Abstract group data - 194472.a

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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': '1.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 194472, 'aut_gen_orders': [72, 3], 'aut_gens': [[17116753, 383833], [1536306, 27530273], [2375584, 17643253]], 'aut_group': '388944.b', 'aut_hash': 5644525262314429270, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 388944, 'aut_permdeg': 2701, 'aut_perms': 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'aut_phi_ratio': 6.252314814814815, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 2701, 1, 1], [3, 5402, 1, 1], [4, 5402, 1, 1], [6, 5402, 1, 1], [9, 5402, 1, 3], [12, 5402, 1, 2], [18, 5402, 1, 3], [36, 5402, 1, 6], [37, 5256, 1, 18], [73, 2664, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PGL(2,73)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 194472, 'autcentquo_group': '388944.b', 'autcentquo_hash': 5644525262314429270, 'autcentquo_nilpotent': False, 'autcentquo_order': 388944, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,73)', 'cc_stats': [[1, 1, 1], [2, 2701, 1], [3, 5402, 1], [4, 5402, 1], [6, 5402, 1], [9, 5402, 3], [12, 5402, 2], [18, 5402, 3], [36, 5402, 6], [37, 5256, 18], [73, 2664, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '194472.a', 'commutator_count': 1, 'commutator_label': '194472.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['194472.a'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 2701, 1, 1], [3, 5402, 1, 1], [4, 5402, 1, 1], [6, 5402, 1, 1], [9, 5402, 3, 1], [12, 5402, 2, 1], [18, 5402, 3, 1], [36, 5402, 6, 1], [37, 5256, 18, 1], [73, 2664, 2, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 95856, 'exponent': 97236, 'exponents_of_order': [3, 2, 1, 1], 'factors_of_aut_order': [2, 3, 37, 73], 'factors_of_order': [2, 3, 37, 73], 'faithful_reps': [[37, 1, 2], [72, 1, 18], [73, 1, 1], [74, 1, 17]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '194472.a', 'hash': 1944427750340150412, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 97236, 'inner_gen_orders': [36, 3], 'inner_gens': [[17116753, 258638], [2152960, 383833]], 'inner_hash': 1944427750340150412, 'inner_nilpotent': False, 'inner_order': 194472, 'inner_split': True, 'inner_tex': '\\PSL(2,73)', 'inner_used': [1, 2], 'irrC_degree': 37, 'irrQ_degree': 73, 'irrQ_dim': 73, 'irrR_degree': 37, 'irrep_stats': [[1, 1], [37, 2], [72, 18], [73, 1], [74, 17]], 'label': '194472.a', 'linC_count': 2, 'linC_degree': 37, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 73, 'linQ_degree_count': 1, 'linQ_dim': 73, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 37, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,73)', 'ngens': 2, '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, 0, 0, 0, 0, 0, 0, 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': 38, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 39, 'number_divisions': 11, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 31, 'number_subgroup_classes': 38, 'number_subgroups': 176087, 'old_label': None, 'order': 194472, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 2701], [3, 5402], [4, 5402], [6, 5402], [9, 16206], [12, 10804], [18, 16206], [36, 32412], [37, 94608], [73, 5328]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [23755913], 'outer_gens': [[23626852, 2967515]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': True, 'permutation_degree': 74, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [73, 1], [74, 4], [148, 1], [222, 2], [444, 1], [1296, 1]], 'representations': {'Lie': [{'d': 2, 'q': 73, 'gens': [17116753, 383833], 'family': 'PSL'}, {'d': 2, 'q': 73, 'family': 'PSU'}, {'d': 3, 'q': 73, 'family': 'Omega'}, {'d': 3, 'q': 73, 'family': 'POmega'}, {'d': 2, 'q': 73, 'family': 'PSigmaL'}], 'Perm': {'d': 74, 'gens': [54492480332728053232437233590503891449028638927178211031084260003437951253592668408173558618528182391540, 26860880276874675439388559521890328926502116302301465864345099068584590499116263762204247120085983871922903]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,73)', 'transitive_degree': 74, '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: 172804199
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 194472, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 389018, 'size': 1}
  • id: 172804210
    {'aut_label': '2A', 'centralizer': '2701.a1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 194472, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 2602590, 'size': 2701}
  • id: 172804221
    {'aut_label': '3A', 'centralizer': '5402.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 194472, 'label': '3A', 'order': 3, 'powers': [3, 1, 3, 3], 'representative': 10580156, 'size': 5402}
  • id: 172804232
    {'aut_label': '4A', 'centralizer': '5402.a1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 194472, 'label': '4A', 'order': 4, 'powers': [2, 4, 4, 4], 'representative': 3101074, 'size': 5402}
  • id: 172804233
    {'aut_label': '6A', 'centralizer': '5402.a1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 194472, 'label': '6A', 'order': 6, 'powers': [3, 2, 5, 5], 'representative': 9204891, 'size': 5402}
  • id: 172804234
    {'aut_label': '9A1', 'centralizer': '5402.a1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 194472, 'label': '9A1', 'order': 9, 'powers': [7, 3, 6, 6], 'representative': 11429323, 'size': 5402}
  • id: 172804235
    {'aut_label': '9A2', 'centralizer': '5402.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 194472, 'label': '9A2', 'order': 9, 'powers': [8, 3, 7, 7], 'representative': 14229256, 'size': 5402}
  • id: 172804236
    {'aut_label': '9A4', 'centralizer': '5402.a1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 194472, 'label': '9A4', 'order': 9, 'powers': [6, 3, 8, 8], 'representative': 26086070, 'size': 5402}
  • id: 172804237
    {'aut_label': '12A1', 'centralizer': '5402.a1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 194472, 'label': '12A1', 'order': 12, 'powers': [5, 4, 9, 9], 'representative': 20798624, 'size': 5402}
  • id: 172804200
    {'aut_label': '12A5', 'centralizer': '5402.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 194472, 'label': '12A5', 'order': 12, 'powers': [5, 4, 10, 10], 'representative': 7555614, 'size': 5402}
  • id: 172804201
    {'aut_label': '18A1', 'centralizer': '5402.a1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 194472, 'label': '18A1', 'order': 18, 'powers': [6, 5, 11, 11], 'representative': 26628428, 'size': 5402}
  • id: 172804202
    {'aut_label': '18A5', 'centralizer': '5402.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 194472, 'label': '18A5', 'order': 18, 'powers': [8, 5, 12, 12], 'representative': 10196604, 'size': 5402}
  • id: 172804203
    {'aut_label': '18A7', 'centralizer': '5402.a1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 194472, 'label': '18A7', 'order': 18, 'powers': [7, 5, 13, 13], 'representative': 12311569, 'size': 5402}
  • id: 172804204
    {'aut_label': '36A1', 'centralizer': '5402.a1.a1', 'counter': 14, 'group_counter': 1, 'group_order': 194472, 'label': '36A1', 'order': 36, 'powers': [11, 9, 14, 14], 'representative': 18869932, 'size': 5402}
  • id: 172804205
    {'aut_label': '36A5', 'centralizer': '5402.a1.a1', 'counter': 15, 'group_counter': 1, 'group_order': 194472, 'label': '36A5', 'order': 36, 'powers': [12, 10, 15, 15], 'representative': 8865140, 'size': 5402}
  • id: 172804206
    {'aut_label': '36A7', 'centralizer': '5402.a1.a1', 'counter': 16, 'group_counter': 1, 'group_order': 194472, 'label': '36A7', 'order': 36, 'powers': [13, 10, 16, 16], 'representative': 13566225, 'size': 5402}
  • id: 172804207
    {'aut_label': '36A11', 'centralizer': '5402.a1.a1', 'counter': 17, 'group_counter': 1, 'group_order': 194472, 'label': '36A11', 'order': 36, 'powers': [13, 9, 17, 17], 'representative': 3462689, 'size': 5402}
  • id: 172804208
    {'aut_label': '36A13', 'centralizer': '5402.a1.a1', 'counter': 18, 'group_counter': 1, 'group_order': 194472, 'label': '36A13', 'order': 36, 'powers': [12, 9, 18, 18], 'representative': 12689655, 'size': 5402}
  • id: 172804209
    {'aut_label': '36A17', 'centralizer': '5402.a1.a1', 'counter': 19, 'group_counter': 1, 'group_order': 194472, 'label': '36A17', 'order': 36, 'powers': [11, 10, 19, 19], 'representative': 361550, 'size': 5402}
  • id: 172804211
    {'aut_label': '37A1', 'centralizer': '5256.a1.a1', 'counter': 20, 'group_counter': 1, 'group_order': 194472, 'label': '37A1', 'order': 37, 'powers': [21, 22, 1, 20], 'representative': 1305353, 'size': 5256}
  • id: 172804212
    {'aut_label': '37A2', 'centralizer': '5256.a1.a1', 'counter': 21, 'group_counter': 1, 'group_order': 194472, 'label': '37A2', 'order': 37, 'powers': [23, 25, 1, 21], 'representative': 21681843, 'size': 5256}
  • id: 172804213
    {'aut_label': '37A3', 'centralizer': '5256.a1.a1', 'counter': 22, 'group_counter': 1, 'group_order': 194472, 'label': '37A3', 'order': 37, 'powers': [25, 28, 1, 22], 'representative': 10459441, 'size': 5256}
  • id: 172804214
    {'aut_label': '37A4', 'centralizer': '5256.a1.a1', 'counter': 23, 'group_counter': 1, 'group_order': 194472, 'label': '37A4', 'order': 37, 'powers': [27, 31, 1, 23], 'representative': 16328935, 'size': 5256}
  • id: 172804215
    {'aut_label': '37A5', 'centralizer': '5256.a1.a1', 'counter': 24, 'group_counter': 1, 'group_order': 194472, 'label': '37A5', 'order': 37, 'powers': [29, 34, 1, 24], 'representative': 5860166, 'size': 5256}
  • id: 172804216
    {'aut_label': '37A6', 'centralizer': '5256.a1.a1', 'counter': 25, 'group_counter': 1, 'group_order': 194472, 'label': '37A6', 'order': 37, 'powers': [31, 37, 1, 25], 'representative': 17383078, 'size': 5256}
  • id: 172804217
    {'aut_label': '37A7', 'centralizer': '5256.a1.a1', 'counter': 26, 'group_counter': 1, 'group_order': 194472, 'label': '37A7', 'order': 37, 'powers': [33, 35, 1, 26], 'representative': 24931795, 'size': 5256}
  • id: 172804218
    {'aut_label': '37A8', 'centralizer': '5256.a1.a1', 'counter': 27, 'group_counter': 1, 'group_order': 194472, 'label': '37A8', 'order': 37, 'powers': [35, 32, 1, 27], 'representative': 8642412, 'size': 5256}
  • id: 172804219
    {'aut_label': '37A9', 'centralizer': '5256.a1.a1', 'counter': 28, 'group_counter': 1, 'group_order': 194472, 'label': '37A9', 'order': 37, 'powers': [37, 29, 1, 28], 'representative': 26162879, 'size': 5256}
  • id: 172804220
    {'aut_label': '37A10', 'centralizer': '5256.a1.a1', 'counter': 29, 'group_counter': 1, 'group_order': 194472, 'label': '37A10', 'order': 37, 'powers': [36, 26, 1, 29], 'representative': 22100175, 'size': 5256}
  • id: 172804222
    {'aut_label': '37A11', 'centralizer': '5256.a1.a1', 'counter': 30, 'group_counter': 1, 'group_order': 194472, 'label': '37A11', 'order': 37, 'powers': [34, 23, 1, 30], 'representative': 2147419, 'size': 5256}
  • id: 172804223
    {'aut_label': '37A12', 'centralizer': '5256.a1.a1', 'counter': 31, 'group_counter': 1, 'group_order': 194472, 'label': '37A12', 'order': 37, 'powers': [32, 20, 1, 31], 'representative': 5441414, 'size': 5256}
  • id: 172804224
    {'aut_label': '37A13', 'centralizer': '5256.a1.a1', 'counter': 32, 'group_counter': 1, 'group_order': 194472, 'label': '37A13', 'order': 37, 'powers': [30, 21, 1, 32], 'representative': 11710093, 'size': 5256}
  • id: 172804225
    {'aut_label': '37A14', 'centralizer': '5256.a1.a1', 'counter': 33, 'group_counter': 1, 'group_order': 194472, 'label': '37A14', 'order': 37, 'powers': [28, 24, 1, 33], 'representative': 4629081, 'size': 5256}
  • id: 172804226
    {'aut_label': '37A15', 'centralizer': '5256.a1.a1', 'counter': 34, 'group_counter': 1, 'group_order': 194472, 'label': '37A15', 'order': 37, 'powers': [26, 27, 1, 34], 'representative': 25439053, 'size': 5256}
  • id: 172804227
    {'aut_label': '37A16', 'centralizer': '5256.a1.a1', 'counter': 35, 'group_counter': 1, 'group_order': 194472, 'label': '37A16', 'order': 37, 'powers': [24, 30, 1, 35], 'representative': 4126733, 'size': 5256}
  • id: 172804228
    {'aut_label': '37A17', 'centralizer': '5256.a1.a1', 'counter': 36, 'group_counter': 1, 'group_order': 194472, 'label': '37A17', 'order': 37, 'powers': [22, 33, 1, 36], 'representative': 212076, 'size': 5256}
  • id: 172804229
    {'aut_label': '37A18', 'centralizer': '5256.a1.a1', 'counter': 37, 'group_counter': 1, 'group_order': 194472, 'label': '37A18', 'order': 37, 'powers': [20, 36, 1, 37], 'representative': 4136480, 'size': 5256}
  • id: 172804230
    {'aut_label': '73A1', 'centralizer': '2664.a1.a1', 'counter': 38, 'group_counter': 1, 'group_order': 194472, 'label': '73A1', 'order': 73, 'powers': [38, 38, 38, 1], 'representative': 28013530, 'size': 2664}
  • id: 172804231
    {'aut_label': '73A1', 'centralizer': '2664.a1.a1', 'counter': 39, 'group_counter': 1, 'group_order': 194472, 'label': '73A5', 'order': 73, 'powers': [39, 39, 39, 1], 'representative': 28014479, 'size': 2664}
• 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: 17579764
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.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], 'schur_index': 1}
  • id: 17579769
    {'cdim': 73, 'counter': 4, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.73a', 'multiplicity': 1, 'nt': [74, 0], 'qdim': 73, 'qvalues': [73, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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], 'schur_index': 1}
  • id: 17579767
    {'cdim': 37, 'counter': 2, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.37a', 'multiplicity': 2, 'nt': [148, 0], 'qdim': 74, 'qvalues': [74, 2, 2, -2, 2, 2, 2, 2, -2, -2, 2, 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, 1, 1], 'schur_index': 1}
  • id: 17579770
    {'cdim': 74, 'counter': 5, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.74a', 'multiplicity': 1, 'nt': [222, 0], 'qdim': 74, 'qvalues': [74, 2, 2, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 17579771
    {'cdim': 74, 'counter': 6, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.74b', 'multiplicity': 1, 'nt': [296, 0], 'qdim': 74, 'qvalues': [74, -2, 2, 0, -2, 2, 2, 2, 0, 0, -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, 1, 1], 'schur_index': 1}
  • id: 17579772
    {'cdim': 74, 'counter': 7, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.74c', 'multiplicity': 1, 'nt': [444, 0], 'qdim': 74, 'qvalues': [74, 2, 2, -2, 2, -1, -1, -1, -2, -2, -1, -1, -1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 17579773
    {'cdim': 74, 'counter': 8, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.74d', 'multiplicity': 2, 'nt': [888, 0], 'qdim': 148, 'qvalues': [148, -4, 4, 0, -4, -2, -2, -2, 0, 0, 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, 2, 2], 'schur_index': 1}
  • id: 17579774
    {'cdim': 74, 'counter': 9, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.74e', 'multiplicity': 3, 'nt': [666, 0], 'qdim': 222, 'qvalues': [222, 6, -3, 6, -3, 0, 0, 0, -3, -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, 3, 3], 'schur_index': 1}
  • id: 17579765
    {'cdim': 74, 'counter': 10, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.74f', 'multiplicity': 3, 'nt': [1332, 0], 'qdim': 222, 'qvalues': [222, 6, -3, -6, -3, 0, 0, 0, 3, 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, 3, 3], 'schur_index': 1}
  • id: 17579766
    {'cdim': 74, 'counter': 11, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.74g', 'multiplicity': 6, 'nt': [2664, 0], 'qdim': 444, 'qvalues': [444, -12, -6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6], 'schur_index': 1}
  • id: 17579768
    {'cdim': 72, 'counter': 3, 'faithful': True, 'group': '194472.a', 'group_order': 194472, 'image': None, 'label': '194472.a.72a', 'multiplicity': 18, 'nt': [2628, 0], 'qdim': 1296, 'qvalues': [1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -18, -18], '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: 38346467
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 194472, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 194472, 'label': '194472.a.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]]]}
  • id: 38346478
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 2, 'cyclotomic_n': 73, 'dim': 37, 'faithful': True, 'field': [-18, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.37a1', 'nt': [148, 0], 'q_character': None, 'values': [[[37, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[1, 0], [1, 5], [1, 7], [1, 10], [1, 11], [1, 13], [1, 14], [1, 15], [1, 17], [1, 20], [1, 21], [1, 22], [1, 26], [1, 28], [1, 29], [1, 30], [1, 31], [1, 33], [1, 34], [1, -34], [1, -33], [1, -31], [1, -30], [1, -29], [1, -28], [1, -26], [1, -22], [1, -21], [1, -20], [1, -17], [1, -15], [1, -14], [1, -13], [1, -11], [1, -10], [1, -7], [1, -5]], [[-1, 5], [-1, 7], [-1, 10], [-1, 11], [-1, 13], [-1, 14], [-1, 15], [-1, 17], [-1, 20], [-1, 21], [-1, 22], [-1, 26], [-1, 28], [-1, 29], [-1, 30], [-1, 31], [-1, 33], [-1, 34], [-1, -34], [-1, -33], [-1, -31], [-1, -30], [-1, -29], [-1, -28], [-1, -26], [-1, -22], [-1, -21], [-1, -20], [-1, -17], [-1, -15], [-1, -14], [-1, -13], [-1, -11], [-1, -10], [-1, -7], [-1, -5]]]}
  • id: 38346489
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 3, 'cyclotomic_n': 73, 'dim': 37, 'faithful': True, 'field': [-18, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.37a2', 'nt': [148, 0], 'q_character': None, 'values': [[[37, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 5], [-1, 7], [-1, 10], [-1, 11], [-1, 13], [-1, 14], [-1, 15], [-1, 17], [-1, 20], [-1, 21], [-1, 22], [-1, 26], [-1, 28], [-1, 29], [-1, 30], [-1, 31], [-1, 33], [-1, 34], [-1, -34], [-1, -33], [-1, -31], [-1, -30], [-1, -29], [-1, -28], [-1, -26], [-1, -22], [-1, -21], [-1, -20], [-1, -17], [-1, -15], [-1, -14], [-1, -13], [-1, -11], [-1, -10], [-1, -7], [-1, -5]], [[1, 0], [1, 5], [1, 7], [1, 10], [1, 11], [1, 13], [1, 14], [1, 15], [1, 17], [1, 20], [1, 21], [1, 22], [1, 26], [1, 28], [1, 29], [1, 30], [1, 31], [1, 33], [1, 34], [1, -34], [1, -33], [1, -31], [1, -30], [1, -29], [1, -28], [1, -26], [1, -22], [1, -21], [1, -20], [1, -17], [1, -15], [1, -14], [1, -13], [1, -11], [1, -10], [1, -7], [1, -5]]]}
  • id: 38346500
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 4, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a1', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 6], [-1, -6]], [[-1, 7], [-1, -7]], [[-1, 8], [-1, -8]], [[-1, 9], [-1, -9]], [[-1, 10], [-1, -10]], [[-1, 11], [-1, -11]], [[-1, 12], [-1, -12]], [[-1, 13], [-1, -13]], [[-1, 14], [-1, -14]], [[-1, 15], [-1, -15]], [[-1, 16], [-1, -16]], [[-1, 17], [-1, -17]], [[-1, 18], [-1, -18]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346471
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a10', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 10], [-1, -10]], [[-1, 17], [-1, -17]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[-1, 14], [-1, -14]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 16], [-1, -16]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[-1, 18], [-1, -18]], [[-1, 8], [-1, -8]], [[-1, 2], [-1, -2]], [[-1, 12], [-1, -12]], [[-1, 15], [-1, -15]], [[-1, 5], [-1, -5]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346472
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a11', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 11], [-1, -11]], [[-1, 15], [-1, -15]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 18], [-1, -18]], [[-1, 8], [-1, -8]], [[-1, 3], [-1, -3]], [[-1, 14], [-1, -14]], [[-1, 12], [-1, -12]], [[-1, 1], [-1, -1]], [[-1, 10], [-1, -10]], [[-1, 16], [-1, -16]], [[-1, 5], [-1, -5]], [[-1, 6], [-1, -6]], [[-1, 17], [-1, -17]], [[-1, 9], [-1, -9]], [[-1, 2], [-1, -2]], [[-1, 13], [-1, -13]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346473
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a12', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 12], [-1, -12]], [[-1, 13], [-1, -13]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[-1, 14], [-1, -14]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[-1, 15], [-1, -15]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[-1, 16], [-1, -16]], [[-1, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[-1, 17], [-1, -17]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346474
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a13', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[-1, 2], [-1, -2]], [[-1, 15], [-1, -15]], [[-1, 9], [-1, -9]], [[-1, 4], [-1, -4]], [[-1, 17], [-1, -17]], [[-1, 7], [-1, -7]], [[-1, 6], [-1, -6]], [[-1, 18], [-1, -18]], [[-1, 5], [-1, -5]], [[-1, 8], [-1, -8]], [[-1, 16], [-1, -16]], [[-1, 3], [-1, -3]], [[-1, 10], [-1, -10]], [[-1, 14], [-1, -14]], [[-1, 1], [-1, -1]], [[-1, 12], [-1, -12]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346475
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a14', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 14], [-1, -14]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[-1, 18], [-1, -18]], [[-1, 4], [-1, -4]], [[-1, 10], [-1, -10]], [[-1, 13], [-1, -13]], [[-1, 1], [-1, -1]], [[-1, 15], [-1, -15]], [[-1, 8], [-1, -8]], [[-1, 6], [-1, -6]], [[-1, 17], [-1, -17]], [[-1, 3], [-1, -3]], [[-1, 11], [-1, -11]], [[-1, 12], [-1, -12]], [[-1, 2], [-1, -2]], [[-1, 16], [-1, -16]], [[-1, 7], [-1, -7]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346476
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a15', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 15], [-1, -15]], [[-1, 7], [-1, -7]], [[-1, 8], [-1, -8]], [[-1, 14], [-1, -14]], [[-1, 1], [-1, -1]], [[-1, 16], [-1, -16]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[-1, 2], [-1, -2]], [[-1, 17], [-1, -17]], [[-1, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[-1, 12], [-1, -12]], [[-1, 3], [-1, -3]], [[-1, 18], [-1, -18]], [[-1, 4], [-1, -4]], [[-1, 11], [-1, -11]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346477
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a16', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 16], [-1, -16]], [[-1, 5], [-1, -5]], [[-1, 11], [-1, -11]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[-1, 15], [-1, -15]], [[-1, 1], [-1, -1]], [[-1, 17], [-1, -17]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[-1, 9], [-1, -9]], [[-1, 7], [-1, -7]], [[-1, 14], [-1, -14]], [[-1, 2], [-1, -2]], [[-1, 18], [-1, -18]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[-1, 8], [-1, -8]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346479
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a17', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 17], [-1, -17]], [[-1, 3], [-1, -3]], [[-1, 14], [-1, -14]], [[-1, 6], [-1, -6]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[-1, 8], [-1, -8]], [[-1, 12], [-1, -12]], [[-1, 5], [-1, -5]], [[-1, 15], [-1, -15]], [[-1, 2], [-1, -2]], [[-1, 18], [-1, -18]], [[-1, 1], [-1, -1]], [[-1, 16], [-1, -16]], [[-1, 4], [-1, -4]], [[-1, 13], [-1, -13]], [[-1, 7], [-1, -7]], [[-1, 10], [-1, -10]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346480
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a18', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 18], [-1, -18]], [[-1, 1], [-1, -1]], [[-1, 17], [-1, -17]], [[-1, 2], [-1, -2]], [[-1, 16], [-1, -16]], [[-1, 3], [-1, -3]], [[-1, 15], [-1, -15]], [[-1, 4], [-1, -4]], [[-1, 14], [-1, -14]], [[-1, 5], [-1, -5]], [[-1, 13], [-1, -13]], [[-1, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[-1, 7], [-1, -7]], [[-1, 11], [-1, -11]], [[-1, 8], [-1, -8]], [[-1, 10], [-1, -10]], [[-1, 9], [-1, -9]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346501
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 5, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a2', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 8], [-1, -8]], [[-1, 10], [-1, -10]], [[-1, 12], [-1, -12]], [[-1, 14], [-1, -14]], [[-1, 16], [-1, -16]], [[-1, 18], [-1, -18]], [[-1, 17], [-1, -17]], [[-1, 15], [-1, -15]], [[-1, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346502
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 6, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a3', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 12], [-1, -12]], [[-1, 15], [-1, -15]], [[-1, 18], [-1, -18]], [[-1, 16], [-1, -16]], [[-1, 13], [-1, -13]], [[-1, 10], [-1, -10]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 8], [-1, -8]], [[-1, 11], [-1, -11]], [[-1, 14], [-1, -14]], [[-1, 17], [-1, -17]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346503
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 7, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a4', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 4], [-1, -4]], [[-1, 8], [-1, -8]], [[-1, 12], [-1, -12]], [[-1, 16], [-1, -16]], [[-1, 17], [-1, -17]], [[-1, 13], [-1, -13]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 11], [-1, -11]], [[-1, 15], [-1, -15]], [[-1, 18], [-1, -18]], [[-1, 14], [-1, -14]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346504
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 8, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a5', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [-1, -5]], [[-1, 10], [-1, -10]], [[-1, 15], [-1, -15]], [[-1, 17], [-1, -17]], [[-1, 12], [-1, -12]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 8], [-1, -8]], [[-1, 13], [-1, -13]], [[-1, 18], [-1, -18]], [[-1, 14], [-1, -14]], [[-1, 9], [-1, -9]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 6], [-1, -6]], [[-1, 11], [-1, -11]], [[-1, 16], [-1, -16]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346505
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 9, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a6', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 6], [-1, -6]], [[-1, 12], [-1, -12]], [[-1, 18], [-1, -18]], [[-1, 13], [-1, -13]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 11], [-1, -11]], [[-1, 17], [-1, -17]], [[-1, 14], [-1, -14]], [[-1, 8], [-1, -8]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 10], [-1, -10]], [[-1, 16], [-1, -16]], [[-1, 15], [-1, -15]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346468
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 10, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a7', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 7], [-1, -7]], [[-1, 14], [-1, -14]], [[-1, 16], [-1, -16]], [[-1, 9], [-1, -9]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 12], [-1, -12]], [[-1, 18], [-1, -18]], [[-1, 11], [-1, -11]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 10], [-1, -10]], [[-1, 17], [-1, -17]], [[-1, 13], [-1, -13]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 8], [-1, -8]], [[-1, 15], [-1, -15]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346469
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 11, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a8', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 8], [-1, -8]], [[-1, 16], [-1, -16]], [[-1, 13], [-1, -13]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 11], [-1, -11]], [[-1, 18], [-1, -18]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 14], [-1, -14]], [[-1, 15], [-1, -15]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[-1, 17], [-1, -17]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346470
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 37, 'dim': 72, 'faithful': True, 'field': [-1, -9, 45, 120, -330, -462, 924, 792, -1287, -715, 1001, 364, -455, -105, 120, 16, -17, -1, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.72a9', 'nt': [2628, 0], 'q_character': None, 'values': [[[72, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 9], [-1, -9]], [[-1, 18], [-1, -18]], [[-1, 10], [-1, -10]], [[-1, 1], [-1, -1]], [[-1, 8], [-1, -8]], [[-1, 17], [-1, -17]], [[-1, 11], [-1, -11]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 16], [-1, -16]], [[-1, 12], [-1, -12]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 15], [-1, -15]], [[-1, 13], [-1, -13]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 14], [-1, -14]], [[-1, 0]], [[-1, 0]]]}
  • id: 38346481
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 1, 'dim': 73, 'faithful': True, 'field': [0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.73a', 'nt': [74, 0], 'q_character': None, 'values': [[[73, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 38346482
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 1, 'dim': 74, 'faithful': True, 'field': [0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74a', 'nt': [222, 0], 'q_character': None, 'values': [[[74, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[1, 0]], [[1, 0]]]}
  • id: 38346483
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 1, 'dim': 74, 'faithful': True, 'field': [0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74b', 'nt': [296, 0], 'q_character': None, 'values': [[[74, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[1, 0]], [[1, 0]]]}
  • id: 38346484
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 1, 'dim': 74, 'faithful': True, 'field': [0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74c', 'nt': [444, 0], 'q_character': None, 'values': [[[74, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[1, 0]], [[1, 0]]]}
  • id: 38346485
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 12, 'dim': 74, 'faithful': True, 'field': [-3, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74d1', 'nt': [888, 0], 'q_character': None, 'values': [[[74, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 38346486
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 12, 'dim': 74, 'faithful': True, 'field': [-3, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74d2', 'nt': [888, 0], 'q_character': None, 'values': [[[74, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 38346487
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 9, 'dim': 74, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74e1', 'nt': [666, 0], 'q_character': None, 'values': [[[74, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[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]], [[1, 0]], [[1, 0]]]}
  • id: 38346488
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 9, 'dim': 74, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74e2', 'nt': [666, 0], 'q_character': None, 'values': [[[74, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -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]], [[1, 0]], [[1, 0]]]}
  • id: 38346490
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 9, 'dim': 74, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74e3', 'nt': [666, 0], 'q_character': None, 'values': [[[74, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 0]], [[-1, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 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]], [[1, 0]], [[1, 0]]]}
  • id: 38346491
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 9, 'dim': 74, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74f1', 'nt': [1332, 0], 'q_character': None, 'values': [[[74, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-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]], [[1, 0]], [[1, 0]]]}
  • id: 38346492
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 9, 'dim': 74, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74f2', 'nt': [1332, 0], 'q_character': None, 'values': [[[74, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -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]], [[1, 0]], [[1, 0]]]}
  • id: 38346493
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 9, 'dim': 74, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74f3', 'nt': [1332, 0], 'q_character': None, 'values': [[[74, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 0]], [[1, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 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]], [[1, 0]], [[1, 0]]]}
  • id: 38346494
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 36, 'dim': 74, 'faithful': True, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74g1', 'nt': [2664, 0], 'q_character': None, 'values': [[[74, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 38346495
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 36, 'dim': 74, 'faithful': True, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74g2', 'nt': [2664, 0], 'q_character': None, 'values': [[[74, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 38346496
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 36, 'dim': 74, 'faithful': True, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74g3', 'nt': [2664, 0], 'q_character': None, 'values': [[[74, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 8], [-1, -8]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 38346497
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 36, 'dim': 74, 'faithful': True, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74g4', 'nt': [2664, 0], 'q_character': None, 'values': [[[74, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 8], [-1, -8]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 38346498
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 36, 'dim': 74, 'faithful': True, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74g5', 'nt': [2664, 0], 'q_character': None, 'values': [[[74, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[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]], [[1, 0]], [[1, 0]]]}
  • id: 38346499
    {'center': '194472.a1.a1', 'center_index': 194472, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 36, 'dim': 74, 'faithful': True, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '194472.a', 'group_counter': 1, 'group_order': 194472, 'image': None, 'image_isoclass': '194472.a', 'image_order': 194472, 'indicator': 1, 'kernel': '194472.a1.a1', 'kernel_order': 1, 'label': '194472.a.74g6', 'nt': [2664, 0], 'q_character': None, 'values': [[[74, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[-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]], [[1, 0]], [[1, 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: 264680476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 194472, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 16206, 'label': '194472.a.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': True, 'solvable': False, 'special_labels': ['D', 'S', 'PC', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '194472.a', 'subgroup_hash': 1944427750340150412, 'subgroup_order': 194472, 'subgroup_tex': '\\PSL(2,73)', 'supersolvable': False, 'sylow': 0}
  • id: 264680487
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.74.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '74.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': 74, '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': '2628.c', 'subgroup_hash': 339484339315138643, 'subgroup_order': 2628, 'subgroup_tex': 'C_{73}:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 264680498
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.148.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '148.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': 148, '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': '1314.7', 'subgroup_hash': 7, 'subgroup_order': 1314, 'subgroup_tex': 'C_{73}:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 264680508
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.222.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '222.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': 222, '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': '876.7', 'subgroup_hash': 7, 'subgroup_order': 876, 'subgroup_tex': 'C_{73}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264680509
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 219, 'label': '194472.a.296.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '296.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': 296, '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': '657.3', 'subgroup_hash': 3, 'subgroup_order': 657, 'subgroup_tex': 'C_{73}:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 264680510
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.444.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '444.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': 444, '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': '438.1', 'subgroup_hash': 1, 'subgroup_order': 438, 'subgroup_tex': 'C_{73}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 264680511
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.666.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '666.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': 666, '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': '292.3', 'subgroup_hash': 3, 'subgroup_order': 292, 'subgroup_tex': 'C_{73}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 264680512
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.888.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '888.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': 888, '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': '219.1', 'subgroup_hash': 1, 'subgroup_order': 219, 'subgroup_tex': 'C_{73}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 264680513
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.1332.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1332.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': 1332, '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': '146.1', 'subgroup_hash': 1, 'subgroup_order': 146, 'subgroup_tex': 'D_{73}', 'supersolvable': True, 'sylow': 0}
  • id: 264680477
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.2628.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2628.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': 2628, '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': '74.1', 'subgroup_hash': 1, 'subgroup_order': 74, 'subgroup_tex': 'D_{37}', 'supersolvable': True, 'sylow': 0}
  • id: 264680478
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 73, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': True, 'direct': None, 'hall': 73, 'label': '194472.a.2664.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2664.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': 2664, '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': '73.1', 'subgroup_hash': 1, 'subgroup_order': 73, 'subgroup_tex': 'C_{73}', 'supersolvable': True, 'sylow': 73}
  • id: 264680479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '194472.a.2701.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2701.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': 2701, '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': '72.6', 'subgroup_hash': 6, 'subgroup_order': 72, 'subgroup_tex': 'D_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 264680480
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 37, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': True, 'direct': None, 'hall': 37, 'label': '194472.a.5256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5256.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': 5256, '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': '37.1', 'subgroup_hash': 1, 'subgroup_order': 37, 'subgroup_tex': 'C_{37}', 'supersolvable': True, 'sylow': 37}
  • id: 264680481
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '194472.a.5402.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5402.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': 5402, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 264680482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.5402.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5402.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': 5402, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 264680483
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.5402.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5402.b1.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': 5402, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 264680484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.8103.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8103.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': 8103, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264680485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.8103.a1.a2', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8103.a1.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': 8103, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 264680486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.8103.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8103.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': 8103, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 264680488
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '194472.a.10804.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10804.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': 10804, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 264680489
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.10804.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10804.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': 10804, '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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 264680490
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.10804.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10804.b1.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': 10804, '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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 264680491
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '194472.a.16206.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16206.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': 16206, '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: 264680492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.16206.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16206.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': 16206, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264680493
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.16206.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16206.b1.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': 16206, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 264680494
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.16206.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16206.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': 16206, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264680495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.16206.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16206.c1.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': 16206, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 264680496
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '194472.a.21608.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21608.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': 21608, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 3}
  • id: 264680497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '194472.a.24309.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24309.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': 24309, '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': 2}
  • id: 264680499
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '194472.a.32412.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32412.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': 32412, '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: 264680500
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.32412.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32412.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': 32412, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264680501
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.32412.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32412.b1.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': 32412, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 264680502
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '194472.a.48618.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48618.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': 48618, '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: 264680503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.48618.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48618.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': 48618, '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: 264680504
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '194472.a.48618.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48618.b1.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': 48618, '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: 264680505
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '194472.a.64824.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64824.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': 64824, '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: 264680506
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '194472.a.97236.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '97236.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': 97236, '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: 264680507
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '194472.a', 'ambient_counter': 1, 'ambient_order': 194472, 'ambient_tex': '\\PSL(2,73)', 'central': True, 'central_factor': False, 'centralizer_order': 194472, 'characteristic': True, 'core_order': 1, 'counter': 38, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '194472.a.194472.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '194472.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '194472.a', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1944427750340150412, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 194472, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,73)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'Phi', 'R', 'U0', 'C1'], '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: 264680476
    {'ambient': '194472.a', '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': '194472.a1.a1', 'complements': ['194472.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['74.a1.a1', '2628.a1.a1', '2701.a1.a1', '8103.a1.a1', '8103.a1.a2'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7266, 5000, 4308, 5000, 7935, 5000, 7894, 5000], 'generators': [12853878, 4979829], 'label': '194472.a.1.a1.a1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['194472.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '194472.a', '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': '194472.a'}
  • id: 264680477
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '2628.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['5256.a1.a1', '97236.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2628, 'diagramx': [9433, -1, 9338, -1, 9580, -1, 9684, -1], 'generators': [9254961, 579254], 'label': '194472.a.2628.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2628.a1.a1', 'old_label': '2628.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2628.a1.a1', 'subgroup_fusion': None, 'weyl_group': '74.1'}
  • id: 264680478
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '2664.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2664.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['888.a1.a1', '1332.a1.a1'], 'contains': ['194472.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 74, 'diagramx': [1610, -1, 8718, -1, 3414, -1, 2569, -1], 'generators': [18378942], 'label': '194472.a.2664.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '74.a1.a1', 'old_label': '2664.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2664.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.2'}
  • id: 264680479
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '2701.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['5402.a1.a1', '5402.b1.a1', '5402.b1.a2', '8103.b1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [6660, -1, 2799, -1, 6657, -1, 5766, -1], 'generators': [20659970, 3706598, 22045871, 24909897, 26711800], 'label': '194472.a.2701.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '2701.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2701.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 264680480
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '5256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2628.a1.a1'], 'contains': ['194472.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2628, 'diagramx': [9433, -1, 9773, -1, 8432, -1, 8607, -1], 'generators': [9254961], 'label': '194472.a.5256.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2628.a1.a1', 'old_label': '5256.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264680481
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '5402.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5402.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['74.a1.a1', '2701.a1.a1'], 'contains': ['10804.a1.a1', '16206.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [4865, -1, 4233, -1, 5438, -1, 4136, -1], 'generators': [5869940, 3782193, 2117611, 5072392], 'label': '194472.a.5402.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '5402.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5402.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264680482
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '5402.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2701.a1.a1'], 'contains': ['10804.a1.a1', '10804.b1.a1', '16206.c1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [6088, -1, 2079, -1, 6527, -1, 5766, -1], 'generators': [20659970, 24909897, 26711800, 5946930], 'label': '194472.a.5402.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '5402.b1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5402.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 264680483
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '5402.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2701.a1.a1'], 'contains': ['10804.a1.a1', '10804.b1.a2', '16206.c1.a2'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [6088, -1, 2825, -1, 6527, -1, 4973, -1], 'generators': [20659970, 22045871, 24909897, 26711800], 'label': '194472.a.5402.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '5402.b1.a2', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5402.b1.a2', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 264680484
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '8103.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['16206.b1.a1', '24309.a1.a1', '32412.b1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 8103, 'diagramx': [8298, -1, 5876, -1, 8716, -1, 8776, -1], 'generators': [23194086, 5108600, 9776646, 8570949], 'label': '194472.a.8103.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8103.a1.a1', 'old_label': '8103.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8103.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264680485
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '8103.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['16206.b1.a2', '24309.a1.a1', '32412.b1.a2'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 8103, 'diagramx': [8298, -1, 1710, -1, 8716, -1, 7894, -1], 'generators': [12670578, 4993772, 5843156, 3772997], 'label': '194472.a.8103.a1.a2', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8103.a1.a2', 'old_label': '8103.a1.a2', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8103.a1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264680486
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '8103.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2701.a1.a1'], 'contains': ['16206.a1.a1', '16206.c1.a1', '16206.c1.a2', '24309.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 8103, 'diagramx': [7087, -1, 5197, -1, 7580, -1, 6558, -1], 'generators': [20659970, 3706598, 22045871, 26711800], 'label': '194472.a.8103.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8103.b1.a1', 'old_label': '8103.b1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8103.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264680487
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '74.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['148.a1.a1', '222.a1.a1', '5402.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 74, 'diagramx': [4000, -1, 4308, -1, 4609, -1, 3575, -1], 'generators': [5869940, 18378942, 3782193, 2117611, 5072392], 'label': '194472.a.74.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '74.a1.a1', 'old_label': '74.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '74.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2628.c'}
  • id: 264680488
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '10804.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5402.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['148.a1.a1', '5402.a1.a1', '5402.b1.a1', '5402.b1.a2'], 'contains': ['21608.a1.a1', '32412.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [4786, -1, 3177, -1, 4645, -1, 3495, -1], 'generators': [5869940, 3782193, 5072392], 'label': '194472.a.10804.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '10804.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10804.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264680489
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '10804.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5402.b1.a1'], 'contains': ['21608.a1.a1', '32412.b1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 5402, 'diagramx': [5683, -1, 435, -1, 6633, -1, 5632, -1], 'generators': [20659970, 24909897, 5946930], 'label': '194472.a.10804.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5402.b1.a1', 'old_label': '10804.b1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10804.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 264680490
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '10804.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5402.b1.a2'], 'contains': ['21608.a1.a1', '32412.b1.a2'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 5402, 'diagramx': [5683, -1, 1039, -1, 6633, -1, 4991, -1], 'generators': [20659970, 22045871, 24909897], 'label': '194472.a.10804.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5402.b1.a2', 'old_label': '10804.b1.a2', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10804.b1.a2', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 264680491
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '16206.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5402.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['222.a1.a1', '5402.a1.a1', '8103.b1.a1'], 'contains': ['32412.a1.a1', '48618.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [3461, -1, 6890, -1, 5686, -1, 4279, -1], 'generators': [3782193, 2117611, 5072392], 'label': '194472.a.16206.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '16206.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16206.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264680492
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '16206.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8103.a1.a1'], 'contains': ['48618.b1.a1', '64824.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 8103, 'diagramx': [8624, -1, 5264, -1, 9639, -1, 9515, -1], 'generators': [23194086, 5108600, 9776646], 'label': '194472.a.16206.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8103.a1.a1', 'old_label': '16206.b1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16206.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264680493
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '16206.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8103.a1.a2'], 'contains': ['48618.b1.a2', '64824.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 8103, 'diagramx': [8624, -1, 1961, -1, 9639, -1, 7894, -1], 'generators': [12670578, 4993772, 3772997], 'label': '194472.a.16206.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8103.a1.a2', 'old_label': '16206.b1.a2', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16206.b1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 264680494
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '16206.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5402.b1.a1', '8103.b1.a1'], 'contains': ['32412.a1.a1', '32412.b1.a1', '48618.b1.a2'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 8103, 'diagramx': [6727, -1, 3412, -1, 7485, -1, 6915, -1], 'generators': [20659970, 26711800, 5946930], 'label': '194472.a.16206.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8103.b1.a1', 'old_label': '16206.c1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16206.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264680495
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '16206.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5402.b1.a2', '8103.b1.a1'], 'contains': ['32412.a1.a1', '32412.b1.a2', '48618.b1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 8103, 'diagramx': [6727, -1, 4342, -1, 7485, -1, 6273, -1], 'generators': [20659970, 22045871, 26711800], 'label': '194472.a.16206.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8103.b1.a1', 'old_label': '16206.c1.a2', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16206.c1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 264680496
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '21608.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5402.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['296.a1.a1', '10804.a1.a1', '10804.b1.a1', '10804.b1.a2'], 'contains': ['64824.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [5213, -1, 227, -1, 4645, -1, 4261, -1], 'generators': [5869940, 3782193], 'label': '194472.a.21608.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '21608.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21608.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264680497
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '24309.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8103.a1.a1', '8103.a1.a2', '8103.b1.a1'], 'contains': ['48618.a1.a1', '48618.b1.a1', '48618.b1.a2'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 24309, 'diagramx': [8624, -1, 7057, -1, 8337, -1, 8535, -1], 'generators': [3706598, 22045871, 26711800], 'label': '194472.a.24309.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24309.a1.a1', 'old_label': '24309.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24309.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 264680498
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '148.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['74.a1.a1'], 'contains': ['296.a1.a1', '444.a1.a1', '10804.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 74, 'diagramx': [3305, -1, 3605, -1, 2136, -1, 1536, -1], 'generators': [5869940, 18378942, 3782193, 5072392], 'label': '194472.a.148.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '74.a1.a1', 'old_label': '148.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '148.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2628.c'}
  • id: 264680499
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '32412.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5402.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['444.a1.a1', '10804.a1.a1', '16206.a1.a1', '16206.c1.a1', '16206.c1.a2'], 'contains': ['64824.a1.a1', '97236.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [3551, -1, 4861, -1, 5497, -1, 4902, -1], 'generators': [3782193, 5072392], 'label': '194472.a.32412.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '32412.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32412.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264680500
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '32412.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8103.a1.a1', '10804.b1.a1', '16206.c1.a1'], 'contains': ['64824.a1.a1', '97236.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 16206, 'diagramx': [6066, -1, 3093, -1, 7201, -1, 6826, -1], 'generators': [20659970, 5946930], 'label': '194472.a.32412.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16206.c1.a1', 'old_label': '32412.b1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32412.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264680501
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '32412.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '97236.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8103.a1.a2', '10804.b1.a2', '16206.c1.a2'], 'contains': ['64824.a1.a1', '97236.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 16206, 'diagramx': [6066, -1, 1358, -1, 7201, -1, 6184, -1], 'generators': [20659970, 22045871], 'label': '194472.a.32412.b1.a2', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16206.c1.a2', 'old_label': '32412.b1.a2', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32412.b1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264680502
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '48618.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5402.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['666.a1.a1', '16206.a1.a1', '24309.a1.a1'], 'contains': ['97236.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [4595, -1, 7402, -1, 6349, -1, 5543, -1], 'generators': [2117611, 5072392], 'label': '194472.a.48618.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '48618.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48618.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264680503
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '48618.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48618.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16206.b1.a1', '16206.c1.a2', '24309.a1.a1'], 'contains': ['97236.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 8103, 'diagramx': [8725, -1, 6597, -1, 8112, -1, 8580, -1], 'generators': [22045871, 26711800], 'label': '194472.a.48618.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8103.a1.a1', 'old_label': '48618.b1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48618.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264680504
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '48618.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48618.b1.a2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16206.b1.a2', '16206.c1.a1', '24309.a1.a1'], 'contains': ['97236.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 8103, 'diagramx': [8725, -1, 4711, -1, 8112, -1, 7850, -1], 'generators': [26711800, 5946930], 'label': '194472.a.48618.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8103.a1.a2', 'old_label': '48618.b1.a2', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48618.b1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 264680505
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '64824.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5402.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['888.a1.a1', '16206.b1.a1', '16206.b1.a2', '21608.a1.a1', '32412.a1.a1', '32412.b1.a1', '32412.b1.a2'], 'contains': ['194472.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [5213, -1, 2456, -1, 5497, -1, 6184, -1], 'generators': [3782193], 'label': '194472.a.64824.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '64824.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64824.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 264680506
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '97236.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2701.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1332.a1.a1', '2628.a1.a1', '32412.a1.a1', '32412.b1.a1', '32412.b1.a2', '48618.a1.a1', '48618.b1.a1', '48618.b1.a2'], 'contains': ['194472.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 2701, 'diagramx': [5830, -1, 6597, -1, 6349, -1, 6826, -1], 'generators': [5072392], 'label': '194472.a.97236.a1.a1', 'mobius_quo': None, 'mobius_sub': -36, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2701.a1.a1', 'old_label': '97236.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '97236.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264680507
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '194472.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': ['2664.a1.a1', '5256.a1.a1', '64824.a1.a1', '97236.a1.a1'], 'contains': [], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5527, 5000, 7561, 5000, 5923, 5000, 6505, 5000], 'generators': [], 'label': '194472.a.194472.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '194472.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '194472.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '194472.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 264680508
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '222.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['74.a1.a1'], 'contains': ['444.a1.a1', '666.a1.a1', '16206.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 74, 'diagramx': [960, -1, 7678, -1, 3923, -1, 3005, -1], 'generators': [18378942, 3782193, 2117611, 5072392], 'label': '194472.a.222.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '74.a1.a1', 'old_label': '222.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '222.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2628.c'}
  • id: 264680509
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '296.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['148.a1.a1'], 'contains': ['888.a1.a1', '21608.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 74, 'diagramx': [3193, -1, 3093, -1, 598, -1, 450, -1], 'generators': [5869940, 18378942, 3782193], 'label': '194472.a.296.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '74.a1.a1', 'old_label': '296.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '296.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2628.c'}
  • id: 264680510
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '444.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['148.a1.a1', '222.a1.a1'], 'contains': ['888.a1.a1', '1332.a1.a1', '32412.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 74, 'diagramx': [1880, -1, 7184, -1, 2006, -1, 1509, -1], 'generators': [18378942, 3782193, 5072392], 'label': '194472.a.444.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '74.a1.a1', 'old_label': '444.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '444.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2628.c'}
  • id: 264680511
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '666.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['222.a1.a1'], 'contains': ['1332.a1.a1', '48618.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 74, 'diagramx': [567, -1, 8508, -1, 3414, -1, 2569, -1], 'generators': [18378942, 2117611, 5072392], 'label': '194472.a.666.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '74.a1.a1', 'old_label': '666.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '666.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2628.c'}
  • id: 264680512
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '888.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['296.a1.a1', '444.a1.a1'], 'contains': ['2664.a1.a1', '64824.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 74, 'diagramx': [2766, -1, 6145, -1, 2101, -1, 1581, -1], 'generators': [18378942, 3782193], 'label': '194472.a.888.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '74.a1.a1', 'old_label': '888.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '888.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2628.c'}
  • id: 264680513
    {'ambient': '194472.a', 'aut_centralizer_order': None, 'aut_label': '1332.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '194472.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['444.a1.a1', '666.a1.a1'], 'contains': ['2664.a1.a1', '97236.a1.a1'], 'core': '194472.a1.a1', 'coset_action_label': None, 'count': 74, 'diagramx': [1184, -1, 8751, -1, 3414, -1, 2569, -1], 'generators': [18378942, 5072392], 'label': '194472.a.1332.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '74.a1.a1', 'old_label': '1332.a1.a1', 'projective_image': '194472.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1332.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2628.c'}