_stats	numeric[]
  element_repr_type	text
  elementary	integer
  eulerian_function	numeric
  exponent	numeric
  exponents_of_order	smallint[]
  factors_of_aut_order	integer[]
  factors_of_order	smallint[]
  faithful_reps	numeric[]
  familial	boolean
  frattini_label	text
  frattini_quotient	text
  hash	bigint
  hyperelementary	integer
  inner_abelian	boolean
  inner_cyclic	boolean
  inner_exponent	numeric
  inner_gen_orders	numeric[]
  inner_gens	numeric[]
  inner_hash	bigint
  inner_nilpotent	boolean
  inner_order	numeric
  inner_split	boolean
  inner_tex	text
  inner_used	smallint[]
  irrC_degree	integer
  irrQ_degree	integer
  irrQ_dim	integer
  irrR_degree	integer
  irrep_stats	numeric[]
  label	text
  linC_count	numeric
  linC_degree	integer
  linFp_degree	integer
  linFq_degree	integer
  linQ_degree	integer
  linQ_degree_count	numeric
  linQ_dim	integer
  linQ_dim_count	numeric
  linR_count	numeric
  linR_degree	integer
  maximal_subgroups_known	boolean
  metabelian	boolean
  metacyclic	boolean
  monomial	boolean
  name	text
  ngens	smallint
  nilpotency_class	smallint
  nilpotent	boolean
  normal_counts	integer[]
  normal_index_bound	numeric
  normal_order_bound	numeric
  normal_subgroups_known	boolean
  number_autjugacy_classes	integer
  number_characteristic_subgroups	integer
  number_conjugacy_classes	integer
  number_divisions	integer
  number_normal_subgroups	integer
  number_subgroup_autclasses	integer
  number_subgroup_classes	integer
  number_subgroups	numeric
  old_label	text
  order	numeric
  order_factorization_type	integer
  order_stats	numeric[]
  outer_abelian	boolean
  outer_cyclic	boolean
  outer_equivalence	boolean
  outer_exponent	numeric
  outer_gen_orders	numeric[]
  outer_gen_pows	numeric[]
  outer_gens	numeric[]
  outer_group	text
  outer_hash	bigint
  outer_nilpotent	boolean
  outer_order	numeric
  outer_permdeg	integer
  outer_perms	numeric[]
  outer_solvable	boolean
  outer_supersolvable	boolean
  outer_tex	text
  pc_rank	smallint
  perfect	boolean
  permutation_degree	integer
  pgroup	smallint
  primary_abelian_invariants	integer[]
  quasisimple	boolean
  rank	smallint
  rational	boolean
  rational_characters_known	boolean
  ratrep_stats	numeric[]
  representations	jsonb
  schur_multiplier	integer[]
  semidirect_product	boolean
  simple	boolean
  smith_abelian_invariants	integer[]
  solvability_type	smallint
  solvable	boolean
  subgroup_inclusions_known	boolean
  subgroup_index_bound	numeric
  supersolvable	boolean
  sylow_subgroups_known	boolean
  tex_name	text
  transitive_degree	integer
  wreath_data	text[]
  wreath_product	boolean

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '36.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [6, 8, 2, 3, 4, 2, 2, 6, 4, 3, 2], 'aut_gens': [[1, 6, 12, 24], [349, 450, 150, 312], [371, 156, 150, 24], [193, 6, 12, 408], [163, 450, 438, 24], [161, 450, 12, 312], [445, 6, 300, 24], [163, 294, 12, 24], [445, 450, 438, 264], [19, 294, 12, 120], [193, 6, 12, 24], [161, 444, 150, 408]], 'aut_group': '4608.tz', 'aut_hash': 2117354285665300604, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 32, 'aut_perms': [63173051988844762678324767590522548, 203928926153275007683371071344984655, 128967085418111069098548820984465250, 7410029074429947518664856977212968, 205049992228685931261644683507316022, 89072881101578891126296799425137682, 185129903315671909966553326670586088, 58029277895239156048886513483910230, 144018880366848157457227099480412134, 178304084934745821286773391248971957, 33431007242996653206317766086632283], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 12, 2, 1], [3, 1, 2, 1], [3, 4, 6, 1], [4, 2, 1, 1], [4, 4, 2, 1], [4, 6, 1, 1], [6, 1, 2, 1], [6, 4, 6, 1], [6, 6, 2, 1], [6, 12, 4, 1], [8, 2, 2, 1], [8, 12, 1, 1], [12, 2, 2, 1], [12, 4, 4, 1], [12, 6, 2, 1], [12, 8, 6, 1], [12, 16, 12, 1], [24, 2, 4, 1], [24, 8, 12, 1], [24, 12, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_8.(D_6\\times S_4)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '24.14', 'autcent_hash': 14, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '192.1472', 'autcentquo_hash': 1472, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_4\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 1], [2, 12, 2], [3, 1, 2], [3, 4, 6], [4, 2, 1], [4, 4, 2], [4, 6, 1], [6, 1, 2], [6, 4, 6], [6, 6, 2], [6, 12, 4], [8, 2, 2], [8, 12, 1], [12, 2, 2], [12, 4, 4], [12, 6, 2], [12, 8, 6], [12, 16, 12], [24, 2, 4], [24, 8, 12], [24, 12, 2]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '96.197', 'commutator_count': 1, 'commutator_label': '16.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 7437, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['192.1017', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 12, 1, 2], [3, 1, 2, 1], [3, 4, 2, 3], [4, 2, 1, 1], [4, 4, 1, 2], [4, 6, 1, 1], [6, 1, 2, 1], [6, 4, 2, 3], [6, 6, 2, 1], [6, 12, 2, 2], [8, 2, 2, 1], [8, 12, 1, 1], [12, 2, 2, 1], [12, 4, 2, 2], [12, 6, 2, 1], [12, 8, 2, 3], [12, 16, 2, 6], [24, 2, 4, 1], [24, 8, 4, 3], [24, 12, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 24, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 0, 12]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '144.193', 'hash': 7437, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 2, 2, 4], 'inner_gens': [[1, 162, 438, 168], [445, 6, 300, 24], [451, 294, 12, 24], [433, 6, 12, 24]], 'inner_hash': 197, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': False, 'inner_tex': 'D_4\\times A_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 36], [2, 9], [3, 12], [4, 18], [6, 3]], 'label': '576.7437', 'linC_count': 12, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 12, 'linQ_dim': 10, 'linQ_dim_count': 12, 'linR_count': 24, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C3*Q16.A4', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 78, 'number_divisions': 40, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 102, 'number_subgroup_classes': 180, 'number_subgroups': 690, 'old_label': None, 'order': 576, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 31], [3, 26], [4, 16], [6, 86], [8, 16], [12, 272], [24, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 3], 'outer_gen_pows': [0, 552, 0, 24, 0], 'outer_gens': [[5, 156, 438, 312], [73, 6, 12, 24], [1, 6, 12, 312], [365, 156, 438, 120], [385, 6, 12, 24]], 'outer_group': '48.51', 'outer_hash': 51, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 9, 'outer_perms': [41041, 90720, 24, 131784, 3], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 51, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 17], [3, 4], [4, 4], [6, 5], [8, 1], [12, 1], [16, 4]], 'representations': {'PC': {'code': '47907158926542281815976003193084404236037355329', 'gens': [1, 3, 4, 5], 'pres': [8, -2, -3, -2, 2, -2, -2, -2, -3, 16, 2313, 3890, 5338, 1170, 14019, 4907, 1619, 6724, 116, 16133, 141, 166]}, 'Perm': {'d': 51, 'gens': [34202242221110636550998493455858890742718540181352519036895704664, 65163588164173777467341570903916315908785568319918426852162610200, 96260936861523015863009563806288686140965599636033825305616660160, 3, 127295944269704443373248767186616990136661866374884191075534157144, 157710263677034700889057248241751003210265097827206093236997814480, 188571616318524698321978730346730728212672482615936697794267040600, 219668661001972286325800853619794696226907423857068936998844987600]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6, 6], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times Q_{16}.A_4', 'transitive_degree': 144, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 110645962
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 7437, 'group_order': 576, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 110645973
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 7437, 'group_order': 576, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 288, 'size': 1}
  • id: 110645984
    {'aut_label': '2B', 'centralizer': '6.g1.a1', 'counter': 3, 'group_counter': 7437, 'group_order': 576, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 12, 'size': 6}
  • id: 110645995
    {'aut_label': '2C', 'centralizer': '12.h1.a1', 'counter': 4, 'group_counter': 7437, 'group_order': 576, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 15, 'size': 12}
  • id: 110646006
    {'aut_label': '2C', 'centralizer': '12.h1.b1', 'counter': 5, 'group_counter': 7437, 'group_order': 576, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 231, 'size': 12}
  • id: 110646017
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 7437, 'group_order': 576, 'label': '3A1', 'order': 3, 'powers': [7, 1], 'representative': 384, 'size': 1}
  • id: 110646028
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 7437, 'group_order': 576, 'label': '3A-1', 'order': 3, 'powers': [6, 1], 'representative': 192, 'size': 1}
  • id: 110646038
    {'aut_label': '3B1', 'centralizer': '4.c1.a1', 'counter': 8, 'group_counter': 7437, 'group_order': 576, 'label': '3B1', 'order': 3, 'powers': [9, 1], 'representative': 4, 'size': 4}
  • id: 110646039
    {'aut_label': '3B1', 'centralizer': '4.c1.a1', 'counter': 9, 'group_counter': 7437, 'group_order': 576, 'label': '3B-1', 'order': 3, 'powers': [8, 1], 'representative': 290, 'size': 4}
  • id: 110645963
    {'aut_label': '3B1', 'centralizer': '4.c1.a1', 'counter': 10, 'group_counter': 7437, 'group_order': 576, 'label': '3C1', 'order': 3, 'powers': [11, 1], 'representative': 196, 'size': 4}
  • id: 110645964
    {'aut_label': '3B1', 'centralizer': '4.c1.a1', 'counter': 11, 'group_counter': 7437, 'group_order': 576, 'label': '3C-1', 'order': 3, 'powers': [10, 1], 'representative': 98, 'size': 4}
  • id: 110645965
    {'aut_label': '3B1', 'centralizer': '4.c1.a1', 'counter': 12, 'group_counter': 7437, 'group_order': 576, 'label': '3D1', 'order': 3, 'powers': [13, 1], 'representative': 388, 'size': 4}
  • id: 110645966
    {'aut_label': '3B1', 'centralizer': '4.c1.a1', 'counter': 13, 'group_counter': 7437, 'group_order': 576, 'label': '3D-1', 'order': 3, 'powers': [12, 1], 'representative': 482, 'size': 4}
  • id: 110645967
    {'aut_label': '4A', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 7437, 'group_order': 576, 'label': '4A', 'order': 4, 'powers': [2, 14], 'representative': 144, 'size': 2}
  • id: 110645968
    {'aut_label': '4B', 'centralizer': '4.b1.a1', 'counter': 15, 'group_counter': 7437, 'group_order': 576, 'label': '4B', 'order': 4, 'powers': [2, 15], 'representative': 291, 'size': 4}
  • id: 110645969
    {'aut_label': '4B', 'centralizer': '4.b1.b1', 'counter': 16, 'group_counter': 7437, 'group_order': 576, 'label': '4C', 'order': 4, 'powers': [2, 16], 'representative': 507, 'size': 4}
  • id: 110645970
    {'aut_label': '4D', 'centralizer': '6.e1.a1', 'counter': 17, 'group_counter': 7437, 'group_order': 576, 'label': '4D', 'order': 4, 'powers': [2, 17], 'representative': 156, 'size': 6}
  • id: 110645971
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 7437, 'group_order': 576, 'label': '6A1', 'order': 6, 'powers': [7, 2], 'representative': 96, 'size': 1}
  • id: 110645972
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 7437, 'group_order': 576, 'label': '6A-1', 'order': 6, 'powers': [6, 2], 'representative': 480, 'size': 1}
  • id: 110645974
    {'aut_label': '6B1', 'centralizer': '4.c1.a1', 'counter': 20, 'group_counter': 7437, 'group_order': 576, 'label': '6B1', 'order': 6, 'powers': [8, 2], 'representative': 2, 'size': 4}
  • id: 110645975
    {'aut_label': '6B1', 'centralizer': '4.c1.a1', 'counter': 21, 'group_counter': 7437, 'group_order': 576, 'label': '6B-1', 'order': 6, 'powers': [9, 2], 'representative': 292, 'size': 4}
  • id: 110645976
    {'aut_label': '6B1', 'centralizer': '4.c1.a1', 'counter': 22, 'group_counter': 7437, 'group_order': 576, 'label': '6C1', 'order': 6, 'powers': [10, 2], 'representative': 386, 'size': 4}
  • id: 110645977
    {'aut_label': '6B1', 'centralizer': '4.c1.a1', 'counter': 23, 'group_counter': 7437, 'group_order': 576, 'label': '6C-1', 'order': 6, 'powers': [11, 2], 'representative': 484, 'size': 4}
  • id: 110645978
    {'aut_label': '6B1', 'centralizer': '4.c1.a1', 'counter': 24, 'group_counter': 7437, 'group_order': 576, 'label': '6D1', 'order': 6, 'powers': [12, 2], 'representative': 194, 'size': 4}
  • id: 110645979
    {'aut_label': '6B1', 'centralizer': '4.c1.a1', 'counter': 25, 'group_counter': 7437, 'group_order': 576, 'label': '6D-1', 'order': 6, 'powers': [13, 2], 'representative': 100, 'size': 4}
  • id: 110645980
    {'aut_label': '6E1', 'centralizer': '6.g1.a1', 'counter': 26, 'group_counter': 7437, 'group_order': 576, 'label': '6E1', 'order': 6, 'powers': [6, 3], 'representative': 204, 'size': 6}
  • id: 110645981
    {'aut_label': '6E1', 'centralizer': '6.g1.a1', 'counter': 27, 'group_counter': 7437, 'group_order': 576, 'label': '6E-1', 'order': 6, 'powers': [7, 3], 'representative': 108, 'size': 6}
  • id: 110645982
    {'aut_label': '6F1', 'centralizer': '12.h1.a1', 'counter': 28, 'group_counter': 7437, 'group_order': 576, 'label': '6F1', 'order': 6, 'powers': [6, 4], 'representative': 207, 'size': 12}
  • id: 110645983
    {'aut_label': '6F1', 'centralizer': '12.h1.a1', 'counter': 29, 'group_counter': 7437, 'group_order': 576, 'label': '6F-1', 'order': 6, 'powers': [7, 4], 'representative': 111, 'size': 12}
  • id: 110645985
    {'aut_label': '6F1', 'centralizer': '12.h1.b1', 'counter': 30, 'group_counter': 7437, 'group_order': 576, 'label': '6G1', 'order': 6, 'powers': [7, 5], 'representative': 39, 'size': 12}
  • id: 110645986
    {'aut_label': '6F1', 'centralizer': '12.h1.b1', 'counter': 31, 'group_counter': 7437, 'group_order': 576, 'label': '6G-1', 'order': 6, 'powers': [6, 5], 'representative': 135, 'size': 12}
  • id: 110645987
    {'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 32, 'group_counter': 7437, 'group_order': 576, 'label': '8A1', 'order': 8, 'powers': [14, 33], 'representative': 72, 'size': 2}
  • id: 110645988
    {'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 33, 'group_counter': 7437, 'group_order': 576, 'label': '8A3', 'order': 8, 'powers': [14, 32], 'representative': 216, 'size': 2}
  • id: 110645989
    {'aut_label': '8B', 'centralizer': '12.f1.a1', 'counter': 34, 'group_counter': 7437, 'group_order': 576, 'label': '8B', 'order': 8, 'powers': [14, 34], 'representative': 84, 'size': 12}
  • id: 110645990
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 35, 'group_counter': 7437, 'group_order': 576, 'label': '12A1', 'order': 12, 'powers': [18, 14], 'representative': 48, 'size': 2}
  • id: 110645991
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 36, 'group_counter': 7437, 'group_order': 576, 'label': '12A-1', 'order': 12, 'powers': [19, 14], 'representative': 528, 'size': 2}
  • id: 110645992
    {'aut_label': '12B1', 'centralizer': '4.b1.a1', 'counter': 37, 'group_counter': 7437, 'group_order': 576, 'label': '12B1', 'order': 12, 'powers': [18, 15], 'representative': 195, 'size': 4}
  • id: 110645993
    {'aut_label': '12B1', 'centralizer': '4.b1.a1', 'counter': 38, 'group_counter': 7437, 'group_order': 576, 'label': '12B-1', 'order': 12, 'powers': [19, 15], 'representative': 99, 'size': 4}
  • id: 110645994
    {'aut_label': '12B1', 'centralizer': '4.b1.b1', 'counter': 39, 'group_counter': 7437, 'group_order': 576, 'label': '12C1', 'order': 12, 'powers': [19, 16], 'representative': 27, 'size': 4}
  • id: 110645996
    {'aut_label': '12B1', 'centralizer': '4.b1.b1', 'counter': 40, 'group_counter': 7437, 'group_order': 576, 'label': '12C-1', 'order': 12, 'powers': [18, 16], 'representative': 123, 'size': 4}
  • id: 110645997
    {'aut_label': '12D1', 'centralizer': '6.e1.a1', 'counter': 41, 'group_counter': 7437, 'group_order': 576, 'label': '12D1', 'order': 12, 'powers': [18, 17], 'representative': 60, 'size': 6}
  • id: 110645998
    {'aut_label': '12D1', 'centralizer': '6.e1.a1', 'counter': 42, 'group_counter': 7437, 'group_order': 576, 'label': '12D-1', 'order': 12, 'powers': [19, 17], 'representative': 102, 'size': 6}
  • id: 110645999
    {'aut_label': '12E1', 'centralizer': '8.c1.a1', 'counter': 43, 'group_counter': 7437, 'group_order': 576, 'label': '12E1', 'order': 12, 'powers': [22, 14], 'representative': 52, 'size': 8}
  • id: 110646000
    {'aut_label': '12E1', 'centralizer': '8.c1.a1', 'counter': 44, 'group_counter': 7437, 'group_order': 576, 'label': '12E-1', 'order': 12, 'powers': [23, 14], 'representative': 242, 'size': 8}
  • id: 110646001
    {'aut_label': '12E1', 'centralizer': '8.c1.a1', 'counter': 45, 'group_counter': 7437, 'group_order': 576, 'label': '12F1', 'order': 12, 'powers': [25, 14], 'representative': 338, 'size': 8}
  • id: 110646002
    {'aut_label': '12E1', 'centralizer': '8.c1.a1', 'counter': 46, 'group_counter': 7437, 'group_order': 576, 'label': '12F-1', 'order': 12, 'powers': [24, 14], 'representative': 532, 'size': 8}
  • id: 110646003
    {'aut_label': '12E1', 'centralizer': '8.c1.a1', 'counter': 47, 'group_counter': 7437, 'group_order': 576, 'label': '12G1', 'order': 12, 'powers': [20, 14], 'representative': 436, 'size': 8}
  • id: 110646004
    {'aut_label': '12E1', 'centralizer': '8.c1.a1', 'counter': 48, 'group_counter': 7437, 'group_order': 576, 'label': '12G-1', 'order': 12, 'powers': [21, 14], 'representative': 434, 'size': 8}
  • id: 110646005
    {'aut_label': '12H1', 'centralizer': '16.b1.a1', 'counter': 49, 'group_counter': 7437, 'group_order': 576, 'label': '12H1', 'order': 12, 'powers': [20, 15], 'representative': 1, 'size': 16}
  • id: 110646007
    {'aut_label': '12H1', 'centralizer': '16.b1.a1', 'counter': 50, 'group_counter': 7437, 'group_order': 576, 'label': '12H-1', 'order': 12, 'powers': [21, 15], 'representative': 5, 'size': 16}
  • id: 110646008
    {'aut_label': '12H1', 'centralizer': '16.b1.a1', 'counter': 51, 'group_counter': 7437, 'group_order': 576, 'label': '12I1', 'order': 12, 'powers': [22, 15], 'representative': 193, 'size': 16}
  • id: 110646009
    {'aut_label': '12H1', 'centralizer': '16.b1.a1', 'counter': 52, 'group_counter': 7437, 'group_order': 576, 'label': '12I-1', 'order': 12, 'powers': [23, 15], 'representative': 101, 'size': 16}
  • id: 110646010
    {'aut_label': '12H1', 'centralizer': '16.b1.a1', 'counter': 53, 'group_counter': 7437, 'group_order': 576, 'label': '12J1', 'order': 12, 'powers': [24, 15], 'representative': 97, 'size': 16}
  • id: 110646011
    {'aut_label': '12H1', 'centralizer': '16.b1.a1', 'counter': 54, 'group_counter': 7437, 'group_order': 576, 'label': '12J-1', 'order': 12, 'powers': [25, 15], 'representative': 197, 'size': 16}
  • id: 110646012
    {'aut_label': '12H1', 'centralizer': '16.b1.b1', 'counter': 55, 'group_counter': 7437, 'group_order': 576, 'label': '12K1', 'order': 12, 'powers': [24, 16], 'representative': 25, 'size': 16}
  • id: 110646013
    {'aut_label': '12H1', 'centralizer': '16.b1.b1', 'counter': 56, 'group_counter': 7437, 'group_order': 576, 'label': '12K-1', 'order': 12, 'powers': [25, 16], 'representative': 125, 'size': 16}
  • id: 110646014
    {'aut_label': '12H1', 'centralizer': '16.b1.b1', 'counter': 57, 'group_counter': 7437, 'group_order': 576, 'label': '12L1', 'order': 12, 'powers': [20, 16], 'representative': 217, 'size': 16}
  • id: 110646015
    {'aut_label': '12H1', 'centralizer': '16.b1.b1', 'counter': 58, 'group_counter': 7437, 'group_order': 576, 'label': '12L-1', 'order': 12, 'powers': [21, 16], 'representative': 221, 'size': 16}
  • id: 110646016
    {'aut_label': '12H1', 'centralizer': '16.b1.b1', 'counter': 59, 'group_counter': 7437, 'group_order': 576, 'label': '12M1', 'order': 12, 'powers': [22, 16], 'representative': 121, 'size': 16}
  • id: 110646018
    {'aut_label': '12H1', 'centralizer': '16.b1.b1', 'counter': 60, 'group_counter': 7437, 'group_order': 576, 'label': '12M-1', 'order': 12, 'powers': [23, 16], 'representative': 29, 'size': 16}
  • id: 110646019
    {'aut_label': '24A1', 'centralizer': '2.b1.a1', 'counter': 61, 'group_counter': 7437, 'group_order': 576, 'label': '24A1', 'order': 24, 'powers': [35, 32], 'representative': 24, 'size': 2}
  • id: 110646020
    {'aut_label': '24A1', 'centralizer': '2.b1.a1', 'counter': 62, 'group_counter': 7437, 'group_order': 576, 'label': '24A-1', 'order': 24, 'powers': [36, 32], 'representative': 408, 'size': 2}
  • id: 110646021
    {'aut_label': '24A1', 'centralizer': '2.b1.a1', 'counter': 63, 'group_counter': 7437, 'group_order': 576, 'label': '24A5', 'order': 24, 'powers': [36, 33], 'representative': 120, 'size': 2}
  • id: 110646022
    {'aut_label': '24A1', 'centralizer': '2.b1.a1', 'counter': 64, 'group_counter': 7437, 'group_order': 576, 'label': '24A-5', 'order': 24, 'powers': [35, 33], 'representative': 312, 'size': 2}
  • id: 110646023
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 65, 'group_counter': 7437, 'group_order': 576, 'label': '24B1', 'order': 24, 'powers': [43, 33], 'representative': 26, 'size': 8}
  • id: 110646024
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 66, 'group_counter': 7437, 'group_order': 576, 'label': '24B-1', 'order': 24, 'powers': [44, 33], 'representative': 124, 'size': 8}
  • id: 110646025
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 67, 'group_counter': 7437, 'group_order': 576, 'label': '24B5', 'order': 24, 'powers': [44, 32], 'representative': 412, 'size': 8}
  • id: 110646026
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 68, 'group_counter': 7437, 'group_order': 576, 'label': '24B-5', 'order': 24, 'powers': [43, 32], 'representative': 38, 'size': 8}
  • id: 110646027
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 69, 'group_counter': 7437, 'group_order': 576, 'label': '24C1', 'order': 24, 'powers': [45, 32], 'representative': 28, 'size': 8}
  • id: 110646029
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 70, 'group_counter': 7437, 'group_order': 576, 'label': '24C-1', 'order': 24, 'powers': [46, 32], 'representative': 122, 'size': 8}
  • id: 110646030
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 71, 'group_counter': 7437, 'group_order': 576, 'label': '24C5', 'order': 24, 'powers': [46, 33], 'representative': 410, 'size': 8}
  • id: 110646031
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 72, 'group_counter': 7437, 'group_order': 576, 'label': '24C-5', 'order': 24, 'powers': [45, 33], 'representative': 316, 'size': 8}
  • id: 110646032
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 73, 'group_counter': 7437, 'group_order': 576, 'label': '24D1', 'order': 24, 'powers': [47, 33], 'representative': 218, 'size': 8}
  • id: 110646033
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 74, 'group_counter': 7437, 'group_order': 576, 'label': '24D-1', 'order': 24, 'powers': [48, 33], 'representative': 76, 'size': 8}
  • id: 110646034
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 75, 'group_counter': 7437, 'group_order': 576, 'label': '24D5', 'order': 24, 'powers': [48, 32], 'representative': 220, 'size': 8}
  • id: 110646035
    {'aut_label': '24B1', 'centralizer': '8.c1.a1', 'counter': 76, 'group_counter': 7437, 'group_order': 576, 'label': '24D-5', 'order': 24, 'powers': [47, 32], 'representative': 74, 'size': 8}
  • id: 110646036
    {'aut_label': '24E1', 'centralizer': '12.f1.a1', 'counter': 77, 'group_counter': 7437, 'group_order': 576, 'label': '24E1', 'order': 24, 'powers': [35, 34], 'representative': 36, 'size': 12}
  • id: 110646037
    {'aut_label': '24E1', 'centralizer': '12.f1.a1', 'counter': 78, 'group_counter': 7437, 'group_order': 576, 'label': '24E-1', 'order': 24, 'powers': [36, 34], 'representative': 132, 'size': 12}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 4693592
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4693603
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4693614
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4693625
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4693627
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4693628
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1f', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 4693629
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1g', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1], 'schur_index': 1}
  • id: 4693630
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1h', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 4693631
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -2, -2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 1, 1, 1, 1, 2, 2, 2, -1, -1, 1, 1, 1, 1, -1, -1, 2, -1, 2, -1, -1, -1, 1, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, -2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4693593
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -2, -2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, -1, -1, 1, 1, 1, 1, -1, -1, -1, 2, -1, -1, 2, -1, 1, -2, 1, -2, 1, 1, -2, 1, -2, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 4693594
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -2, -2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 2, -1, 2, -2, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1], 'schur_index': 1}
  • id: 4693595
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 4693596
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 1, 1, -2, -2, -2, -1, -1, -1, -1, 1, 1, -1, -1, 2, -1, 2, -1, -1, -1, 1, 1, 2, -1, 2, -2, -1, -1, 1, 1, -1, -2, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4693597
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 1, 1, -2, -2, -2, -1, -1, -1, -1, 1, 1, -1, -1, -1, 2, -1, -1, 2, -1, 1, -2, -1, 2, -1, 1, 2, -1, -2, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, 1, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 4693598
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 1, 1, -2, -2, -2, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 2, -1, 2, -2, 1, -1, -1, -1, 1, -1, 2, 1, -2, 2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, 1, 1], 'schur_index': 1}
  • id: 4693599
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2], 'schur_index': 1}
  • id: 4693600
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1q', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 1, 1, -1, -1, -2, -2, -2, -1, -1, 1, 1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -2, 1, -2, 2, 1, 1, -1, -1, 1, 2, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4693601
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1r', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 1, 1, -1, -1, -2, -2, -2, -1, -1, 1, 1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, 1, -2, 1, -1, -2, 1, 2, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, 1, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 4693602
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1s', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -1, -1, 2, -1, -1, 2, -1, -1, 2, 2, -2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 1, 1, -1, -1, -2, -2, -2, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, 1, 1, 1, -1, 1, -2, -1, 2, -2, -1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, 1, 1], 'schur_index': 1}
  • id: 4693604
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.1t', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2], 'schur_index': 1}
  • id: 4693605
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693610
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.3a', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, -1, 3, 3, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 3, 3, -1, 3, 3, 3, 3, 3, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4693611
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.3b', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 1, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, -3, -1, 3, 3, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, -3, -3, 1, 3, 3, -3, -3, 3, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4693612
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.3c', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -1, 1, -1, 3, 3, 0, 0, 0, 0, 0, 0, 3, -3, 3, -1, 3, 3, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, -3, -3, 1, 3, 3, 3, 3, -3, -3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4693613
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.3d', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -1, 1, 1, 3, 3, 0, 0, 0, 0, 0, 0, 3, -3, -3, -1, 3, 3, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 3, 3, -1, 3, 3, -3, -3, -3, -3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4693606
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.2b', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, -2, -2, -2, -2, 4, -2, 4, -2, -4, 0, 0, 4, -2, -2, -2, -2, 4, -2, -2, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, -2, -4, 2, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693607
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.2c', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, -2, -2, -2, 4, -2, -2, -2, 4, -4, 0, 0, 4, -2, -2, 4, -2, -2, 4, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, -2, 2, -4, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693608
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.2d', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, -2, -2, 4, -2, -2, 4, -2, -2, -4, 0, 0, 4, -2, -2, -2, 4, -2, -2, 4, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, -2, 2, 2, 2, -4, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693609
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.2e', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, -4, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 4, 4, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693615
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.3e', 'multiplicity': 2, 'nt': [12, 20], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -2, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, 6, -2, -3, -3, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 6, 6, -2, -3, -3, -3, -3, -3, -3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4693616
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.3f', 'multiplicity': 2, 'nt': [18, 25], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 2, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, -6, -2, -3, -3, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, -6, -6, 2, -3, -3, 3, 3, -3, -3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4693617
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.3g', 'multiplicity': 2, 'nt': [18, 25], 'qdim': 6, 'qvalues': [6, 6, -2, 2, -2, -3, -3, 0, 0, 0, 0, 0, 0, 6, -6, 6, -2, -3, -3, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -6, -6, 2, -3, -3, -3, -3, 3, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4693618
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.3h', 'multiplicity': 2, 'nt': [18, 25], 'qdim': 6, 'qvalues': [6, 6, -2, 2, 2, -3, -3, 0, 0, 0, 0, 0, 0, 6, -6, -6, -2, -3, -3, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, 6, 6, -2, -3, -3, 3, 3, 3, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4693624
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.6a', 'multiplicity': 1, 'nt': [12, 51], 'qdim': 6, 'qvalues': [6, 6, 2, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, -6, 0, 0, -2, 6, 6, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693619
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.4a', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 8, 8, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, -8, -8, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693626
    {'cdim': 6, 'counter': 40, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.6b', 'multiplicity': 2, 'nt': [36, 313], 'qdim': 12, 'qvalues': [12, 12, 4, 0, 0, -6, -6, 0, 0, 0, 0, 0, 0, -12, 0, 0, -4, -6, -6, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693620
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.4b', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 16, 16, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -16, -16, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693621
    {'cdim': 4, 'counter': 36, 'faithful': True, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.4c', 'multiplicity': 4, 'nt': [144, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, -8, -8, -8, 4, 4, -8, 4, 4, 0, 0, 0, 0, 8, 8, -4, 8, -4, -4, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693622
    {'cdim': 4, 'counter': 37, 'faithful': True, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.4d', 'multiplicity': 4, 'nt': [144, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, -8, -8, 4, -8, 4, 4, 4, -8, 0, 0, 0, 0, 8, 8, 8, -4, -4, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4693623
    {'cdim': 4, 'counter': 38, 'faithful': True, 'group': '576.7437', 'group_order': 576, 'image': None, 'label': '576.7437.4e', 'multiplicity': 4, 'nt': [144, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, -8, -8, 4, 4, -8, 4, -8, 4, 0, 0, 0, 0, 8, 8, -4, -4, 8, -4, -4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 7553421
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 576, 'label': '576.7437.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7553432
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 288, 'label': '576.7437.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7553443
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 288, 'label': '576.7437.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7553454
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 288, 'label': '576.7437.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7553465
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 192, 'label': '576.7437.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 7553476
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 192, 'label': '576.7437.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 7553487
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 192, 'label': '576.7437.1f1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 7553497
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 192, 'label': '576.7437.1f2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 7553498
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 192, 'label': '576.7437.1g1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 7553422
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 192, 'label': '576.7437.1g2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 7553423
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 192, 'label': '576.7437.1h1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]]]}
  • id: 7553424
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 192, 'label': '576.7437.1h2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]]]}
  • id: 7553425
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.b1', 'kernel_order': 96, 'label': '576.7437.1i1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 7553426
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.b1', 'kernel_order': 96, 'label': '576.7437.1i2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 7553427
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.c1', 'kernel_order': 96, 'label': '576.7437.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 7553428
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.c1', 'kernel_order': 96, 'label': '576.7437.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 7553429
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 96, 'label': '576.7437.1k1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 7553430
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 96, 'label': '576.7437.1k2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 7553431
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 96, 'label': '576.7437.1l1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]]]}
  • id: 7553433
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 96, 'label': '576.7437.1l2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]]]}
  • id: 7553434
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.e1', 'kernel_order': 96, 'label': '576.7437.1m1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 7553435
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.e1', 'kernel_order': 96, 'label': '576.7437.1m2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 7553436
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.f1', 'kernel_order': 96, 'label': '576.7437.1n1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 7553437
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.f1', 'kernel_order': 96, 'label': '576.7437.1n2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 7553438
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 25, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.d1', 'kernel_order': 96, 'label': '576.7437.1o1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 7553439
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 26, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.d1', 'kernel_order': 96, 'label': '576.7437.1o2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 7553440
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 27, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 96, 'label': '576.7437.1p1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]]]}
  • id: 7553441
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 28, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 96, 'label': '576.7437.1p2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]]]}
  • id: 7553442
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 29, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.b1', 'kernel_order': 96, 'label': '576.7437.1q1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 7553444
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 30, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.b1', 'kernel_order': 96, 'label': '576.7437.1q2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 7553445
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 31, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.c1', 'kernel_order': 96, 'label': '576.7437.1r1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 7553446
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 32, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.c1', 'kernel_order': 96, 'label': '576.7437.1r2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 7553447
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 33, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 96, 'label': '576.7437.1s1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 7553448
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 34, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 96, 'label': '576.7437.1s2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 7553449
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 35, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 96, 'label': '576.7437.1t1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]]]}
  • id: 7553450
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 576, 'counter': 36, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 96, 'label': '576.7437.1t2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]]]}
  • id: 7553451
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  • id: 7553452
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 144, 'counter': 38, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1.b1', 'kernel_order': 24, 'label': '576.7437.2b1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553453
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 144, 'counter': 39, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1.b1', 'kernel_order': 24, 'label': '576.7437.2b2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553455
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 144, 'counter': 40, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1.c1', 'kernel_order': 24, 'label': '576.7437.2c1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553456
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 144, 'counter': 41, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1.c1', 'kernel_order': 24, 'label': '576.7437.2c2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553457
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 144, 'counter': 42, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1.a1', 'kernel_order': 24, 'label': '576.7437.2d1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553458
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 144, 'counter': 43, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1.a1', 'kernel_order': 24, 'label': '576.7437.2d2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553459
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 144, 'counter': 44, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 24, 'label': '576.7437.2e1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553460
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 144, 'counter': 45, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 24, 'label': '576.7437.2e2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553461
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 46, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 48, 'label': '576.7437.3a', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7553462
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 47, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 24, 'label': '576.7437.3b', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7553463
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 48, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.b1', 'kernel_order': 24, 'label': '576.7437.3c', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7553464
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 49, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.a1', 'kernel_order': 24, 'label': '576.7437.3d', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7553466
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 50, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 16, 'label': '576.7437.3e1', 'nt': [12, 20], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 7553467
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 51, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 16, 'label': '576.7437.3e2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 7553468
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 52, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 8, 'label': '576.7437.3f1', 'nt': [18, 25], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[-3, -1]], [[-3, 1]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]]]}
  • id: 7553469
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 53, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 8, 'label': '576.7437.3f2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[-3, 1]], [[-3, -1]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]]]}
  • id: 7553470
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 54, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.b1', 'kernel_order': 8, 'label': '576.7437.3g1', 'nt': [18, 25], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[-3, 1]], [[-3, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]]]}
  • id: 7553471
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 55, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.b1', 'kernel_order': 8, 'label': '576.7437.3g2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[-3, -1]], [[-3, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]]]}
  • id: 7553472
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 56, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 8, 'label': '576.7437.3h1', 'nt': [18, 25], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 7553473
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 48, 'counter': 57, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 8, 'label': '576.7437.3h2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 7553474
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 58, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '192.1017', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 3, 'label': '576.7437.4a1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 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, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 7553475
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 59, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '192.1017', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 3, 'label': '576.7437.4a2', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 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, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 7553477
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 60, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '192.1017', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 3, 'label': '576.7437.4b1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 8]], [[-2, 8]], [[-2, 8]], [[2, 4]], [[2, 4]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-2, 4]], [[-2, 4]], [[2, 8]], [[2, 8]], [[2, 8]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-1, 1], [-1, 7]], [[1, 1], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 1], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 1], [-1, 7]], [[1, 1], [1, 7]], [[-1, 1], [-1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553478
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 61, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '192.1017', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 3, 'label': '576.7437.4b2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 4]], [[2, 4]], [[2, 4]], [[-2, 8]], [[-2, 8]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 8]], [[2, 8]], [[-2, 4]], [[-2, 4]], [[-2, 4]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 1], [-1, 7]], [[1, 1], [1, 7]], [[1, 1], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 1], [1, 7]], [[-1, 1], [-1, 7]], [[-1, 1], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553479
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 62, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '192.1017', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 3, 'label': '576.7437.4b3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 8]], [[-2, 8]], [[-2, 8]], [[2, 4]], [[2, 4]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-2, 4]], [[-2, 4]], [[2, 8]], [[2, 8]], [[2, 8]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[1, 1], [1, 7]], [[-1, 1], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 1], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 1], [1, 7]], [[-1, 1], [-1, 7]], [[1, 1], [1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553480
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 63, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '192.1017', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 3, 'label': '576.7437.4b4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 4]], [[2, 4]], [[2, 4]], [[-2, 8]], [[-2, 8]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 8]], [[2, 8]], [[-2, 4]], [[-2, 4]], [[-2, 4]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 1], [1, 7]], [[-1, 1], [-1, 7]], [[-1, 1], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 1], [-1, 7]], [[1, 1], [1, 7]], [[1, 1], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553481
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 64, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4c1', 'nt': [144, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4]], [[4, 8]], [[-2, 0]], [[2, 4]], [[-2, 8]], [[-2, 0]], [[2, 4]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[-4, 8]], [[2, 8]], [[2, 0]], [[2, 8]], [[-2, 4]], [[2, 0]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 7]], [[-2, 3], [2, 5], [2, 7]], [[2, 3], [-2, 5], [-2, 7]], [[2, 1], [2, 7]], [[1, 3], [1, -3]], [[1, 1], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 1], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, 7]], [[1, 3], [1, -3]], [[-1, 1], [-1, 7]], [[-1, 3], [-1, -3]], [[-1, 3], [1, 5], [1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553482
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 65, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4c2', 'nt': [144, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 8]], [[-4, 4]], [[-2, 0]], [[-2, 8]], [[2, 4]], [[-2, 0]], [[-2, 8]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 8]], [[4, 4]], [[-2, 4]], [[2, 0]], [[-2, 4]], [[2, 8]], [[2, 0]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [2, 5], [2, 7]], [[-2, 1], [-2, 7]], [[2, 1], [2, 7]], [[2, 3], [-2, 5], [-2, 7]], [[1, 3], [1, -3]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 1], [-1, 7]], [[1, 1], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 1], [1, 7]], [[-1, 3], [-1, -3]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [1, -3]], [[-1, 3], [1, 5], [1, 7]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553483
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 66, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4c3', 'nt': [144, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4]], [[4, 8]], [[-2, 0]], [[2, 4]], [[-2, 8]], [[-2, 0]], [[2, 4]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[-4, 8]], [[2, 8]], [[2, 0]], [[2, 8]], [[-2, 4]], [[2, 0]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 7]], [[2, 3], [-2, 5], [-2, 7]], [[-2, 3], [2, 5], [2, 7]], [[-2, 1], [-2, 7]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 1], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [1, -3]], [[1, 1], [1, 7]], [[-1, 3], [-1, -3]], [[1, 1], [1, 7]], [[1, 3], [1, -3]], [[1, 3], [-1, 5], [-1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553484
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 67, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4c4', 'nt': [144, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 8]], [[-4, 4]], [[-2, 0]], [[-2, 8]], [[2, 4]], [[-2, 0]], [[-2, 8]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 8]], [[4, 4]], [[-2, 4]], [[2, 0]], [[-2, 4]], [[2, 8]], [[2, 0]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [-2, 5], [-2, 7]], [[2, 1], [2, 7]], [[-2, 1], [-2, 7]], [[-2, 3], [2, 5], [2, 7]], [[-1, 3], [-1, -3]], [[-1, 3], [1, 5], [1, 7]], [[1, 1], [1, 7]], [[-1, 1], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 1], [-1, 7]], [[1, 3], [1, -3]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [-1, -3]], [[1, 3], [-1, 5], [-1, 7]], [[1, 3], [1, -3]], [[1, 1], [1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553485
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 68, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4d1', 'nt': [144, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4]], [[4, 8]], [[-2, 8]], [[-2, 0]], [[2, 4]], [[2, 4]], [[-2, 8]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[-4, 8]], [[2, 0]], [[-2, 4]], [[-2, 4]], [[2, 0]], [[2, 8]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 7]], [[-2, 3], [2, 5], [2, 7]], [[2, 3], [-2, 5], [-2, 7]], [[2, 1], [2, 7]], [[-1, 1], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 1], [-1, 7]], [[1, 1], [1, 7]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [-1, 5], [-1, 7]], [[1, 3], [1, -3]], [[-1, 3], [1, 5], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 1], [1, 7]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]]]}
  • id: 7553486
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 69, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4d2', 'nt': [144, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 8]], [[-4, 4]], [[2, 4]], [[-2, 0]], [[-2, 8]], [[-2, 8]], [[2, 4]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 8]], [[4, 4]], [[2, 0]], [[2, 8]], [[2, 8]], [[2, 0]], [[-2, 4]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [2, 5], [2, 7]], [[-2, 1], [-2, 7]], [[2, 1], [2, 7]], [[2, 3], [-2, 5], [-2, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 1], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, 7]], [[1, 3], [1, -3]], [[-1, 1], [-1, 7]], [[-1, 1], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]]]}
  • id: 7553488
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 70, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4d3', 'nt': [144, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4]], [[4, 8]], [[-2, 8]], [[-2, 0]], [[2, 4]], [[2, 4]], [[-2, 8]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[-4, 8]], [[2, 0]], [[-2, 4]], [[-2, 4]], [[2, 0]], [[2, 8]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 7]], [[2, 3], [-2, 5], [-2, 7]], [[-2, 3], [2, 5], [2, 7]], [[-2, 1], [-2, 7]], [[1, 1], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 1], [1, 7]], [[-1, 1], [-1, 7]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [1, 5], [1, 7]], [[-1, 3], [-1, -3]], [[1, 3], [-1, 5], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 1], [-1, 7]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]]]}
  • id: 7553489
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 71, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4d4', 'nt': [144, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 8]], [[-4, 4]], [[2, 4]], [[-2, 0]], [[-2, 8]], [[-2, 8]], [[2, 4]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 8]], [[4, 4]], [[2, 0]], [[2, 8]], [[2, 8]], [[2, 0]], [[-2, 4]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [-2, 5], [-2, 7]], [[2, 1], [2, 7]], [[-2, 1], [-2, 7]], [[-2, 3], [2, 5], [2, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 1], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, 7]], [[-1, 3], [-1, -3]], [[1, 1], [1, 7]], [[1, 1], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]]]}
  • id: 7553490
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 72, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4e1', 'nt': [144, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4]], [[4, 8]], [[2, 4]], [[-2, 8]], [[-2, 0]], [[-2, 8]], [[-2, 0]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[-4, 8]], [[-2, 4]], [[2, 8]], [[2, 0]], [[2, 8]], [[-2, 4]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 7]], [[-2, 3], [2, 5], [2, 7]], [[2, 3], [-2, 5], [-2, 7]], [[2, 1], [2, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [-1, 5], [-1, 7]], [[1, 1], [1, 7]], [[1, 1], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 1], [-1, 7]], [[1, 3], [1, -3]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 1], [-1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553491
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 73, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4e2', 'nt': [144, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 8]], [[-4, 4]], [[-2, 8]], [[2, 4]], [[-2, 0]], [[2, 4]], [[-2, 0]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 8]], [[4, 4]], [[2, 8]], [[-2, 4]], [[2, 0]], [[-2, 4]], [[2, 8]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [2, 5], [2, 7]], [[-2, 1], [-2, 7]], [[2, 1], [2, 7]], [[2, 3], [-2, 5], [-2, 7]], [[-1, 1], [-1, 7]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 1], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 3], [1, -3]], [[1, 1], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553492
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 74, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4e3', 'nt': [144, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4]], [[4, 8]], [[2, 4]], [[-2, 8]], [[-2, 0]], [[-2, 8]], [[-2, 0]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[-4, 8]], [[-2, 4]], [[2, 8]], [[2, 0]], [[2, 8]], [[-2, 4]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 7]], [[2, 3], [-2, 5], [-2, 7]], [[-2, 3], [2, 5], [2, 7]], [[-2, 1], [-2, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 3], [1, 5], [1, 7]], [[-1, 1], [-1, 7]], [[-1, 1], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[1, 1], [1, 7]], [[-1, 3], [-1, -3]], [[-1, 3], [1, 5], [1, 7]], [[1, 1], [1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553493
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 6, 'counter': 75, 'cyclotomic_n': 24, 'dim': 4, 'faithful': True, 'field': [4, 0, 2, 0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '576.7437', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 1, 'label': '576.7437.4e4', 'nt': [144, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 8]], [[-4, 4]], [[-2, 8]], [[2, 4]], [[-2, 0]], [[2, 4]], [[-2, 0]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 8]], [[4, 4]], [[2, 8]], [[-2, 4]], [[2, 0]], [[-2, 4]], [[2, 8]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [-2, 5], [-2, 7]], [[2, 1], [2, 7]], [[-2, 1], [-2, 7]], [[-2, 3], [2, 5], [2, 7]], [[1, 1], [1, 7]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, 7]], [[-1, 3], [1, 5], [1, 7]], [[-1, 3], [1, 5], [1, 7]], [[1, 1], [1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, 7]], [[1, 3], [-1, 5], [-1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 7553494
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 12, 'counter': 76, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '96.197', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 6, 'label': '576.7437.6a', 'nt': [12, 51], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553495
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 12, 'counter': 77, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '288.980', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 2, 'label': '576.7437.6b1', 'nt': [36, 313], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7553496
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 12, 'counter': 78, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '576.7437', 'group_counter': 7437, 'group_order': 576, 'image': None, 'image_isoclass': '288.980', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 2, 'label': '576.7437.6b2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 67648129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 576, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '576.7437.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.7437', 'subgroup_hash': 7437, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times Q_{16}.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 67648221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.984', 'subgroup_hash': 984, 'subgroup_order': 288, 'subgroup_tex': 'Q_8.C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 67648232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.984', 'subgroup_hash': 984, 'subgroup_order': 288, 'subgroup_tex': 'Q_8.C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 67648243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 288, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.638', 'subgroup_hash': 638, 'subgroup_order': 288, 'subgroup_tex': 'C_{24}.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 67648254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 192, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1465', 'subgroup_hash': 1465, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 67648265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 192, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '576.7437.3.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1017', 'subgroup_hash': 1017, 'subgroup_order': 192, 'subgroup_tex': 'Q_{16}.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 67648276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 192, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '576.7437.3.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1017', 'subgroup_hash': 1017, 'subgroup_order': 192, 'subgroup_tex': 'Q_{16}.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 67648287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 192, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '576.7437.3.b1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1017', 'subgroup_hash': 1017, 'subgroup_order': 192, 'subgroup_tex': 'Q_{16}.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 67648298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 144, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.157', 'subgroup_hash': 157, 'subgroup_order': 144, 'subgroup_tex': '\\SL(2,3):C_6', 'supersolvable': False, 'sylow': 0}
  • id: 67648130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.157', 'subgroup_hash': 157, 'subgroup_order': 144, 'subgroup_tex': '\\SL(2,3):C_6', 'supersolvable': False, 'sylow': 0}
  • id: 67648141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.157', 'subgroup_hash': 157, 'subgroup_order': 144, 'subgroup_tex': '\\SL(2,3):C_6', 'supersolvable': False, 'sylow': 0}
  • id: 67648152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 48, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.4.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.108', 'subgroup_hash': 108, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.224', 'subgroup_hash': 224, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 67648174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.224', 'subgroup_hash': 224, 'subgroup_order': 96, 'subgroup_tex': 'C_6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 67648185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.201', 'subgroup_hash': 201, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 67648196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.201', 'subgroup_hash': 201, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 67648207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.201', 'subgroup_hash': 201, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 67648218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.201', 'subgroup_hash': 201, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 67648220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.201', 'subgroup_hash': 201, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 67648222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 96, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.b1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.201', 'subgroup_hash': 201, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 67648223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 96, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.178', 'subgroup_hash': 178, 'subgroup_order': 96, 'subgroup_tex': '\\OD_{16}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 96, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.74', 'subgroup_hash': 74, 'subgroup_order': 96, 'subgroup_tex': 'C_8.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 67648225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 96, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.74', 'subgroup_hash': 74, 'subgroup_order': 96, 'subgroup_tex': 'C_8.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 67648226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 96, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.6.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.74', 'subgroup_hash': 74, 'subgroup_order': 96, 'subgroup_tex': 'C_8.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 67648227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.182', 'subgroup_hash': 182, 'subgroup_order': 96, 'subgroup_tex': 'D_8:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.183', 'subgroup_hash': 183, 'subgroup_order': 96, 'subgroup_tex': 'D_8:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.6.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.183', 'subgroup_hash': 183, 'subgroup_order': 96, 'subgroup_tex': 'D_8:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.179', 'subgroup_hash': 179, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': True, 'core_order': 72, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 67648233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.38', 'subgroup_hash': 38, 'subgroup_order': 72, 'subgroup_tex': 'Q_8\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 67648234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.38', 'subgroup_hash': 38, 'subgroup_order': 72, 'subgroup_tex': 'Q_8\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 67648235
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.14', 'subgroup_hash': 14, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 67648236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 64, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 2, 'label': '576.7437.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 67648237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67648239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67648240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.12.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67648241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': True, 'centralizer_order': 72, 'characteristic': True, 'core_order': 48, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.27', 'subgroup_hash': 27, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648247
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 67648248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.24', 'subgroup_hash': 24, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67648257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67648258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67648259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.k1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67648260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.k1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67648261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.k1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67648262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.m1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.27', 'subgroup_hash': 27, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.27', 'subgroup_hash': 27, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.12.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.27', 'subgroup_hash': 27, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 32, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67648273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 32, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67648274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 32, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648282
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 24, 'counter': 75, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.7437.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 67648283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 24, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 67648285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 67648286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': True, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.24.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 67648288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648290
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648292
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648294
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648295
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648301
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 92, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 67648302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.m1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.24.m1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648308
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 99, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 67648131
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.24.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 67648132
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.24.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 67648133
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 16, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': True, 'centralizer_order': 72, 'characteristic': True, 'core_order': 16, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648140
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67648147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.36.k1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648153
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 12, 'counter': 120, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.7437.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.49', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': ['U1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648154
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648155
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648156
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648157
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648158
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648159
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 126, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648160
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648161
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648162
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648164
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648165
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 131, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648166
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 132, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648167
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 133, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648168
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.g1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648169
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.48.g1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67648170
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648171
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.48.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648172
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '576.7437.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 67648173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 139, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.47', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 140, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.72.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.47', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648176
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 8, 'counter': 141, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.7437.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.47', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 8, 'counter': 142, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '576.7437.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times C_3^2', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67648181
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67648182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648184
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648186
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.72.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648191
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67648192
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 6, 'counter': 156, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.7437.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.197', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 197, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_4\\times A_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648193
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648194
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.96.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648195
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.96.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648197
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648198
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 161, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648199
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 162, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.96.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67648200
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 4, 'counter': 163, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.7437.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.193', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 193, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:C_6^2', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648201
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67648202
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67648203
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.144.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67648204
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648205
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 168, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.144.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648206
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 169, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67648208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67648209
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '576.7437.144.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67648210
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 3, 'counter': 172, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '576.7437.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1017', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1017, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'Q_{16}.A_4', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 67648211
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 67648212
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.192.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 67648213
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.192.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 67648214
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 2, 'counter': 176, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.7437.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.980', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 980, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3.C_6^2', 'simple': True, 'solvable': True, 'special_labels': ['D2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648215
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.288.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648216
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648217
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '576.7437.288.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67648219
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.7437', 'ambient_counter': 7437, 'ambient_order': 576, 'ambient_tex': 'C_3\\times Q_{16}.A_4', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 1, 'counter': 180, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '576.7437.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '576.7437', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7437, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times Q_{16}.A_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

  Column	Type
  ambient	text
  aut_centralizer_order	numeric
  aut_label	text
  aut_quo_index	numeric
  aut_stab_index	numeric
  aut_weyl_group	text
  aut_weyl_index	numeric
  centralizer	text
  complements	text[]
  conjugacy_class_count	numeric
  contained_in	text[]
  contains	text[]
  core	text
  coset_action_label	text
  count	numeric
  diagramx	smallint[]
  generators	numeric[]
  label	text
  mobius_quo	bigint
  mobius_sub	bigint
  normal_closure	text
  normal_contained_in	text[]
  normal_contains	text[]
  normalizer	text
  old_label	text
  projective_image	text
  quotient_action_image	text
  quotient_action_kernel	text
  quotient_action_kernel_order	numeric
  quotient_fusion	jsonb
  short_label	text
  subgroup_fusion	integer[]
  weyl_group	text

  
  
  • id: 67648215
    {'ambient': '576.7437', 'aut_centralizer_order': 768, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '144.b1.a1', '144.f1.a1', '144.f1.b1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1919, -1, 8513, -1, 8169, -1, 3585, -1], 'generators': [150], 'label': '576.7437.288.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '288.b1.a1', 'projective_image': '576.7437', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648129
    {'ambient': '576.7437', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.a1.a1', 'complements': ['576.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1', '4.c1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7942, 5902, 2210, 4664, 2445, 5274, 6574, 4187], 'generators': [3, 432, 6, 72, 192, 288, 444, 290], 'label': '576.7437.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.b1', '2.a1.a1', '2.b1.a1', '3.a1.a1', '3.b1.a1', '3.b1.c1', '3.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648130
    {'ambient': '576.7437', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.j1.a1', '12.k1.a1', '12.k1.b1', '12.k1.c1', '16.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3308, -1, 2280, -1, 2415, -1, 8718, -1], 'generators': [3, 288, 444, 290, 192, 6], 'label': '576.7437.4.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648131
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '8.c1.a1', '12.n1.b1'], 'contains': ['48.f1.b1', '72.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9811, -1, 2098, -1, 2297, -1, 5876, -1], 'generators': [72, 98, 144, 288], 'label': '576.7437.24.n1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.n1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648132
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.c1', '8.c1.a1', '12.n1.c1'], 'contains': ['48.f1.c1', '72.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9811, -1, 878, -1, 2297, -1, 6526, -1], 'generators': [72, 482, 144, 288], 'label': '576.7437.24.n1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.n1.c1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648133
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.a1.a1', '16.b1.a1', '16.b1.b1'], 'contains': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.b1.b1', '96.b1.c1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3610, -1, 638, -1, 1972, -1, 8637, -1], 'generators': [288, 290, 192], 'label': '576.7437.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.a1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648134
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '36.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.b1.b1', '12.b1.c1', '18.a1.a1', '18.a1.b1', '18.b1.a1'], 'contains': ['72.c1.a1', '72.f1.a1', '72.g1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4268, 3680, 5846, 5698, 6449, 4710, 6163, 4376], 'generators': [6, 444, 144], 'label': '576.7437.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1', '12.b1.c1', '12.b1.b1', '18.a1.b1', '18.a1.a1', '18.b1.a1'], 'normal_contains': ['72.c1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648135
    {'ambient': '576.7437', 'aut_centralizer_order': 144, 'aut_label': '36.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.43', 'aut_weyl_index': 144, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.n1.a1', '12.n1.b1', '12.n1.c1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.a1.b1', '72.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8422, 7459, 1993, 2707, 3027, 9190, 6018, 6291], 'generators': [3, 72], 'label': '576.7437.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['9.a1.a1', '12.c1.a1'], 'normal_contains': ['72.a1.b1', '72.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648136
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.a1.a1', '18.c1.a1', '18.d1.a1'], 'contains': ['72.a1.a1', '72.d1.a1', '72.f1.a1', '72.h1.a1', '72.i1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5451, -1, 5709, -1, 6197, -1, 2961, -1], 'generators': [3, 6, 144], 'label': '576.7437.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648137
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '18.a1.b1', '18.c1.a1', '18.d1.b1'], 'contains': ['72.a1.b1', '72.d1.b1', '72.f1.a1', '72.h1.b1', '72.i1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5451, -1, 6290, -1, 6197, -1, 3107, -1], 'generators': [507, 6, 144], 'label': '576.7437.36.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648138
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 144, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.a1.a1', '18.d1.b1', '18.e1.a1'], 'contains': ['72.e1.a1', '72.f1.a1', '72.i1.a1', '72.j1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3954, -1, 6977, -1, 7909, -1, 1581, -1], 'generators': [447, 6, 144], 'label': '576.7437.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648139
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 144, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '18.a1.b1', '18.d1.a1', '18.e1.a1'], 'contains': ['72.e1.b1', '72.f1.a1', '72.i1.b1', '72.j1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3954, -1, 7275, -1, 7909, -1, 2268, -1], 'generators': [87, 6, 144], 'label': '576.7437.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.d1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648140
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.b1.a1', '18.c1.a1', '18.e1.a1'], 'contains': ['72.b1.a1', '72.f1.a1', '72.k1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7498, -1, 3493, -1, 4392, -1, 1799, -1], 'generators': [6, 72], 'label': '576.7437.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648141
    {'ambient': '576.7437', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.a1.a1', '12.j1.b1', '12.k1.d1', '12.k1.e1', '12.k1.f1', '16.b1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3308, -1, 3523, -1, 2415, -1, 9413, -1], 'generators': [507, 288, 444, 290, 192, 6], 'label': '576.7437.4.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.b1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648142
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.b1.a1', '18.d1.a1', '18.d1.b1'], 'contains': ['72.f1.a1', '72.k1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6960, -1, 4525, -1, 5557, -1, 525, -1], 'generators': [366, 444], 'label': '576.7437.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67648143
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.a1.a1'], 'contains': ['72.d1.a1', '72.e1.a1', '72.g1.a1', '72.h1.a1', '72.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2265, -1, 7888, -1, 9408, -1, 3867, -1], 'generators': [3, 150, 444], 'label': '576.7437.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67648144
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '18.a1.b1'], 'contains': ['72.d1.b1', '72.e1.b1', '72.g1.a1', '72.h1.b1', '72.j1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2265, -1, 8555, -1, 9408, -1, 5437, -1], 'generators': [507, 150, 444], 'label': '576.7437.36.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '36.g1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67648145
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.c1.a1', '18.d1.b1'], 'contains': ['72.a1.b1', '72.i1.a1', '72.k1.a1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6114, -1, 4126, -1, 4712, -1, 683, -1], 'generators': [507, 366], 'label': '576.7437.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648146
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '18.c1.a1', '18.d1.a1'], 'contains': ['72.a1.a1', '72.i1.b1', '72.k1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6114, -1, 3990, -1, 4712, -1, 1059, -1], 'generators': [3, 366], 'label': '576.7437.36.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.h1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648147
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.k1.a1', '12.k1.b1', '12.k1.c1', '18.a1.a1'], 'contains': ['72.c1.a1', '72.h1.a1', '72.j1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3537, -1, 5145, -1, 7595, -1, 7788, -1], 'generators': [3, 6, 444], 'label': '576.7437.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648148
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '12.k1.d1', '12.k1.e1', '12.k1.f1', '18.a1.b1'], 'contains': ['72.c1.a1', '72.h1.b1', '72.j1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3537, -1, 6058, -1, 7595, -1, 7935, -1], 'generators': [507, 6, 444], 'label': '576.7437.36.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '36.i1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648149
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.43', 'aut_weyl_index': 144, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '18.c1.a1', '18.e1.a1'], 'contains': ['72.b1.a1', '72.i1.a1', '72.i1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6726, -1, 4244, -1, 3867, -1, 1414, -1], 'generators': [9, 72], 'label': '576.7437.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.j1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648150
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.43', 'aut_weyl_index': 144, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.d1.a1', '18.d1.b1', '18.e1.a1'], 'contains': ['72.i1.a1', '72.i1.b1', '72.k1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5882, -1, 5261, -1, 5322, -1, 133, -1], 'generators': [87, 366], 'label': '576.7437.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.k1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648151
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.43', 'aut_weyl_index': 144, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a2', '18.d1.a1', '18.d1.b1', '18.e1.a1'], 'contains': ['72.i1.a1', '72.i1.b1', '72.k1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5882, -1, 4970, -1, 5322, -1, 388, -1], 'generators': [447, 366], 'label': '576.7437.36.k1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.k1.a2', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a2', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648152
    {'ambient': '576.7437', 'aut_centralizer_order': 3, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.19764', 'aut_weyl_index': 12, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.b1.a1', '8.b1.b1', '8.c1.a1', '12.c1.a1', '12.n1.a1', '12.n1.b1', '12.n1.c1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8675, -1, 1136, -1, 1078, -1, 6461, -1], 'generators': [3, 288, 432, 72, 290, 192], 'label': '576.7437.4.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '4.c1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648153
    {'ambient': '576.7437', 'aut_centralizer_order': 1152, 'aut_label': '48.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.a1.b1', '24.b1.a1', '24.g1.a1', '24.j1.a1', '24.j1.b1', '24.l1.a1'], 'contains': ['96.a1.a1', '144.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4756, 4412, 6749, 1773, 4493, 5489, 3356, 7044], 'generators': [144, 192, 288], 'label': '576.7437.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.b1', '24.a1.a1', '24.b1.a1'], 'normal_contains': ['96.a1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '96.197', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.13', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648154
    {'ambient': '576.7437', 'aut_centralizer_order': 384, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.e1.b1', '24.f1.a1', '24.f1.b1', '24.g1.a1', '24.h1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '144.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1096, -1, 9205, -1, 8429, -1, 3534, -1], 'generators': [150, 288, 192], 'label': '576.7437.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648155
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.f1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '144.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [724, -1, 8911, -1, 7466, -1, 3177, -1], 'generators': [9, 288, 192], 'label': '576.7437.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648156
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.f1.b1', '24.i1.b1', '24.j1.b1', '24.k1.b1'], 'contains': ['96.a1.a1', '96.d1.b1', '144.c1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [724, -1, 9394, -1, 7466, -1, 3996, -1], 'generators': [225, 288, 192], 'label': '576.7437.48.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '48.c1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648157
    {'ambient': '576.7437', 'aut_centralizer_order': 288, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.e1.a1', '24.i1.a1'], 'contains': ['96.a1.a1', '144.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2884, -1, 6627, -1, 5431, -1, 4736, -1], 'generators': [3, 192, 288], 'label': '576.7437.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648158
    {'ambient': '576.7437', 'aut_centralizer_order': 288, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.a1.b1', '24.e1.b1', '24.i1.b1'], 'contains': ['96.a1.a1', '144.d1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2884, -1, 7573, -1, 5431, -1, 5691, -1], 'generators': [507, 192, 288], 'label': '576.7437.48.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '48.d1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648159
    {'ambient': '576.7437', 'aut_centralizer_order': 384, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.i1.b1', '24.k1.a1', '24.k1.b1'], 'contains': ['96.a1.a1', '144.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1505, -1, 8152, -1, 6788, -1, 4876, -1], 'generators': [6, 192, 288], 'label': '576.7437.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648160
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '16.a1.a1', '24.m1.a1', '24.m1.b1', '24.n1.a1'], 'contains': ['96.b1.a1', '144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8899, -1, 1557, -1, 2314, -1, 7582, -1], 'generators': [144, 290, 288], 'label': '576.7437.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '48.f1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648161
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '16.a1.a1', '24.m1.c1', '24.m1.d1', '24.n1.b1'], 'contains': ['96.b1.b1', '144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8899, -1, 2559, -1, 2314, -1, 6987, -1], 'generators': [144, 98, 288], 'label': '576.7437.48.f1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '48.f1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648162
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.c1', '16.a1.a1', '24.m1.e1', '24.m1.f1', '24.n1.c1'], 'contains': ['96.b1.c1', '144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8899, -1, 1219, -1, 2314, -1, 7442, -1], 'generators': [144, 482, 288], 'label': '576.7437.48.f1.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '48.f1.c1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648163
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '12.h1.a1', '12.j1.a1', '18.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2277, 8181, 7633, 446, 7901, 4269, 4199, 8111], 'generators': [3, 288, 192, 6, 444, 144], 'label': '576.7437.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '18.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648164
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '16.b1.a1', '24.m1.a1'], 'contains': ['96.b1.a1', '144.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7491, -1, 779, -1, 2571, -1, 8118, -1], 'generators': [3, 290, 288], 'label': '576.7437.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.g1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648165
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.d1', '16.b1.b1', '24.m1.b1'], 'contains': ['96.b1.a1', '144.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7491, -1, 2787, -1, 2571, -1, 8815, -1], 'generators': [507, 290, 288], 'label': '576.7437.48.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.b1', 'old_label': '48.g1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648166
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.b1', '16.b1.a1', '24.m1.c1'], 'contains': ['96.b1.b1', '144.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7491, -1, 1926, -1, 2571, -1, 7837, -1], 'generators': [3, 98, 288], 'label': '576.7437.48.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.g1.c1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648167
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.e1', '16.b1.b1', '24.m1.d1'], 'contains': ['96.b1.b1', '144.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7491, -1, 3026, -1, 2571, -1, 8258, -1], 'generators': [507, 98, 288], 'label': '576.7437.48.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.b1', 'old_label': '48.g1.d1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648168
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.c1', '16.b1.a1', '24.m1.e1'], 'contains': ['96.b1.c1', '144.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7491, -1, 218, -1, 2571, -1, 7978, -1], 'generators': [3, 482, 288], 'label': '576.7437.48.g1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.g1.e1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648169
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.f1', '16.b1.b1', '24.m1.f1'], 'contains': ['96.b1.c1', '144.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7491, -1, 2332, -1, 2571, -1, 8459, -1], 'generators': [507, 482, 288], 'label': '576.7437.48.g1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.b1', 'old_label': '48.g1.f1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648170
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1'], 'contains': ['96.c1.a1', '96.d1.a1', '144.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [250, -1, 9636, -1, 9025, -1, 2100, -1], 'generators': [447, 150, 192], 'label': '576.7437.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.a1', 'old_label': '48.h1.a1', 'projective_image': '192.1017', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648171
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1'], 'contains': ['96.c1.a1', '96.d1.b1', '144.f1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [250, -1, 9825, -1, 9025, -1, 2317, -1], 'generators': [87, 150, 192], 'label': '576.7437.48.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.b1', 'old_label': '48.h1.b1', 'projective_image': '192.1017', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648172
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1'], 'contains': ['192.a1.a1', '192.b1.a1', '192.b1.b1', '192.b1.c1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3084, -1, 798, -1, 2448, -1, 8075, -1], 'generators': [290, 192], 'label': '576.7437.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '64.a1.a1', 'projective_image': '192.1017', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648173
    {'ambient': '576.7437', 'aut_centralizer_order': 288, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.m1.a1', '24.m1.c1', '24.m1.e1', '36.b1.a1', '36.c1.a1', '36.h1.b1'], 'contains': ['144.a1.a1', '144.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5760, 6958, 1844, 2770, 4274, 6432, 5449, 6006], 'generators': [3, 144], 'label': '576.7437.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['18.a1.a1', '24.a1.a1', '36.b1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648174
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.b1', '12.e1.b1', '12.h1.b1', '12.j1.b1', '18.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2277, 8181, 8004, 1432, 7901, 4269, 4597, 7061], 'generators': [507, 288, 192, 6, 444, 144], 'label': '576.7437.6.a1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.b1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '18.a1.b1', '24.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648175
    {'ambient': '576.7437', 'aut_centralizer_order': 288, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.m1.b1', '24.m1.d1', '24.m1.f1', '36.b1.a1', '36.c1.b1', '36.h1.a1'], 'contains': ['144.a1.a1', '144.d1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5760, 6958, 2799, 2392, 4274, 6432, 5564, 5604], 'generators': [507, 144], 'label': '576.7437.72.a1.b1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '72.a1.b1', 'normal_contained_in': ['18.a1.b1', '24.a1.b1', '36.b1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648176
    {'ambient': '576.7437', 'aut_centralizer_order': 1152, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.n1.a1', '24.n1.b1', '24.n1.c1', '36.b1.a1', '36.e1.a1', '36.j1.a1'], 'contains': ['144.a1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8141, 5310, 2536, 3311, 3569, 7888, 4391, 6408], 'generators': [72], 'label': '576.7437.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['18.b1.a1', '24.b1.a1', '36.b1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648216
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '144.c1.a1', '144.f1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1679, -1, 7986, -1, 7679, -1, 3324, -1], 'generators': [9], 'label': '576.7437.288.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '288.c1.a1', 'projective_image': '576.7437', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648177
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '72.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.d1.b1', '24.d1.c1', '36.a1.a1', '36.i1.a1', '36.i1.b1'], 'contains': ['144.e1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3553, 2467, 5145, 6280, 6175, 3695, 7710, 4119], 'generators': [6, 444], 'label': '576.7437.72.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.c1.a1', 'normal_contained_in': ['24.c1.a1', '24.d1.a1', '24.d1.c1', '24.d1.b1', '36.a1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 67648178
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.c1.a1', '36.g1.a1'], 'contains': ['144.b1.a1', '144.c1.a1', '144.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2660, -1, 7686, -1, 7947, -1, 3831, -1], 'generators': [3, 150], 'label': '576.7437.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648179
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '36.c1.b1', '36.g1.b1'], 'contains': ['144.b1.a1', '144.c1.b1', '144.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2660, -1, 8111, -1, 7947, -1, 4277, -1], 'generators': [507, 150], 'label': '576.7437.72.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '72.d1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648180
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.d1.a1', '36.g1.a1'], 'contains': ['144.b1.a1', '144.c1.a1', '144.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1840, -1, 8376, -1, 8727, -1, 2787, -1], 'generators': [447, 150, 288], 'label': '576.7437.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648181
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '36.d1.b1', '36.g1.b1'], 'contains': ['144.b1.a1', '144.c1.b1', '144.f1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1840, -1, 9167, -1, 8727, -1, 3708, -1], 'generators': [87, 150, 288], 'label': '576.7437.72.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '72.e1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648182
    {'ambient': '576.7437', 'aut_centralizer_order': 384, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.a1.a1', '36.c1.a1', '36.c1.b1', '36.d1.a1', '36.d1.b1', '36.e1.a1', '36.f1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5111, -1, 6541, -1, 6460, -1, 2961, -1], 'generators': [6, 144], 'label': '576.7437.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648183
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '12.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.a1.a1', '36.g1.a1', '36.g1.b1'], 'contains': ['144.b1.a1', '144.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2857, -1, 7910, -1, 8144, -1, 5003, -1], 'generators': [150, 444], 'label': '576.7437.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648184
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.c1.a1', '36.g1.a1', '36.i1.a1'], 'contains': ['144.c1.a1', '144.d1.a1', '144.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3836, -1, 6353, -1, 7094, -1, 4557, -1], 'generators': [3, 6], 'label': '576.7437.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648185
    {'ambient': '576.7437', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': ['96.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.k1.a1', '18.a1.a1', '24.m1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8389, 6180, 2037, 4381, 3118, 2834, 7860, 3595], 'generators': [3, 288, 444, 144, 290, 6], 'label': '576.7437.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1', '3.b1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648186
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '36.c1.b1', '36.g1.b1', '36.i1.b1'], 'contains': ['144.c1.b1', '144.d1.b1', '144.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3836, -1, 7389, -1, 7094, -1, 5283, -1], 'generators': [507, 6], 'label': '576.7437.72.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '72.h1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648187
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '36.c1.a1', '36.d1.a1', '36.h1.a1', '36.j1.a1', '36.k1.a1', '36.k1.a2'], 'contains': ['144.a1.a1', '144.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4827, -1, 5471, -1, 5650, -1, 2483, -1], 'generators': [9, 144], 'label': '576.7437.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648188
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '36.c1.b1', '36.d1.b1', '36.h1.b1', '36.j1.a1', '36.k1.a1', '36.k1.a2'], 'contains': ['144.a1.a1', '144.c1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4827, -1, 5577, -1, 5650, -1, 2598, -1], 'generators': [225, 144], 'label': '576.7437.72.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.i1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648189
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.d1.a1', '36.g1.a1', '36.i1.a1'], 'contains': ['144.c1.a1', '144.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2257, -1, 7533, -1, 7751, -1, 4162, -1], 'generators': [447, 6], 'label': '576.7437.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.j1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648190
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '36.d1.b1', '36.g1.b1', '36.i1.b1'], 'contains': ['144.c1.b1', '144.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2257, -1, 8010, -1, 7751, -1, 5118, -1], 'generators': [87, 6], 'label': '576.7437.72.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '72.j1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648191
    {'ambient': '576.7437', 'aut_centralizer_order': 384, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.e1.a1', '36.f1.a1', '36.h1.a1', '36.h1.b1', '36.k1.a1', '36.k1.a2'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6591, -1, 4601, -1, 4712, -1, 605, -1], 'generators': [366], 'label': '576.7437.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.k1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648192
    {'ambient': '576.7437', 'aut_centralizer_order': 2304, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.c1.b1', '48.d1.a1', '48.d1.b1', '48.e1.a1'], 'contains': ['192.a1.a1', '288.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1578, 3134, 8575, 1815, 6788, 4680, 4680, 6207], 'generators': [288, 192], 'label': '576.7437.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.c1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '96.197', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.197', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648193
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '32.a1.a1', '48.f1.a1', '48.g1.a1', '48.g1.b1'], 'contains': ['192.b1.a1', '288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7217, -1, 1557, -1, 2658, -1, 8197, -1], 'generators': [288, 290], 'label': '576.7437.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '96.b1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648194
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '32.a1.a1', '48.f1.b1', '48.g1.c1', '48.g1.d1'], 'contains': ['192.b1.b1', '288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7217, -1, 2269, -1, 2658, -1, 7837, -1], 'generators': [288, 98], 'label': '576.7437.96.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '96.b1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648195
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.c1', '32.a1.a1', '48.f1.c1', '48.g1.e1', '48.g1.f1'], 'contains': ['192.b1.c1', '288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7217, -1, 1187, -1, 2658, -1, 7952, -1], 'generators': [288, 482], 'label': '576.7437.96.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '96.b1.c1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648196
    {'ambient': '576.7437', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': ['96.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.b1'], 'contains': ['12.b1.b1', '12.k1.b1', '18.a1.a1', '24.m1.c1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8389, 6180, 4009, 8531, 3118, 2834, 6977, 720], 'generators': [3, 288, 444, 144, 98, 6], 'label': '576.7437.6.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.b1', 'normal_contained_in': ['2.a1.a1', '3.b1.b1'], 'normal_contains': ['12.b1.b1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648197
    {'ambient': '576.7437', 'aut_centralizer_order': 384, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.h1.a1', '48.h1.b1'], 'contains': ['192.a1.a1', '288.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [697, -1, 9479, -1, 8390, -1, 3463, -1], 'generators': [150, 192], 'label': '576.7437.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '96.c1.a1', 'projective_image': '192.1017', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648198
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.h1.a1'], 'contains': ['192.a1.a1', '288.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [500, -1, 9379, -1, 8158, -1, 3251, -1], 'generators': [9, 192], 'label': '576.7437.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.d1.a1', 'projective_image': '192.1017', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648199
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.h1.b1'], 'contains': ['192.a1.a1', '288.c1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [500, -1, 9647, -1, 8158, -1, 3708, -1], 'generators': [225, 192], 'label': '576.7437.96.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.d1.b1', 'projective_image': '192.1017', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648200
    {'ambient': '576.7437', 'aut_centralizer_order': 2304, 'aut_label': '144.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.f1.a1', '48.f1.b1', '48.f1.c1', '72.a1.a1', '72.a1.b1', '72.b1.a1', '72.f1.a1', '72.i1.a1', '72.i1.b1', '72.k1.a1'], 'contains': ['288.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5552, 4412, 2693, 2655, 4603, 5489, 4452, 5805], 'generators': [144], 'label': '576.7437.144.a1.a1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['36.a1.a1', '48.a1.a1', '72.a1.b1', '72.a1.a1', '72.b1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.47', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648201
    {'ambient': '576.7437', 'aut_centralizer_order': 768, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.d1.a1', '72.d1.b1', '72.e1.a1', '72.e1.b1', '72.f1.a1', '72.g1.a1'], 'contains': ['288.a1.a1', '288.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2514, -1, 8052, -1, 7947, -1, 3961, -1], 'generators': [150, 288], 'label': '576.7437.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648202
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '72.d1.a1', '72.e1.a1', '72.h1.a1', '72.i1.a1', '72.j1.a1'], 'contains': ['288.a1.a1', '288.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2290, -1, 7560, -1, 7537, -1, 3831, -1], 'generators': [9, 288], 'label': '576.7437.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648203
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '72.d1.b1', '72.e1.b1', '72.h1.b1', '72.i1.b1', '72.j1.b1'], 'contains': ['288.a1.a1', '288.c1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2290, -1, 8165, -1, 7537, -1, 4219, -1], 'generators': [225, 288], 'label': '576.7437.144.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '144.c1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648204
    {'ambient': '576.7437', 'aut_centralizer_order': 576, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.g1.a1', '48.g1.c1', '48.g1.e1', '72.a1.a1', '72.d1.a1', '72.h1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3989, -1, 2374, -1, 5864, -1, 5220, -1], 'generators': [3], 'label': '576.7437.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '144.d1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648205
    {'ambient': '576.7437', 'aut_centralizer_order': 576, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '48.g1.b1', '48.g1.d1', '48.g1.f1', '72.a1.b1', '72.d1.b1', '72.h1.b1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3989, -1, 4061, -1, 5864, -1, 5628, -1], 'generators': [507], 'label': '576.7437.144.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '144.d1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648206
    {'ambient': '576.7437', 'aut_centralizer_order': 768, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '72.c1.a1', '72.f1.a1', '72.g1.a1', '72.h1.a1', '72.h1.b1', '72.j1.a1', '72.j1.b1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2877, -1, 7428, -1, 6985, -1, 4876, -1], 'generators': [6], 'label': '576.7437.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648207
    {'ambient': '576.7437', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': ['96.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.c1'], 'contains': ['12.b1.c1', '12.k1.c1', '18.a1.a1', '24.m1.e1'], 'core': '6.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8389, 6180, 1601, 2366, 3118, 2834, 7270, 5135], 'generators': [3, 288, 444, 144, 482, 6], 'label': '576.7437.6.b1.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.c1', 'normal_contained_in': ['2.a1.a1', '3.b1.c1'], 'normal_contains': ['12.b1.c1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.c1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.c1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648208
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '72.e1.a1'], 'contains': ['288.b1.a1', '288.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1940, -1, 8377, -1, 8664, -1, 2994, -1], 'generators': [447, 150], 'label': '576.7437.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.a1', 'old_label': '144.f1.a1', 'projective_image': '576.7437', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648209
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.b1', '72.e1.b1'], 'contains': ['288.b1.a1', '288.c1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1940, -1, 9193, -1, 8664, -1, 3585, -1], 'generators': [87, 150], 'label': '576.7437.144.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.b1', 'old_label': '144.f1.b1', 'projective_image': '576.7437', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648210
    {'ambient': '576.7437', 'aut_centralizer_order': 2304, 'aut_label': '192.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '1.a1.a1', 'complements': ['3.b1.a1', '3.b1.b1', '3.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.c1.a1', '96.d1.a1', '96.d1.b1'], 'contains': ['576.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1453, 3921, 8769, 1973, 7198, 4311, 3821, 6207], 'generators': [192], 'label': '576.7437.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['96.a1.a1'], 'normal_contains': ['576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '192.1017', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.1017', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648211
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.b1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5853, -1, 851, -1, 2658, -1, 8075, -1], 'generators': [290], 'label': '576.7437.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '192.b1.a1', 'projective_image': '576.7437', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648212
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.b1.b1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5853, -1, 2087, -1, 2658, -1, 7837, -1], 'generators': [98], 'label': '576.7437.192.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '192.b1.b1', 'projective_image': '576.7437', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648213
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.b1.c1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5853, -1, 745, -1, 2658, -1, 7952, -1], 'generators': [482], 'label': '576.7437.192.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '192.b1.c1', 'projective_image': '576.7437', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648214
    {'ambient': '576.7437', 'aut_centralizer_order': 4608, 'aut_label': '288.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '96.b1.b1', '96.b1.c1', '144.a1.a1', '144.b1.a1', '144.c1.a1', '144.c1.b1', '144.d1.a1', '144.d1.b1', '144.e1.a1'], 'contains': ['576.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2675, 3153, 5064, 2450, 6859, 5049, 4777, 5805], 'generators': [288], 'label': '576.7437.288.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['72.c1.a1', '96.a1.a1', '144.a1.a1'], 'normal_contains': ['576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '288.980', 'quotient_action_image': '1.1', 'quotient_action_kernel': '288.980', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648217
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.b1', '144.c1.b1', '144.f1.b1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1679, -1, 8989, -1, 7679, -1, 4162, -1], 'generators': [225], 'label': '576.7437.288.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '288.c1.b1', 'projective_image': '576.7437', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648218
    {'ambient': '576.7437', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': ['96.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.k1.d1', '18.a1.b1', '24.m1.b1'], 'core': '6.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8389, 6180, 3224, 6028, 3118, 2834, 8218, 3081], 'generators': [507, 288, 444, 144, 290, 6], 'label': '576.7437.6.b1.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.d1', 'normal_contained_in': ['2.a1.b1', '3.b1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.d1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.d1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648219
    {'ambient': '576.7437', 'aut_centralizer_order': None, 'aut_label': '576.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.b1.b1', '192.b1.c1', '288.a1.a1', '288.b1.a1', '288.c1.a1', '288.c1.b1'], 'contains': [], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1919, 3402, 5116, 2272, 7198, 4680, 4618, 6006], 'generators': [], 'label': '576.7437.576.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['192.a1.a1', '288.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '576.7437', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67648220
    {'ambient': '576.7437', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': ['96.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.b1.b1'], 'contains': ['12.b1.b1', '12.k1.e1', '18.a1.b1', '24.m1.d1'], 'core': '6.b1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [8389, 6180, 4279, 9014, 3118, 2834, 7124, 207], 'generators': [507, 288, 444, 144, 98, 6], 'label': '576.7437.6.b1.e1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.e1', 'normal_contained_in': ['2.a1.b1', '3.b1.b1'], 'normal_contains': ['12.b1.b1', '18.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.e1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.e1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648221
    {'ambient': '576.7437', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1152.157559', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['288.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '8.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4150, 6375, 2280, 3704, 2445, 2834, 7337, 3254], 'generators': [3, 444, 162, 144, 288, 290, 192], 'label': '576.7437.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.b1.c1', '6.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '96.197', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648222
    {'ambient': '576.7437', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': ['96.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.b1.c1'], 'contains': ['12.b1.c1', '12.k1.f1', '18.a1.b1', '24.m1.f1'], 'core': '6.b1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [8389, 6180, 1782, 5063, 3118, 2834, 8067, 4108], 'generators': [507, 288, 444, 144, 482, 6], 'label': '576.7437.6.b1.f1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.f1', 'normal_contained_in': ['2.a1.b1', '3.b1.c1'], 'normal_contains': ['12.b1.c1', '18.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.f1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.f1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648223
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 24, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.a1', '12.g1.a1', '18.b1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7710, 4579, 5258, 3274, 5426, 7468, 3614, 9344], 'generators': [6, 288, 144, 444, 72, 192], 'label': '576.7437.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '18.b1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648224
    {'ambient': '576.7437', 'aut_centralizer_order': 16, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '18.b1.a1', '24.n1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9606, 2986, 1910, 7109, 2866, 5705, 6741, 4622], 'generators': [72, 288, 444, 290, 144, 162], 'label': '576.7437.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.b1.a1', '3.b1.a1'], 'normal_contains': ['12.b1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648225
    {'ambient': '576.7437', 'aut_centralizer_order': 16, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.b1'], 'contains': ['12.b1.b1', '18.b1.a1', '24.n1.b1'], 'core': '6.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9606, 2986, 3716, 9554, 2866, 5705, 6035, 1234], 'generators': [72, 288, 444, 98, 144, 162], 'label': '576.7437.6.d1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.b1', 'normal_contained_in': ['2.b1.a1', '3.b1.b1'], 'normal_contains': ['12.b1.b1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648226
    {'ambient': '576.7437', 'aut_centralizer_order': 16, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.c1'], 'contains': ['12.b1.c1', '18.b1.a1', '24.n1.c1'], 'core': '6.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9606, 2986, 1368, 5546, 2866, 5705, 6180, 5649], 'generators': [72, 288, 444, 482, 144, 162], 'label': '576.7437.6.d1.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.c1', 'normal_contained_in': ['2.b1.a1', '3.b1.c1'], 'normal_contains': ['12.b1.c1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.c1', 'projective_image': '288.980', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1.c1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648227
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2310', 'aut_weyl_index': 36, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.c1.a1', '12.d1.a1', '12.d1.b1', '12.f1.a1', '12.i1.a1', '12.i1.b1', '12.l1.a1', '18.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7137, -1, 5618, -1, 4231, -1, 2830, -1], 'generators': [3, 288, 432, 6, 72, 192], 'label': '576.7437.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648228
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.e1.b1', '12.g1.a1', '12.i1.b1', '12.m1.a1', '12.m1.a2', '18.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5096, -1, 6272, -1, 6375, -1, 1527, -1], 'generators': [3, 288, 432, 366, 444, 192], 'label': '576.7437.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67648229
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 36, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.b1', '12.e1.a1', '12.g1.a1', '12.i1.a1', '12.m1.a1', '12.m1.a2', '18.d1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5096, -1, 6661, -1, 6375, -1, 1090, -1], 'generators': [507, 288, 432, 366, 444, 192], 'label': '576.7437.6.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67648230
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.56076', 'aut_weyl_index': 18, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.a1', '12.e1.b1', '12.f1.a1', '12.l1.a1', '12.m1.a1', '12.m1.a2', '18.e1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6289, -1, 5924, -1, 4893, -1, 2277, -1], 'generators': [447, 288, 432, 6, 72, 192], 'label': '576.7437.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648231
    {'ambient': '576.7437', 'aut_centralizer_order': 32, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.d1.b1', '24.d1.c1', '32.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3029, 884, 2568, 8164, 1800, 1133, 9413, 2300], 'generators': [290, 288, 192, 6, 444], 'label': '576.7437.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['24.c1.a1', '24.d1.a1', '24.d1.c1', '24.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 67648248
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.f1.b1'], 'contains': ['24.g1.a1', '24.l1.a1', '36.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6090, -1, 5846, -1, 6375, -1, 600, -1], 'generators': [366, 288, 444, 192, 432], 'label': '576.7437.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67648232
    {'ambient': '576.7437', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1152.157559', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['288.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '6.a1.b1', '6.b1.d1', '6.b1.e1', '6.b1.f1', '8.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4150, 6375, 3170, 5199, 2445, 2834, 7632, 2322], 'generators': [507, 444, 162, 144, 288, 290, 192], 'label': '576.7437.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.b1', '6.b1.d1', '6.b1.f1', '6.b1.e1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '96.197', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648233
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '24.a1.a1', '24.m1.a1', '24.m1.c1', '24.m1.e1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4339, -1, 474, -1, 191, -1, 7442, -1], 'generators': [3, 288, 144, 290, 192], 'label': '576.7437.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.b1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648234
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '4.c1.a1'], 'contains': ['16.a1.a1', '16.b1.b1', '24.a1.b1', '24.m1.b1', '24.m1.d1', '24.m1.f1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4339, -1, 2929, -1, 191, -1, 7754, -1], 'generators': [507, 288, 144, 290, 192], 'label': '576.7437.8.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.b1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648235
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '24.n1.a1', '24.n1.b1', '24.n1.c1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9153, -1, 1032, -1, 1184, -1, 5972, -1], 'generators': [72, 288, 290, 192, 144], 'label': '576.7437.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.c1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648236
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '768.1089306', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': ['64.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1'], 'contains': ['18.a1.a1', '18.a1.b1', '18.b1.a1', '18.c1.a1', '18.d1.a1', '18.d1.b1', '18.e1.a1'], 'core': '9.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6990, 6847, 4543, 3924, 5926, 9344, 3906, 6218], 'generators': [3, 6, 444, 72], 'label': '576.7437.9.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.a1.a1', 'normal_contained_in': ['3.a1.a1', '3.b1.a1', '3.b1.c1', '3.b1.b1'], 'normal_contains': ['18.a1.b1', '18.a1.a1', '18.b1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '288.980', 'quotient_action_image': '3.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648237
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '12.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.c1.a1'], 'contains': ['24.c1.a1', '24.g1.a1', '24.h1.a1', '36.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2295, 3680, 7680, 2592, 7674, 4259, 4696, 6860], 'generators': [6, 288, 444, 144, 192], 'label': '576.7437.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.b1', '6.a1.a1', '6.c1.a1'], 'normal_contains': ['24.c1.a1', '36.a1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648238
    {'ambient': '576.7437', 'aut_centralizer_order': 32, 'aut_label': '12.b1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.b1.d1', '6.d1.a1'], 'contains': ['24.d1.a1', '36.a1.a1', '48.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8975, 2366, 2518, 7135, 2352, 2804, 8223, 3210], 'generators': [144, 288, 290, 6, 444], 'label': '576.7437.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.d1', '6.b1.a1', '6.d1.a1'], 'normal_contains': ['24.d1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648239
    {'ambient': '576.7437', 'aut_centralizer_order': 32, 'aut_label': '12.b1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.b1', '6.b1.e1', '6.d1.b1'], 'contains': ['24.d1.b1', '36.a1.a1', '48.f1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8975, 2366, 3746, 9176, 2352, 2804, 7101, 1312], 'generators': [144, 288, 98, 6, 444], 'label': '576.7437.12.b1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.a1.a1', '6.b1.e1', '6.b1.b1', '6.d1.b1'], 'normal_contains': ['24.d1.b1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648240
    {'ambient': '576.7437', 'aut_centralizer_order': 32, 'aut_label': '12.b1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.c1', '6.b1.f1', '6.d1.c1'], 'contains': ['24.d1.c1', '36.a1.a1', '48.f1.c1'], 'core': '12.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8975, 2366, 1706, 6317, 2352, 2804, 7974, 3863], 'generators': [144, 288, 482, 6, 444], 'label': '576.7437.12.b1.c1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.c1', 'normal_contained_in': ['4.a1.a1', '6.b1.f1', '6.b1.c1', '6.d1.c1'], 'normal_contains': ['24.d1.c1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.c1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.c1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648241
    {'ambient': '576.7437', 'aut_centralizer_order': 72, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.254', 'aut_weyl_index': 72, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.a1.b1', '24.b1.a1', '36.b1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8384, 9116, 4420, 871, 3058, 9252, 4213, 8468], 'generators': [3, 288, 72, 192, 432], 'label': '576.7437.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['24.a1.b1', '24.a1.a1', '24.b1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648242
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.g1.a1', '24.i1.a1', '24.j1.a1', '36.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3646, -1, 7448, -1, 7217, -1, 3256, -1], 'generators': [3, 288, 6, 144, 192], 'label': '576.7437.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648243
    {'ambient': '576.7437', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '24.b1.a1', 'complements': ['288.c1.a1', '288.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.a1', '6.d1.a1', '6.d1.b1', '6.d1.c1', '8.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7942, 4032, 1997, 6254, 1988, 4546, 6158, 4187], 'generators': [72, 444, 6, 290, 288, 192, 144], 'label': '576.7437.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.c1.a1', '6.d1.a1', '6.d1.c1', '6.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '96.197', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648244
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.e1.a1', '6.f1.b1'], 'contains': ['24.a1.b1', '24.e1.b1', '24.g1.a1', '24.i1.b1', '24.j1.b1', '36.c1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3646, -1, 8385, -1, 7217, -1, 3522, -1], 'generators': [507, 288, 6, 144, 192], 'label': '576.7437.12.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648245
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 72, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.f1.b1', '6.g1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.j1.a1', '24.k1.a1', '36.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2710, -1, 8175, -1, 8855, -1, 2387, -1], 'generators': [447, 288, 6, 144, 192], 'label': '576.7437.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648246
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 72, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.f1.b1', '24.g1.a1', '24.j1.b1', '24.k1.b1', '36.d1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2710, -1, 8596, -1, 8855, -1, 3013, -1], 'generators': [87, 288, 6, 144, 192], 'label': '576.7437.12.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648247
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '24.l1.a1', '36.e1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7833, -1, 5175, -1, 3881, -1, 2626, -1], 'generators': [6, 288, 72, 192, 144], 'label': '576.7437.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648249
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.e1.a1', '24.f1.a1', '24.h1.a1', '24.i1.a1', '24.k1.a1', '36.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1128, -1, 8942, -1, 9230, -1, 3972, -1], 'generators': [3, 288, 150, 444, 192], 'label': '576.7437.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67648250
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1'], 'contains': ['24.e1.b1', '24.f1.b1', '24.h1.a1', '24.i1.b1', '24.k1.b1', '36.g1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1128, -1, 9258, -1, 9230, -1, 4453, -1], 'generators': [507, 288, 150, 444, 192], 'label': '576.7437.12.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '12.h1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67648251
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.b1'], 'contains': ['24.a1.b1', '24.j1.a1', '24.l1.a1', '36.h1.a1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5380, -1, 6514, -1, 4660, -1, 1313, -1], 'generators': [507, 288, 366, 192, 432], 'label': '576.7437.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648252
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.j1.b1', '24.l1.a1', '36.h1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5380, -1, 6207, -1, 4660, -1, 1666, -1], 'generators': [3, 288, 366, 192, 432], 'label': '576.7437.12.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648253
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '24.i1.a1', '24.k1.a1', '36.i1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1739, -1, 7216, -1, 8131, -1, 5382, -1], 'generators': [3, 288, 6, 444, 192], 'label': '576.7437.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648254
    {'ambient': '576.7437', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408639471', 'aut_weyl_index': 3, 'centralizer': '96.a1.a1', 'complements': ['192.b1.b1', '192.b1.a1', '192.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.a1.b1', '6.c1.a1', '6.e1.a1', '6.f1.a1', '6.f1.b1', '6.g1.a1', '9.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6859, 7828, 5924, 1826, 5426, 7591, 3614, 7586], 'generators': [3, 432, 192, 6, 288, 444, 72], 'label': '576.7437.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.b1', '6.a1.a1', '6.c1.a1', '9.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '96.197', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648255
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.b1'], 'contains': ['24.c1.a1', '24.i1.b1', '24.k1.b1', '36.i1.b1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1739, -1, 7963, -1, 8131, -1, 5648, -1], 'generators': [507, 288, 6, 444, 192], 'label': '576.7437.12.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '12.j1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648256
    {'ambient': '576.7437', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1'], 'contains': ['24.d1.a1', '36.i1.a1', '48.g1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7345, -1, 2086, -1, 2672, -1, 9153, -1], 'generators': [3, 288, 290, 162, 444], 'label': '576.7437.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.k1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648257
    {'ambient': '576.7437', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.b1'], 'contains': ['24.d1.b1', '36.i1.a1', '48.g1.c1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7345, -1, 3477, -1, 2672, -1, 8532, -1], 'generators': [3, 288, 98, 162, 444], 'label': '576.7437.12.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.k1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648258
    {'ambient': '576.7437', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.c1'], 'contains': ['24.d1.c1', '36.i1.a1', '48.g1.e1'], 'core': '24.d1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [7345, -1, 1923, -1, 2672, -1, 8718, -1], 'generators': [3, 288, 482, 162, 444], 'label': '576.7437.12.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.k1.c1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.c1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648259
    {'ambient': '576.7437', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.b1.d1'], 'contains': ['24.d1.a1', '36.i1.b1', '48.g1.b1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7345, -1, 3314, -1, 2672, -1, 9921, -1], 'generators': [507, 288, 290, 162, 444], 'label': '576.7437.12.k1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '12.k1.d1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.d1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648260
    {'ambient': '576.7437', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.b1.e1'], 'contains': ['24.d1.b1', '36.i1.b1', '48.g1.d1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7345, -1, 3908, -1, 2672, -1, 8967, -1], 'generators': [507, 288, 98, 162, 444], 'label': '576.7437.12.k1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '12.k1.e1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.e1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648261
    {'ambient': '576.7437', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.b1.f1'], 'contains': ['24.d1.c1', '36.i1.b1', '48.g1.f1'], 'core': '24.d1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [7345, -1, 2355, -1, 2672, -1, 9673, -1], 'generators': [507, 288, 482, 162, 444], 'label': '576.7437.12.k1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '12.k1.f1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.f1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648262
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.254', 'aut_weyl_index': 72, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.j1.a1', '24.j1.b1', '36.j1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6581, -1, 5490, -1, 3471, -1, 2169, -1], 'generators': [9, 288, 72, 192, 432], 'label': '576.7437.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.l1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648263
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.254', 'aut_weyl_index': 72, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.f1.b1', '6.g1.a1'], 'contains': ['24.j1.a1', '24.j1.b1', '24.l1.a1', '36.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4786, -1, 6763, -1, 5150, -1, 95, -1], 'generators': [87, 288, 366, 192, 144], 'label': '576.7437.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648264
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.254', 'aut_weyl_index': 72, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.f1.b1', '6.g1.a1'], 'contains': ['24.j1.a1', '24.j1.b1', '24.l1.a1', '36.k1.a2'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4786, -1, 6953, -1, 5150, -1, 313, -1], 'generators': [447, 288, 366, 192, 144], 'label': '576.7437.12.m1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a2', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a2', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648265
    {'ambient': '576.7437', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '768.1089306', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': ['192.a1.a1', '192.b1.c1', '192.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.b1.d1', '6.d1.a1', '9.a1.a1', '12.n1.a1'], 'core': '3.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8373, 5393, 1929, 4664, 2866, 6012, 6835, 4985], 'generators': [3, 444, 162, 72, 288, 290, 432], 'label': '576.7437.3.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.d1', '6.b1.a1', '6.d1.a1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.a1', 'projective_image': '288.980', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648266
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.254', 'aut_weyl_index': 72, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '4.c1.a1'], 'contains': ['24.m1.a1', '24.m1.b1', '24.n1.a1', '36.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9671, -1, 1178, -1, 736, -1, 6816, -1], 'generators': [3, 288, 72, 290, 432], 'label': '576.7437.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '12.n1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648267
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.254', 'aut_weyl_index': 72, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.b1', '4.c1.a1'], 'contains': ['24.m1.c1', '24.m1.d1', '24.n1.b1', '36.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9671, -1, 1511, -1, 736, -1, 6233, -1], 'generators': [3, 288, 72, 98, 432], 'label': '576.7437.12.n1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '12.n1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648268
    {'ambient': '576.7437', 'aut_centralizer_order': 6, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.254', 'aut_weyl_index': 72, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.c1', '4.c1.a1'], 'contains': ['24.m1.e1', '24.m1.f1', '24.n1.c1', '36.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9671, -1, 423, -1, 736, -1, 6494, -1], 'generators': [3, 288, 72, 482, 432], 'label': '576.7437.12.n1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '12.n1.c1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648269
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1'], 'contains': ['32.a1.a1', '48.a1.a1', '48.f1.a1', '48.f1.b1', '48.f1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4884, -1, 914, -1, 1026, -1, 7584, -1], 'generators': [144, 290, 192, 288], 'label': '576.7437.16.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.a1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648270
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '8.b1.a1'], 'contains': ['32.a1.a1', '48.d1.a1', '48.g1.a1', '48.g1.c1', '48.g1.e1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3814, -1, 101, -1, 1953, -1, 8976, -1], 'generators': [3, 290, 192, 288], 'label': '576.7437.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '16.b1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648271
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '16.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '8.b1.b1'], 'contains': ['32.a1.a1', '48.d1.b1', '48.g1.b1', '48.g1.d1', '48.g1.f1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3814, -1, 2860, -1, 1953, -1, 9556, -1], 'generators': [507, 290, 192, 288], 'label': '576.7437.16.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.b1', 'old_label': '16.b1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648272
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '18.a1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.c1.a1', '36.d1.a1', '36.g1.a1', '36.i1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3779, 6495, 6199, 3326, 8514, 5694, 4979, 5135], 'generators': [3, 6, 444, 144], 'label': '576.7437.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.a1', '6.b1.c1', '6.b1.b1', '9.a1.a1'], 'normal_contains': ['36.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648273
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '18.a1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.b1.d1', '6.b1.e1', '6.b1.f1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.c1.b1', '36.d1.b1', '36.g1.b1', '36.i1.b1'], 'core': '18.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3779, 6495, 6726, 4911, 8514, 5694, 5159, 4504], 'generators': [507, 6, 444, 144], 'label': '576.7437.18.a1.b1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.b1', 'normal_contained_in': ['6.a1.b1', '6.b1.d1', '6.b1.f1', '6.b1.e1', '9.a1.a1'], 'normal_contains': ['36.a1.a1', '72.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648274
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '18.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.d1.b1', '6.d1.c1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.e1.a1', '36.f1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8450, 5005, 3809, 5698, 5891, 7345, 3759, 5816], 'generators': [6, 444, 72], 'label': '576.7437.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.c1.a1', '6.d1.a1', '6.d1.c1', '6.d1.b1', '9.a1.a1'], 'normal_contains': ['36.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648275
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.254', 'aut_weyl_index': 72, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.c1.b1', '36.e1.a1', '36.h1.a1', '36.h1.b1', '36.j1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7522, -1, 3547, -1, 4231, -1, 2830, -1], 'generators': [3, 6, 72], 'label': '576.7437.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648276
    {'ambient': '576.7437', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '768.1089306', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': ['192.a1.a1', '192.b1.a1', '192.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.b1', '6.b1.e1', '6.d1.b1', '9.a1.a1', '12.n1.b1'], 'core': '3.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8373, 5393, 4009, 8122, 2866, 6012, 6386, 1234], 'generators': [3, 444, 162, 72, 288, 98, 432], 'label': '576.7437.3.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.e1', '6.b1.b1', '6.d1.b1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.b1', 'projective_image': '288.980', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.b1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648277
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.226', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.d1.b1', '36.f1.a1', '36.h1.b1', '36.k1.a1', '36.k1.a2'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5725, -1, 4829, -1, 6834, -1, 1047, -1], 'generators': [3, 366, 444], 'label': '576.7437.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67648278
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.226', 'aut_weyl_index': 72, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.b1', '9.a1.a1'], 'contains': ['36.c1.b1', '36.d1.a1', '36.f1.a1', '36.h1.a1', '36.k1.a1', '36.k1.a2'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5725, -1, 4985, -1, 6834, -1, 867, -1], 'generators': [507, 366, 444], 'label': '576.7437.18.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.d1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67648279
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2317', 'aut_weyl_index': 36, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.d1.b1', '36.e1.a1', '36.j1.a1', '36.k1.a1', '36.k1.a2'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6793, -1, 4655, -1, 5524, -1, 1951, -1], 'generators': [447, 6, 72], 'label': '576.7437.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67648280
    {'ambient': '576.7437', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.d1.a1', '12.i1.b1'], 'contains': ['48.a1.a1', '48.d1.a1', '72.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4704, 8300, 5795, 1406, 3580, 6668, 4086, 7904], 'generators': [3, 144, 192, 288], 'label': '576.7437.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -4, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648281
    {'ambient': '576.7437', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.c1.a1', '12.d1.b1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.d1.b1', '72.a1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4704, 8300, 7144, 687, 3580, 6668, 4782, 7139], 'generators': [507, 144, 192, 288], 'label': '576.7437.24.a1.b1', 'mobius_quo': 0, 'mobius_sub': -4, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['6.a1.b1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648282
    {'ambient': '576.7437', 'aut_centralizer_order': 576, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.c1.a1', '12.f1.a1', '12.l1.a1'], 'contains': ['48.a1.a1', '72.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8078, 5930, 3897, 1999, 3271, 8216, 3251, 8535], 'generators': [72, 192, 144, 288], 'label': '576.7437.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': -4, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['6.c1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '96.197', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67648283
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.j1.a1', '12.j1.b1'], 'contains': ['48.e1.a1', '72.c1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1818, 2411, 6636, 4087, 5883, 3531, 6346, 5018], 'generators': [6, 444, 192, 288], 'label': '576.7437.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['72.c1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 67648284
    {'ambient': '576.7437', 'aut_centralizer_order': 64, 'aut_label': '24.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.k1.a1', '12.k1.d1'], 'contains': ['72.c1.a1', '96.b1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7012, 1292, 2411, 7912, 2743, 2383, 9892, 3210], 'generators': [290, 162, 444, 288], 'label': '576.7437.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1'], 'normal_contains': ['72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 67648285
    {'ambient': '576.7437', 'aut_centralizer_order': 64, 'aut_label': '24.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.b1', '12.k1.b1', '12.k1.e1'], 'contains': ['72.c1.a1', '96.b1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7012, 1292, 3144, 9066, 2743, 2383, 9236, 2300], 'generators': [98, 162, 444, 288], 'label': '576.7437.24.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.d1.b1', 'normal_contained_in': ['8.a1.a1', '12.b1.b1'], 'normal_contains': ['72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 67648286
    {'ambient': '576.7437', 'aut_centralizer_order': 64, 'aut_label': '24.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.c1', '12.k1.c1', '12.k1.f1'], 'contains': ['72.c1.a1', '96.b1.c1'], 'core': '24.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7012, 1292, 1872, 7461, 2743, 2383, 9755, 3863], 'generators': [482, 162, 444, 288], 'label': '576.7437.24.d1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.d1.c1', 'normal_contained_in': ['8.a1.a1', '12.b1.c1'], 'normal_contains': ['72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.c1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 67648287
    {'ambient': '576.7437', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '768.1089306', 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': ['192.a1.a1', '192.b1.b1', '192.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.c1', '6.b1.f1', '6.d1.c1', '9.a1.a1', '12.n1.c1'], 'core': '3.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8373, 5393, 1601, 4040, 2866, 6012, 6638, 5649], 'generators': [3, 444, 162, 72, 288, 482, 432], 'label': '576.7437.3.b1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.f1', '6.b1.c1', '6.d1.c1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.c1', 'projective_image': '288.980', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.c1', 'subgroup_fusion': None, 'weyl_group': '96.197'}
  • id: 67648288
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.h1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.d1.a1', '72.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1444, -1, 9044, -1, 8658, -1, 3431, -1], 'generators': [3, 150, 192, 288], 'label': '576.7437.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648289
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.h1.b1'], 'contains': ['48.b1.a1', '48.c1.b1', '48.d1.b1', '72.d1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1444, -1, 9478, -1, 8658, -1, 4304, -1], 'generators': [507, 150, 192, 288], 'label': '576.7437.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.e1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648290
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.h1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.h1.a1', '72.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [189, -1, 9682, -1, 9810, -1, 2034, -1], 'generators': [447, 150, 288, 192], 'label': '576.7437.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648291
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '24.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.h1.b1'], 'contains': ['48.b1.a1', '48.c1.b1', '48.h1.b1', '72.e1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [189, -1, 9899, -1, 9810, -1, 2762, -1], 'generators': [87, 150, 288, 192], 'label': '576.7437.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.f1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648292
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1', '12.e1.b1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.e1.a1', '72.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2985, -1, 7930, -1, 6799, -1, 2507, -1], 'generators': [6, 144, 192, 288], 'label': '576.7437.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648293
    {'ambient': '576.7437', 'aut_centralizer_order': 96, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '12.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.h1.a1', '12.h1.b1'], 'contains': ['48.b1.a1', '48.e1.a1', '72.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [965, -1, 8853, -1, 9033, -1, 5000, -1], 'generators': [150, 444, 192, 288], 'label': '576.7437.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.h1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648294
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.h1.a1', '12.j1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '72.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2228, -1, 7704, -1, 7245, -1, 4543, -1], 'generators': [3, 6, 192, 288], 'label': '576.7437.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.i1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648295
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.h1.b1', '12.j1.b1'], 'contains': ['48.c1.b1', '48.d1.b1', '48.e1.a1', '72.h1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2228, -1, 8400, -1, 7245, -1, 5675, -1], 'generators': [507, 6, 192, 288], 'label': '576.7437.24.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.i1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648296
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.e1.a1', '12.i1.a1', '12.l1.a1', '12.m1.a1', '12.m1.a2'], 'contains': ['48.a1.a1', '48.c1.a1', '72.i1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4330, -1, 7389, -1, 5035, -1, 871, -1], 'generators': [9, 144, 192, 288], 'label': '576.7437.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.j1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648297
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '24.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.e1.b1', '12.i1.b1', '12.l1.a1', '12.m1.a1', '12.m1.a2'], 'contains': ['48.a1.a1', '48.c1.b1', '72.i1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4330, -1, 8138, -1, 5035, -1, 1247, -1], 'generators': [225, 144, 192, 288], 'label': '576.7437.24.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.j1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648298
    {'ambient': '576.7437', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.b1.b1', '12.b1.c1', '16.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3959, 2384, 2666, 6590, 1761, 1133, 7595, 2155], 'generators': [144, 288, 444, 290, 192, 162], 'label': '576.7437.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.b1', '2.a1.a1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.b1.c1', '12.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67648299
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.h1.a1', '12.j1.a1'], 'contains': ['48.c1.a1', '48.e1.a1', '72.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [591, -1, 8609, -1, 8284, -1, 3649, -1], 'generators': [447, 6, 192, 288], 'label': '576.7437.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.k1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648300
    {'ambient': '576.7437', 'aut_centralizer_order': 24, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.h1.b1', '12.j1.b1'], 'contains': ['48.c1.b1', '48.e1.a1', '72.j1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [591, -1, 9234, -1, 8284, -1, 5218, -1], 'generators': [87, 6, 192, 288], 'label': '576.7437.24.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.k1.b1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648301
    {'ambient': '576.7437', 'aut_centralizer_order': 192, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.g1.a1', '12.i1.a1', '12.i1.b1', '12.m1.a1', '12.m1.a2'], 'contains': ['48.a1.a1', '72.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6152, -1, 6005, -1, 4086, -1, 260, -1], 'generators': [366, 192, 432, 288], 'label': '576.7437.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.l1.a1', 'projective_image': '96.197', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67648302
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.b1.a1', '12.n1.a1'], 'contains': ['48.f1.a1', '48.g1.a1', '72.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8904, -1, 722, -1, 1542, -1, 8118, -1], 'generators': [3, 144, 290, 288], 'label': '576.7437.24.m1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.m1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648303
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.d1', '8.b1.b1', '12.n1.a1'], 'contains': ['48.f1.a1', '48.g1.b1', '72.a1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8904, -1, 2255, -1, 1542, -1, 8554, -1], 'generators': [507, 144, 290, 288], 'label': '576.7437.24.m1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.m1.b1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648304
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '8.b1.a1', '12.n1.b1'], 'contains': ['48.f1.b1', '48.g1.c1', '72.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8904, -1, 1664, -1, 1542, -1, 6846, -1], 'generators': [3, 144, 98, 288], 'label': '576.7437.24.m1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.m1.c1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648305
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.e1', '8.b1.b1', '12.n1.b1'], 'contains': ['48.f1.b1', '48.g1.d1', '72.a1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8904, -1, 2830, -1, 1542, -1, 7127, -1], 'generators': [507, 144, 98, 288], 'label': '576.7437.24.m1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.m1.d1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648306
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '8.b1.a1', '12.n1.c1'], 'contains': ['48.f1.c1', '48.g1.e1', '72.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8904, -1, 218, -1, 1542, -1, 7345, -1], 'generators': [3, 144, 482, 288], 'label': '576.7437.24.m1.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.m1.e1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.e1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648307
    {'ambient': '576.7437', 'aut_centralizer_order': 12, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.f1', '8.b1.b1', '12.n1.c1'], 'contains': ['48.f1.c1', '48.g1.f1', '72.a1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8904, -1, 1474, -1, 1542, -1, 8336, -1], 'generators': [507, 144, 482, 288], 'label': '576.7437.24.m1.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.m1.f1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.f1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67648308
    {'ambient': '576.7437', 'aut_centralizer_order': 48, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '8.c1.a1', '12.n1.a1'], 'contains': ['48.f1.a1', '72.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9811, -1, 1159, -1, 2297, -1, 6666, -1], 'generators': [72, 290, 144, 288], 'label': '576.7437.24.n1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.n1.a1', 'projective_image': '288.980', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}