Abstract group data - 288.571

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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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [4, 12, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4, 24], [155, 102, 52, 284], [155, 258, 52, 264], [13, 146, 4, 180], [145, 2, 20, 172], [117, 102, 20, 132], [249, 106, 4, 128]], 'aut_group': None, 'aut_hash': 922240014224639854, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 28, 'aut_perms': [23893122458336793996255875445, 264659976567683055854906118030, 294418941234028927055085765807, 137780252850896408766372318060, 6281362741462488469138796456, 294822837478203628524535212909], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 4, 1], [2, 18, 2, 1], [2, 36, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [4, 4, 1, 1], [4, 12, 2, 1], [6, 2, 2, 3], [6, 4, 1, 1], [6, 4, 2, 1], [6, 12, 4, 1], [12, 4, 4, 2], [12, 12, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2.C_2^6.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '72.40', 'autcentquo_hash': 40, 'autcentquo_nilpotent': False, 'autcentquo_order': 72, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SOPlus(4,2)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 4], [2, 18, 2], [2, 36, 1], [3, 2, 2], [3, 4, 1], [4, 4, 1], [4, 12, 2], [6, 2, 6], [6, 4, 3], [6, 12, 4], [12, 4, 8], [12, 12, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '72.46', 'commutator_count': 1, 'commutator_label': '36.14', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 571, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 4], [2, 18, 1, 2], [2, 36, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [4, 4, 1, 1], [4, 12, 1, 2], [6, 2, 1, 6], [6, 4, 1, 3], [6, 12, 1, 4], [12, 4, 2, 4], [12, 12, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1344, 'exponent': 12, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '72.46', 'hash': 571, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 3, 6], 'inner_gens': [[1, 2, 4, 284], [1, 2, 20, 264], [1, 10, 4, 24], [53, 50, 4, 24]], 'inner_hash': 46, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': False, 'inner_tex': 'S_3\\times D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 22], [4, 12]], 'label': '288.571', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D6:D12', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 19, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 42, 'number_divisions': 36, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 126, 'number_subgroup_classes': 287, 'number_subgroups': 1538, 'old_label': None, 'order': 288, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 99], [3, 8], [4, 28], [6, 72], [12, 80]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[157, 2, 4, 24], [157, 158, 20, 184], [157, 158, 4, 284], [145, 2, 4, 24], [3, 2, 260, 36]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [5041, 1, 368040, 367927, 1174342], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [4, 12], [8, 2]], 'representations': {'PC': {'code': 67916681432948544053566420000119305, 'gens': [1, 2, 3, 5], 'pres': [7, 2, 2, 2, 3, 2, 2, 3, 219, 58, 234, 9944, 4631, 102, 10757, 5052, 124, 9806, 4717]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [91655875958721143, 25038638872036405, 125101740314276878]}, 'GLZN': {'d': 2, 'p': 60, 'gens': [10174373, 10671311, 6696031, 346333, 217201, 6264929, 217801]}, 'Perm': {'d': 14, 'gens': [6314117381, 6354404021, 18575, 5329, 12316, 13971242880, 20122058880]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_6:D_{12}', 'transitive_degree': 48, '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: 103723931
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 571, 'group_order': 288, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 103723942
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 571, 'group_order': 288, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 12, 'size': 1}
  • id: 103723953
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 571, 'group_order': 288, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 156, 'size': 1}
  • id: 103723964
    {'aut_label': '2C', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 571, 'group_order': 288, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 144, 'size': 1}
  • id: 103723968
    {'aut_label': '2D', 'centralizer': '6.e1', 'counter': 5, 'group_counter': 571, 'group_order': 288, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 105, 'size': 6}
  • id: 103723969
    {'aut_label': '2D', 'centralizer': '6.e1', 'counter': 6, 'group_counter': 571, 'group_order': 288, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 65, 'size': 6}
  • id: 103723970
    {'aut_label': '2D', 'centralizer': '6.e1', 'counter': 7, 'group_counter': 571, 'group_order': 288, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 19, 'size': 6}
  • id: 103723971
    {'aut_label': '2D', 'centralizer': '6.e1', 'counter': 8, 'group_counter': 571, 'group_order': 288, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 155, 'size': 6}
  • id: 103723972
    {'aut_label': '2H', 'centralizer': '18.c1', 'counter': 9, 'group_counter': 571, 'group_order': 288, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 118, 'size': 18}
  • id: 103723932
    {'aut_label': '2H', 'centralizer': '18.c1', 'counter': 10, 'group_counter': 571, 'group_order': 288, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 194, 'size': 18}
  • id: 103723933
    {'aut_label': '2J', 'centralizer': '36.f1', 'counter': 11, 'group_counter': 571, 'group_order': 288, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 82, 'size': 36}
  • id: 103723934
    {'aut_label': '3A', 'centralizer': '2.b1', 'counter': 12, 'group_counter': 571, 'group_order': 288, 'label': '3A', 'order': 3, 'powers': [12, 1], 'representative': 104, 'size': 2}
  • id: 103723935
    {'aut_label': '3A', 'centralizer': '2.b1', 'counter': 13, 'group_counter': 571, 'group_order': 288, 'label': '3B', 'order': 3, 'powers': [13, 1], 'representative': 8, 'size': 2}
  • id: 103723936
    {'aut_label': '3C', 'centralizer': '4.d1', 'counter': 14, 'group_counter': 571, 'group_order': 288, 'label': '3C', 'order': 3, 'powers': [14, 1], 'representative': 200, 'size': 4}
  • id: 103723937
    {'aut_label': '4A', 'centralizer': '4.d1', 'counter': 15, 'group_counter': 571, 'group_order': 288, 'label': '4A', 'order': 4, 'powers': [4, 15], 'representative': 72, 'size': 4}
  • id: 103723938
    {'aut_label': '4B', 'centralizer': '12.m1', 'counter': 16, 'group_counter': 571, 'group_order': 288, 'label': '4B', 'order': 4, 'powers': [2, 16], 'representative': 45, 'size': 12}
  • id: 103723939
    {'aut_label': '4B', 'centralizer': '12.m1', 'counter': 17, 'group_counter': 571, 'group_order': 288, 'label': '4C', 'order': 4, 'powers': [3, 17], 'representative': 79, 'size': 12}
  • id: 103723940
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 18, 'group_counter': 571, 'group_order': 288, 'label': '6A', 'order': 6, 'powers': [12, 2], 'representative': 196, 'size': 2}
  • id: 103723941
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 19, 'group_counter': 571, 'group_order': 288, 'label': '6B', 'order': 6, 'powers': [13, 3], 'representative': 148, 'size': 2}
  • id: 103723943
    {'aut_label': '6C', 'centralizer': '2.b1', 'counter': 20, 'group_counter': 571, 'group_order': 288, 'label': '6C', 'order': 6, 'powers': [12, 4], 'representative': 64, 'size': 2}
  • id: 103723944
    {'aut_label': '6C', 'centralizer': '2.b1', 'counter': 21, 'group_counter': 571, 'group_order': 288, 'label': '6D', 'order': 6, 'powers': [13, 4], 'representative': 160, 'size': 2}
  • id: 103723945
    {'aut_label': '6E', 'centralizer': '2.b1', 'counter': 22, 'group_counter': 571, 'group_order': 288, 'label': '6E', 'order': 6, 'powers': [13, 2], 'representative': 20, 'size': 2}
  • id: 103723946
    {'aut_label': '6E', 'centralizer': '2.b1', 'counter': 23, 'group_counter': 571, 'group_order': 288, 'label': '6F', 'order': 6, 'powers': [12, 3], 'representative': 52, 'size': 2}
  • id: 103723947
    {'aut_label': '6G', 'centralizer': '4.d1', 'counter': 24, 'group_counter': 571, 'group_order': 288, 'label': '6G', 'order': 6, 'powers': [14, 2], 'representative': 100, 'size': 4}
  • id: 103723948
    {'aut_label': '6G', 'centralizer': '4.d1', 'counter': 25, 'group_counter': 571, 'group_order': 288, 'label': '6H', 'order': 6, 'powers': [14, 3], 'representative': 60, 'size': 4}
  • id: 103723949
    {'aut_label': '6I', 'centralizer': '4.d1', 'counter': 26, 'group_counter': 571, 'group_order': 288, 'label': '6I', 'order': 6, 'powers': [14, 4], 'representative': 48, 'size': 4}
  • id: 103723950
    {'aut_label': '6J', 'centralizer': '12.h1', 'counter': 27, 'group_counter': 571, 'group_order': 288, 'label': '6J', 'order': 6, 'powers': [13, 5], 'representative': 97, 'size': 12}
  • id: 103723951
    {'aut_label': '6J', 'centralizer': '12.h1', 'counter': 28, 'group_counter': 571, 'group_order': 288, 'label': '6K', 'order': 6, 'powers': [13, 6], 'representative': 49, 'size': 12}
  • id: 103723952
    {'aut_label': '6J', 'centralizer': '12.h1', 'counter': 29, 'group_counter': 571, 'group_order': 288, 'label': '6L', 'order': 6, 'powers': [12, 7], 'representative': 99, 'size': 12}
  • id: 103723954
    {'aut_label': '6J', 'centralizer': '12.h1', 'counter': 30, 'group_counter': 571, 'group_order': 288, 'label': '6M', 'order': 6, 'powers': [12, 8], 'representative': 51, 'size': 12}
  • id: 103723955
    {'aut_label': '12A1', 'centralizer': '4.d1', 'counter': 31, 'group_counter': 571, 'group_order': 288, 'label': '12A1', 'order': 12, 'powers': [26, 15], 'representative': 24, 'size': 4}
  • id: 103723956
    {'aut_label': '12A1', 'centralizer': '4.d1', 'counter': 32, 'group_counter': 571, 'group_order': 288, 'label': '12A5', 'order': 12, 'powers': [26, 15], 'representative': 120, 'size': 4}
  • id: 103723957
    {'aut_label': '12B1', 'centralizer': '4.d1', 'counter': 33, 'group_counter': 571, 'group_order': 288, 'label': '12B1', 'order': 12, 'powers': [20, 15], 'representative': 32, 'size': 4}
  • id: 103723958
    {'aut_label': '12B1', 'centralizer': '4.d1', 'counter': 34, 'group_counter': 571, 'group_order': 288, 'label': '12B5', 'order': 12, 'powers': [20, 15], 'representative': 124, 'size': 4}
  • id: 103723959
    {'aut_label': '12A1', 'centralizer': '4.d1', 'counter': 35, 'group_counter': 571, 'group_order': 288, 'label': '12C1', 'order': 12, 'powers': [26, 15], 'representative': 40, 'size': 4}
  • id: 103723960
    {'aut_label': '12A1', 'centralizer': '4.d1', 'counter': 36, 'group_counter': 571, 'group_order': 288, 'label': '12C5', 'order': 12, 'powers': [26, 15], 'representative': 128, 'size': 4}
  • id: 103723961
    {'aut_label': '12B1', 'centralizer': '4.d1', 'counter': 37, 'group_counter': 571, 'group_order': 288, 'label': '12D1', 'order': 12, 'powers': [21, 15], 'representative': 80, 'size': 4}
  • id: 103723962
    {'aut_label': '12B1', 'centralizer': '4.d1', 'counter': 38, 'group_counter': 571, 'group_order': 288, 'label': '12D5', 'order': 12, 'powers': [21, 15], 'representative': 224, 'size': 4}
  • id: 103723963
    {'aut_label': '12E1', 'centralizer': '12.m1', 'counter': 39, 'group_counter': 571, 'group_order': 288, 'label': '12E1', 'order': 12, 'powers': [22, 16], 'representative': 25, 'size': 12}
  • id: 103723965
    {'aut_label': '12E1', 'centralizer': '12.m1', 'counter': 40, 'group_counter': 571, 'group_order': 288, 'label': '12E5', 'order': 12, 'powers': [22, 16], 'representative': 121, 'size': 12}
  • id: 103723966
    {'aut_label': '12E1', 'centralizer': '12.m1', 'counter': 41, 'group_counter': 571, 'group_order': 288, 'label': '12F1', 'order': 12, 'powers': [23, 17], 'representative': 27, 'size': 12}
  • id: 103723967
    {'aut_label': '12E1', 'centralizer': '12.m1', 'counter': 42, 'group_counter': 571, 'group_order': 288, 'label': '12F5', 'order': 12, 'powers': [23, 17], 'representative': 123, 'size': 12}
• gps_qchar •

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

  
  
  • id: 2447111
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2447122
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2447133
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2447141
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 2447142
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 2447143
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 2447144
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 2447145
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2447146
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, -1, -1, 2, 2, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, -1, -1, 0, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 0, 0], 'schur_index': 1}
  • id: 2447112
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -1, 2, -1, 2, 0, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 0, 0, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1], 'schur_index': 1}
  • id: 2447113
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, -2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, -2, 2, -2, 2, -2, -2, -2, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447114
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 0, -2, 2, -2, 2, -2, -2, -2, 2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447115
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447116
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447117
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, -2, 2, 0, 2, 2, 2, 0, 0, 0, -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], 'schur_index': 1}
  • id: 2447118
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 2, -2, 0, 2, 2, 2, 0, 0, 0, -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], 'schur_index': 1}
  • id: 2447119
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, -1, 2, -1, -2, 0, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 1, 0, 0, 1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, -1, -1], 'schur_index': 1}
  • id: 2447120
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, -1, 2, -1, 2, 0, -2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 1, 0, 0, 1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1], 'schur_index': 1}
  • id: 2447121
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 2, -1, -1, -2, 2, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, -2, -1, -1, 0, 0], 'schur_index': 1}
  • id: 2447123
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 2, -1, -1, 2, -2, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 1, 1, 0, -1, -1, -1, 2, -1, -1, -1, 2, 1, 1, 0, 0], 'schur_index': 1}
  • id: 2447124
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2m', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, -1, -1, -2, -2, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, -1, -1, 0, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 0, 0], 'schur_index': 1}
  • id: 2447125
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2n', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -1, 2, -1, -2, 0, -2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 0, 0, -1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1], 'schur_index': 1}
  • id: 2447126
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2o', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -4, 4, 0, 0, 0, 4, -2, -2, 0, 0, 0, -4, 4, -4, -2, 2, 2, 2, -2, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447127
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2p', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, -4, 0, 0, 0, 4, -2, -2, 0, 0, 0, -4, 4, -4, -2, 2, 2, 2, -2, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447128
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2q', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 0, -2, 2, 2, -4, 4, -4, -2, 2, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447129
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.2r', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 0, -2, 2, 2, -4, 4, -4, -2, 2, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447130
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 4, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, -2, -2, 1, -2, 1, 1, 1, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447131
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4b', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 0, 2, -2, 2, 4, -4, -4, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447132
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4c', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 0, 4, -4, -4, 2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447134
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4d', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 0, 2, 2, -2, -4, -4, 4, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447135
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4e', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 0, -4, -4, 4, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447136
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4f', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, -4, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 2, 2, -1, 2, -1, -1, -1, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447137
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4g', 'multiplicity': 1, 'nt': [12, 81], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 2, 2, -2, 2, 2, -2, -1, -1, 1, 0, 0, 0, 0, 0, 0, -3, 0, 3, 3, -3, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447138
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4h', 'multiplicity': 1, 'nt': [12, 81], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 2, 2, -2, 2, 2, -2, -1, -1, 1, 0, 0, 0, 0, 0, 0, 3, 0, -3, -3, 3, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447139
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4i', 'multiplicity': 2, 'nt': [24, 229], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 0, 0, 0, 4, -4, 4, -4, 4, 4, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2447140
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '288.571', 'group_order': 288, 'image': None, 'label': '288.571.4j', 'multiplicity': 2, 'nt': [24, 229], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 0, 0, 0, -4, 4, 4, 4, -4, 4, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 3130029
    {'center': '1.a1', 'center_index': 1, 'center_order': 288, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 288, 'label': '288.571.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 3130040
    {'center': '1.a1', 'center_index': 1, 'center_order': 288, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 144, 'label': '288.571.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 3130051
    {'center': '1.a1', 'center_index': 1, 'center_order': 288, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 144, 'label': '288.571.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3130062
    {'center': '1.a1', 'center_index': 1, 'center_order': 288, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 144, 'label': '288.571.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3130066
    {'center': '1.a1', 'center_index': 1, 'center_order': 288, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 144, 'label': '288.571.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 3130067
    {'center': '1.a1', 'center_index': 1, 'center_order': 288, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 144, 'label': '288.571.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 3130068
    {'center': '1.a1', 'center_index': 1, 'center_order': 288, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 144, 'label': '288.571.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3130069
    {'center': '1.a1', 'center_index': 1, 'center_order': 288, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 144, 'label': '288.571.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3130070
    {'center': '6.a1', 'center_index': 6, 'center_order': 48, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 48, 'label': '288.571.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130030
    {'center': '6.a1', 'center_index': 6, 'center_order': 48, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 48, 'label': '288.571.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3130031
    {'center': '4.a1', 'center_index': 4, 'center_order': 72, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 36, 'label': '288.571.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130032
    {'center': '4.a1', 'center_index': 4, 'center_order': 72, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 36, 'label': '288.571.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130033
    {'center': '4.a1', 'center_index': 4, 'center_order': 72, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 36, 'label': '288.571.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 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]]]}
  • id: 3130034
    {'center': '4.a1', 'center_index': 4, 'center_order': 72, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 36, 'label': '288.571.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 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]]]}
  • id: 3130035
    {'center': '4.b1', 'center_index': 4, 'center_order': 72, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1', 'kernel_order': 36, 'label': '288.571.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130036
    {'center': '4.b1', 'center_index': 4, 'center_order': 72, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1', 'kernel_order': 36, 'label': '288.571.2h', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130037
    {'center': '6.a1', 'center_index': 6, 'center_order': 48, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 24, 'label': '288.571.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 3130038
    {'center': '6.a1', 'center_index': 6, 'center_order': 48, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 24, 'label': '288.571.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 3130039
    {'center': '6.a1', 'center_index': 6, 'center_order': 48, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 24, 'label': '288.571.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130041
    {'center': '6.a1', 'center_index': 6, 'center_order': 48, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 24, 'label': '288.571.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130042
    {'center': '6.a1', 'center_index': 6, 'center_order': 48, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 24, 'label': '288.571.2m', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130043
    {'center': '6.a1', 'center_index': 6, 'center_order': 48, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 24, 'label': '288.571.2n', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 3130044
    {'center': '12.a1', 'center_index': 12, 'center_order': 24, 'counter': 23, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 12, 'label': '288.571.2o1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 3130045
    {'center': '12.a1', 'center_index': 12, 'center_order': 24, 'counter': 24, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 12, 'label': '288.571.2o2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 3130046
    {'center': '12.a1', 'center_index': 12, 'center_order': 24, 'counter': 25, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 12, 'label': '288.571.2p1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 3130047
    {'center': '12.a1', 'center_index': 12, 'center_order': 24, 'counter': 26, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 12, 'label': '288.571.2p2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 3130048
    {'center': '12.a1', 'center_index': 12, 'center_order': 24, 'counter': 27, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 12, 'label': '288.571.2q1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 3130049
    {'center': '12.a1', 'center_index': 12, 'center_order': 24, 'counter': 28, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 12, 'label': '288.571.2q2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 3130050
    {'center': '12.a1', 'center_index': 12, 'center_order': 24, 'counter': 29, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 12, 'label': '288.571.2r1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 3130052
    {'center': '12.a1', 'center_index': 12, 'center_order': 24, 'counter': 30, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 12, 'label': '288.571.2r2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 3130053
    {'center': '36.a1', 'center_index': 36, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 8, 'label': '288.571.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130054
    {'center': '24.b1', 'center_index': 24, 'center_order': 12, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 6, 'label': '288.571.4b', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[-4, 0]], [[-4, 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]]]}
  • id: 3130055
    {'center': '24.b1', 'center_index': 24, 'center_order': 12, 'counter': 33, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 6, 'label': '288.571.4c', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130056
    {'center': '24.b1', 'center_index': 24, 'center_order': 12, 'counter': 34, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1', 'kernel_order': 6, 'label': '288.571.4d', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 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]]]}
  • id: 3130057
    {'center': '24.b1', 'center_index': 24, 'center_order': 12, 'counter': 35, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1', 'kernel_order': 6, 'label': '288.571.4e', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130058
    {'center': '36.a1', 'center_index': 36, 'center_order': 8, 'counter': 36, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 4, 'label': '288.571.4f', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130059
    {'center': '72.a1', 'center_index': 72, 'center_order': 4, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '144.154', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1', 'kernel_order': 2, 'label': '288.571.4g', 'nt': [12, 81], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130060
    {'center': '72.a1', 'center_index': 72, 'center_order': 4, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '144.154', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1', 'kernel_order': 2, 'label': '288.571.4h', 'nt': [12, 81], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130061
    {'center': '72.a1', 'center_index': 72, 'center_order': 4, 'counter': 39, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 2, 'label': '288.571.4i1', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130063
    {'center': '72.a1', 'center_index': 72, 'center_order': 4, 'counter': 40, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 2, 'label': '288.571.4i2', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130064
    {'center': '72.a1', 'center_index': 72, 'center_order': 4, 'counter': 41, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 2, 'label': '288.571.4j1', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3130065
    {'center': '72.a1', 'center_index': 72, 'center_order': 4, 'counter': 42, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '288.571', 'group_counter': 571, 'group_order': 288, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 2, 'label': '288.571.4j2', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-2, 1], [-2, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 51640827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 288, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '288.571.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.571', 'subgroup_hash': 571, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640887
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 144, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 144, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.170', 'subgroup_hash': 170, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 144, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, '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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 72, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 72, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640839
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640859
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640860
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640871
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640882
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '288.571.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, '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': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 2}
  • id: 51640884
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640886
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640893
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640897
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640899
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.12.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640904
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640907
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 51640912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640915
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640916
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640917
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640918
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640926
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 75, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.24.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640927
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640929
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640934
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640935
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640936
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.24.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640937
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.24.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 51640938
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.24.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '288.571.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 51640940
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 8, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51640944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51640945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51640946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51640947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 51640949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640950
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 97, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.571.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640951
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 98, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.571.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.36', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640952
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 99, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.571.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640829
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640830
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.48.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640831
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.48.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51640832
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.48.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640833
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.48.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640834
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.48.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640835
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.48.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640836
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.48.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '288.571.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640838
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640840
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.72.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640841
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640842
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640843
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640847
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51640848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '288.571.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51640849
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 119, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.571.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.89', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 89, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:D_{12}', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 51640851
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.96.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 51640852
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 121, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.571.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.144', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 144, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{12}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 51640853
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 2, 'counter': 122, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '288.571.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.154', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 154, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 51640854
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 51640855
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 51640856
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '288.571.144.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 51640857
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '288.571', 'ambient_counter': 571, 'ambient_order': 288, 'ambient_tex': 'D_6:D_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 1, 'counter': 126, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '288.571.288.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '288.571', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 571, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_{12}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 51640846
    {'ambient': '288.571', 'aut_centralizer_order': 128, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1', '24.t1', '36.f1', '36.i1'], 'contains': ['144.b1', '144.e1'], 'core': '144.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [1409, -1, 6433, -1], 'generators': [74, 144], 'label': '288.571.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1', 'old_label': '72.h1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640847
    {'ambient': '288.571', 'aut_centralizer_order': 1152, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1', '24.v1', '36.a1', '36.i1'], 'contains': ['144.b1'], 'core': '144.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1161, -1, 5269, -1], 'generators': [72], 'label': '288.571.72.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '72.i1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640827
    {'ambient': '288.571', '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': '72.a1', 'complements': ['288.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '3.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7561, 3175, 6215, 3194], 'generators': [1, 8, 144, 2, 96, 72, 156], 'label': '288.571.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51640828
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '288.889', 'aut_weyl_index': 16, 'centralizer': '72.a1', 'complements': ['72.j1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.b1', '8.f1', '8.i1', '12.k1', '12.l1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4509, 2852, 7149, 2672], 'generators': [74, 96, 156, 144, 8], 'label': '288.571.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.b1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51640829
    {'ambient': '288.571', 'aut_centralizer_order': 576, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '24.h1', '24.k1', '24.n1'], 'contains': ['96.b1', '144.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2042, -1, 4861, -1], 'generators': [12, 96], 'label': '288.571.48.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '48.d1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640830
    {'ambient': '288.571', 'aut_centralizer_order': 1152, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.n1', '24.r1', '24.t1', '24.v1'], 'contains': ['96.b1', '144.b1'], 'core': '144.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [630, -1, 4702, -1], 'generators': [144, 96], 'label': '288.571.48.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '48.e1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640831
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '24.c1', '24.d1', '24.o1', '24.w1'], 'contains': ['96.a1', '144.c1'], 'core': '96.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3800, -1, 2460, -1], 'generators': [3, 104], 'label': '288.571.48.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.f1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640832
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '24.a1', '24.e1', '24.p1', '24.w1'], 'contains': ['96.a1', '144.c1'], 'core': '96.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4097, -1, 2618, -1], 'generators': [3, 8], 'label': '288.571.48.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.g1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640833
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '24.f1', '24.g1', '24.q1', '24.w1'], 'contains': ['96.a1', '144.d1'], 'core': '96.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3513, -1, 1828, -1], 'generators': [2, 104], 'label': '288.571.48.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.h1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640834
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '24.h1', '24.r1'], 'contains': ['96.b1', '144.d1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [845, -1, 2302, -1], 'generators': [2, 96], 'label': '288.571.48.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.i1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640835
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '24.i1', '24.j1', '24.s1'], 'contains': ['96.a1', '144.e1'], 'core': '96.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4493, -1, 6903, -1], 'generators': [74, 104], 'label': '288.571.48.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1', 'old_label': '48.j1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640836
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '24.k1', '24.t1'], 'contains': ['96.b1', '144.e1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1638, -1, 6696, -1], 'generators': [74, 96], 'label': '288.571.48.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '48.k1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640837
    {'ambient': '288.571', 'aut_centralizer_order': 2304, 'aut_label': '72.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.n1', '36.a1', '36.d1', '36.e1', '36.f1', '36.g1'], 'contains': ['144.a1', '144.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5995, 6078, 5438, 6678], 'generators': [156, 144], 'label': '288.571.72.a1', 'mobius_quo': 2, 'mobius_sub': -72, 'normal_closure': '72.a1', 'normal_contained_in': ['24.b1', '36.a1'], 'normal_contains': ['144.a1', '144.b1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '72.46', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.46', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640838
    {'ambient': '288.571', 'aut_centralizer_order': 192, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.c1', '36.b1', '36.c1', '36.d1'], 'contains': ['144.a1', '144.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7605, -1, 4217, -1], 'generators': [3, 12], 'label': '288.571.72.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.b1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640839
    {'ambient': '288.571', 'aut_centralizer_order': 144, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 144, 'centralizer': '4.d1', 'complements': ['72.j1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.b1', '8.j1', '12.b1', '12.n1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3723, 8590, 5045, 8115], 'generators': [72, 144, 156, 8, 96], 'label': '288.571.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.b1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640840
    {'ambient': '288.571', 'aut_centralizer_order': 192, 'aut_label': '72.b2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.e1', '36.c1', '36.d1'], 'contains': ['144.a1', '144.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5724, -1, 3328, -1], 'generators': [3, 156], 'label': '288.571.72.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '72.b2', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640841
    {'ambient': '288.571', 'aut_centralizer_order': 64, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '24.g1', '24.h1', '36.c1', '36.e1'], 'contains': ['144.a1', '144.d1'], 'core': '144.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5317, -1, 2968, -1], 'generators': [2, 12], 'label': '288.571.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '72.c1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640842
    {'ambient': '288.571', 'aut_centralizer_order': 64, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '36.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.i1', '24.j1', '24.k1', '36.b1', '36.f1'], 'contains': ['144.a1', '144.e1'], 'core': '144.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6170, -1, 7406, -1], 'generators': [74, 12], 'label': '288.571.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.d1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640843
    {'ambient': '288.571', 'aut_centralizer_order': 192, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '12.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.l1', '24.m1', '36.b1', '36.g1'], 'contains': ['144.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8658, -1, 8014, -1], 'generators': [75], 'label': '288.571.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '72.e1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640844
    {'ambient': '288.571', 'aut_centralizer_order': 192, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.o1', '24.p1', '36.d1', '36.h1'], 'contains': ['144.b1', '144.c1'], 'core': '144.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3444, -1, 3148, -1], 'generators': [3, 144], 'label': '288.571.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '72.f1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640845
    {'ambient': '288.571', 'aut_centralizer_order': 128, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.q1', '24.r1', '36.e1', '36.h1', '36.i1'], 'contains': ['144.b1', '144.d1'], 'core': '144.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [1636, -1, 2788, -1], 'generators': [2, 144], 'label': '288.571.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.g1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640848
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.w1', '36.c1', '36.h1'], 'contains': ['144.c1', '144.d1'], 'core': '288.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4691, -1, 2133, -1], 'generators': [1, 2], 'label': '288.571.72.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '72.j1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640849
    {'ambient': '288.571', 'aut_centralizer_order': 1152, 'aut_label': '96.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1', 'complements': ['3.a1'], 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '48.a1', '48.b1', '48.c1', '48.f1', '48.g1', '48.h1', '48.j1'], 'contains': ['288.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3788, 3008, 4048, 4503], 'generators': [104], 'label': '288.571.96.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': ['32.a1', '48.a1', '48.b1', '48.c1'], 'normal_contains': ['288.a1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '288.571', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.21', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640850
    {'ambient': '288.571', 'aut_centralizer_order': 48, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '24.b1', 'complements': ['72.j1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.e1'], 'contains': ['8.b1', '8.g1', '12.c1', '12.m1'], 'core': '4.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [7736, 4689, 8471, 6491], 'generators': [75, 8, 144, 96, 156], 'label': '288.571.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1', '2.b1', '2.e1'], 'normal_contains': ['8.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640851
    {'ambient': '288.571', 'aut_centralizer_order': 1152, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.d1', '48.e1', '48.i1', '48.k1'], 'contains': ['288.a1'], 'core': '288.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1882, -1, 4228, -1], 'generators': [96], 'label': '288.571.96.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '96.b1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640852
    {'ambient': '288.571', 'aut_centralizer_order': 2304, 'aut_label': '144.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['48.a1', '48.b1', '48.d1', '72.a1', '72.b1', '72.b2', '72.c1', '72.d1', '72.e1'], 'contains': ['288.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6069, 5197, 4544, 5920], 'generators': [12], 'label': '288.571.144.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': ['48.a1', '48.b1', '72.a1'], 'normal_contains': ['288.a1'], 'normalizer': '1.a1', 'old_label': '144.a1', 'projective_image': '144.144', 'quotient_action_image': '1.1', 'quotient_action_kernel': '144.144', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640853
    {'ambient': '288.571', 'aut_centralizer_order': 4608, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '48.e1', '72.a1', '72.f1', '72.g1', '72.h1', '72.i1'], 'contains': ['288.a1'], 'core': '144.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1840, 4315, 4386, 5212], 'generators': [144], 'label': '288.571.144.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.b1', 'normal_contained_in': ['48.c1', '72.a1'], 'normal_contains': ['288.a1'], 'normalizer': '1.a1', 'old_label': '144.b1', 'projective_image': '144.154', 'quotient_action_image': '1.1', 'quotient_action_kernel': '144.154', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640854
    {'ambient': '288.571', 'aut_centralizer_order': 192, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '6.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.f1', '48.g1', '72.b1', '72.b2', '72.f1', '72.j1'], 'contains': ['288.a1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4111, -1, 3148, -1], 'generators': [3], 'label': '288.571.144.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '144.c1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640855
    {'ambient': '288.571', 'aut_centralizer_order': 128, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.h1', '48.i1', '72.c1', '72.g1', '72.j1'], 'contains': ['288.a1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2658, -1, 2546, -1], 'generators': [2], 'label': '288.571.144.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '144.d1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640856
    {'ambient': '288.571', 'aut_centralizer_order': 128, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '36.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1', '48.k1', '72.d1', '72.h1'], 'contains': ['288.a1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2816, -1, 6696, -1], 'generators': [74], 'label': '288.571.144.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '144.e1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640857
    {'ambient': '288.571', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '96.b1', '144.a1', '144.b1', '144.c1', '144.d1', '144.e1'], 'contains': [], 'core': '288.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2816, 4315, 4228, 5212], 'generators': [], 'label': '288.571.288.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '288.a1', 'normal_contained_in': ['96.a1', '144.a1', '144.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '288.a1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640858
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.f1', '8.g1', '12.d1', '12.e1'], 'core': '8.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7184, -1, 9213, -1], 'generators': [1, 96, 74, 156, 8], 'label': '288.571.4.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.f1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51640859
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1'], 'contains': ['8.a1', '8.d1', '8.e1', '8.k1', '12.f1', '12.g1'], 'core': '8.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5253, -1, 2043, -1], 'generators': [1, 96, 2, 12, 8], 'label': '288.571.4.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.g1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51640860
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.889', 'aut_weyl_index': 16, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['8.c1', '8.h1', '8.k1', '12.o1'], 'core': '8.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [3010, -1, 684, -1], 'generators': [1, 96, 2, 144, 8], 'label': '288.571.4.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.h1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51640861
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 16, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1'], 'contains': ['8.c1', '8.i1', '8.j1', '12.p1', '12.q1'], 'core': '8.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2151, -1, 4735, -1], 'generators': [2, 96, 72, 144, 8], 'label': '288.571.4.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '4.i1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 51640862
    {'ambient': '288.571', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '24.b1', 'complements': ['48.i1', '48.h1', '48.g1', '48.k1', '48.j1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.c1', '18.b1'], 'core': '6.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8771, 8381, 6046, 9375], 'generators': [3, 8, 72, 12, 144], 'label': '288.571.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.a1', '12.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '72.46', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640863
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.c1', '12.d1', '12.h1', '12.k1', '18.a1'], 'core': '12.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [8413, -1, 7742, -1], 'generators': [1, 8, 74, 144, 156], 'label': '288.571.6.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640864
    {'ambient': '288.571', 'aut_centralizer_order': 24, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.b1', '12.h1', '12.m1', '18.b1'], 'core': '12.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7951, -1, 6354, -1], 'generators': [3, 144, 72, 104, 12], 'label': '288.571.6.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51640865
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 8, 'centralizer': '72.a1', 'complements': ['144.d1', '144.c1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.e1', '4.f1', '6.b1', '6.d1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7750, 5156, 7742, 5074], 'generators': [1, 96, 8, 74, 144, 156], 'label': '288.571.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51640866
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.e1', '12.k1', '12.m1', '18.a1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9044, -1, 8106, -1], 'generators': [1, 104, 74, 144, 156], 'label': '288.571.6.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640867
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '12.f1', '12.g1', '12.h1', '12.i1', '12.o1', '18.c1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6740, -1, 3288, -1], 'generators': [1, 104, 2, 156, 144], 'label': '288.571.6.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640868
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.b1', '12.i1', '12.k1', '12.p1', '18.d1'], 'core': '12.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [5774, -1, 5405, -1], 'generators': [2, 104, 72, 156, 144], 'label': '288.571.6.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640869
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 24, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1'], 'contains': ['12.j1', '12.l1', '12.n1', '12.q1', '18.d1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [793, -1, 5765, -1], 'generators': [2, 96, 72, 156, 144], 'label': '288.571.6.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '6.g1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640870
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.e1', '3.a1'], 'contains': ['12.c1', '12.i1', '12.m1', '18.e1'], 'core': '12.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [9319, -1, 7456, -1], 'generators': [73, 104, 2, 12, 144], 'label': '288.571.6.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640871
    {'ambient': '288.571', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.b1', 'complements': ['36.i1', '36.b1'], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.f1', '4.g1'], 'contains': ['16.a1', '16.c1', '24.a1', '24.c1'], 'core': '8.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6184, 4959, 3528, 4631], 'generators': [3, 12, 96, 8], 'label': '288.571.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.a1', '24.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '144.144', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640872
    {'ambient': '288.571', 'aut_centralizer_order': 576, 'aut_label': '8.b1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.b1', '24.b1', '24.n1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4081, 3808, 4814, 3558], 'generators': [156, 144, 8, 96], 'label': '288.571.8.b1', 'mobius_quo': 2, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.b1', '24.b1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640873
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.186', 'aut_weyl_index': 32, 'centralizer': '72.a1', 'complements': ['36.b1'], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.h1', '4.i1'], 'contains': ['16.b1', '16.d1', '24.q1', '24.r1'], 'core': '8.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [1993, 1411, 684, 1590], 'generators': [2, 144, 8, 96], 'label': '288.571.8.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.b1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '144.154', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51640874
    {'ambient': '288.571', 'aut_centralizer_order': 48, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.g1'], 'contains': ['16.a1', '16.c1', '24.d1', '24.e1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4633, -1, 2364, -1], 'generators': [3, 156, 96, 8], 'label': '288.571.8.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.d1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640875
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.g1'], 'contains': ['16.a1', '16.d1', '24.f1', '24.g1', '24.h1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3737, -1, 1049, -1], 'generators': [2, 12, 8, 96], 'label': '288.571.8.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.e1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51640876
    {'ambient': '288.571', 'aut_centralizer_order': 12, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '24.b1', 'complements': ['144.d1', '144.c1', '144.e1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.e1', '6.a1', '6.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7358, 7002, 6046, 6826], 'generators': [3, 8, 144, 72, 96, 12], 'label': '288.571.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '4.e1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640877
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.f1'], 'contains': ['16.a1', '16.e1', '24.i1', '24.j1', '24.k1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4955, -1, 9072, -1], 'generators': [74, 12, 8, 96], 'label': '288.571.8.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.f1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51640878
    {'ambient': '288.571', 'aut_centralizer_order': 48, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '4.f1'], 'contains': ['16.a1', '24.l1', '24.m1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7401, -1, 9836, -1], 'generators': [75, 96, 156, 8], 'label': '288.571.8.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.g1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640879
    {'ambient': '288.571', 'aut_centralizer_order': 48, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.h1'], 'contains': ['16.b1', '16.c1', '24.o1', '24.p1'], 'core': '16.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3238, -1, 1380, -1], 'generators': [3, 144, 96, 8], 'label': '288.571.8.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.h1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640880
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.186', 'aut_weyl_index': 32, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.i1'], 'contains': ['16.b1', '16.e1', '24.s1', '24.t1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2428, -1, 6496, -1], 'generators': [74, 144, 8, 96], 'label': '288.571.8.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.i1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 51640881
    {'ambient': '288.571', 'aut_centralizer_order': 144, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '4.i1'], 'contains': ['16.b1', '24.u1', '24.v1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1561, -1, 4544, -1], 'generators': [72, 8, 96, 144], 'label': '288.571.8.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.j1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640882
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '72.40', 'aut_weyl_index': 64, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.g1', '4.h1'], 'contains': ['16.c1', '16.d1', '24.w1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2961, -1, 69, -1], 'generators': [1, 2, 8, 96], 'label': '288.571.8.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.k1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51640883
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 36, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.a1', '18.b1', '18.c1', '18.d1', '18.e1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9706, -1, 6751, -1], 'generators': [1, 2, 72], 'label': '288.571.9.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51640884
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '12.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.a1', '6.d1', '6.e1'], 'contains': ['24.a1', '24.b1', '24.e1', '24.p1', '36.d1'], 'core': '12.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7698, 6007, 4193, 6068], 'generators': [3, 156, 144, 8], 'label': '288.571.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640885
    {'ambient': '288.571', 'aut_centralizer_order': 288, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '4.d1', 'complements': ['24.w1'], 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.a1', '6.c1', '6.f1'], 'contains': ['24.b1', '24.u1', '36.a1'], 'core': '12.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6777, 9398, 5475, 9286], 'generators': [72, 156, 104, 144], 'label': '288.571.12.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': ['4.d1', '6.a1'], 'normal_contains': ['24.b1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640886
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '24.b1', 'complements': ['24.w1'], 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '6.a1', '6.b1', '6.h1'], 'contains': ['24.b1', '24.m1', '36.g1'], 'core': '12.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9102, 7687, 8348, 7662], 'generators': [75, 144, 156, 8], 'label': '288.571.12.c1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1', 'normal_contained_in': ['4.e1', '6.a1'], 'normal_contains': ['24.b1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640887
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.90180', 'aut_weyl_index': 4, 'centralizer': '72.a1', 'complements': ['144.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.g1', '4.h1', '6.e1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5737, 1733, 3099, 507], 'generators': [1, 96, 8, 2, 156, 144], 'label': '288.571.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51640888
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '6.b1'], 'contains': ['24.c1', '24.i1', '24.m1', '36.b1'], 'core': '48.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7962, -1, 9356, -1], 'generators': [1, 74, 156, 8], 'label': '288.571.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.d1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640889
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '6.d1'], 'contains': ['24.a1', '24.j1', '24.l1', '36.b1'], 'core': '24.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8237, -1, 9555, -1], 'generators': [1, 74, 156, 104], 'label': '288.571.12.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '12.e1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640890
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.g1', '6.e1'], 'contains': ['24.c1', '24.e1', '24.f1', '24.w1', '36.c1'], 'core': '48.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5115, -1, 1701, -1], 'generators': [1, 2, 12, 104], 'label': '288.571.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.f1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640891
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.g1', '6.e1'], 'contains': ['24.a1', '24.d1', '24.g1', '24.w1', '36.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5528, -1, 2043, -1], 'generators': [1, 2, 12, 8], 'label': '288.571.12.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.g1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640892
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.b1', '6.c1', '6.e1'], 'contains': ['24.b1', '24.c1', '24.d1', '24.o1', '36.d1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7282, -1, 3848, -1], 'generators': [3, 156, 144, 104], 'label': '288.571.12.h1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.h1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640893
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.e1', '6.f1', '6.h1'], 'contains': ['24.b1', '24.f1', '24.g1', '24.q1', '36.e1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6104, -1, 2684, -1], 'generators': [2, 156, 144, 104], 'label': '288.571.12.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.i1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640894
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.g1'], 'contains': ['24.h1', '24.n1', '24.r1', '36.e1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [975, -1, 3027, -1], 'generators': [2, 156, 144, 96], 'label': '288.571.12.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '12.j1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640895
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.b1', '6.d1', '6.f1'], 'contains': ['24.b1', '24.i1', '24.j1', '24.s1', '36.f1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6435, -1, 7691, -1], 'generators': [74, 156, 144, 104], 'label': '288.571.12.k1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.k1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640896
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.g1'], 'contains': ['24.k1', '24.n1', '24.t1', '36.f1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1307, -1, 7348, -1], 'generators': [74, 156, 144, 96], 'label': '288.571.12.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '12.l1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640897
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '6.c1', '6.d1', '6.h1'], 'contains': ['24.b1', '24.l1', '36.g1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8669, -1, 8710, -1], 'generators': [75, 144, 104, 156], 'label': '288.571.12.m1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.m1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640898
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.90180', 'aut_weyl_index': 4, 'centralizer': '72.a1', 'complements': ['144.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.d1', '4.i1', '6.f1', '6.g1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4111, 3175, 5405, 3194], 'generators': [2, 96, 8, 72, 156, 144], 'label': '288.571.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51640899
    {'ambient': '288.571', 'aut_centralizer_order': 144, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.g1'], 'contains': ['24.n1', '24.v1', '36.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [553, -1, 5833, -1], 'generators': [72, 156, 96, 144], 'label': '288.571.12.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '12.n1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640900
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.h1', '6.e1'], 'contains': ['24.o1', '24.p1', '24.q1', '24.w1', '36.h1'], 'core': '48.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [3521, -1, 330, -1], 'generators': [1, 2, 144, 104], 'label': '288.571.12.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.o1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640901
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '6.f1'], 'contains': ['24.q1', '24.s1', '24.u1', '36.i1'], 'core': '48.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [2854, -1, 5003, -1], 'generators': [2, 72, 144, 104], 'label': '288.571.12.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.p1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640902
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '6.g1'], 'contains': ['24.r1', '24.t1', '24.v1', '36.i1'], 'core': '144.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [76, -1, 5199, -1], 'generators': [2, 72, 144, 96], 'label': '288.571.12.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '12.q1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640903
    {'ambient': '288.571', 'aut_centralizer_order': 576, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.b1', '8.d1', '8.e1', '8.f1', '8.g1'], 'contains': ['32.a1', '48.a1', '48.b1', '48.d1'], 'core': '16.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4489, 3704, 4740, 4631], 'generators': [12, 8, 96], 'label': '288.571.16.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['32.a1', '48.a1', '48.b1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '144.144', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640904
    {'ambient': '288.571', 'aut_centralizer_order': 576, 'aut_label': '16.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.c1', '8.h1', '8.i1', '8.j1'], 'contains': ['32.a1', '48.c1', '48.e1'], 'core': '16.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1862, 2293, 3624, 3292], 'generators': [144, 8, 96], 'label': '288.571.16.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.b1', '8.c1'], 'normal_contains': ['32.a1', '48.c1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '144.154', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640905
    {'ambient': '288.571', 'aut_centralizer_order': 48, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.d1', '8.h1', '8.k1'], 'contains': ['32.a1', '48.f1', '48.g1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3875, -1, 1442, -1], 'generators': [3, 96, 8], 'label': '288.571.16.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.c1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640906
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.40', 'aut_weyl_index': 64, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '8.e1', '8.k1'], 'contains': ['32.a1', '48.h1', '48.i1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2104, -1, 853, -1], 'generators': [2, 8, 96], 'label': '288.571.16.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.d1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51640907
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.40', 'aut_weyl_index': 64, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '8.i1'], 'contains': ['32.a1', '48.j1', '48.k1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2990, -1, 6927, -1], 'generators': [74, 8, 96], 'label': '288.571.16.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.e1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51640908
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '6.d1', '9.a1'], 'contains': ['36.b1', '36.d1', '36.f1', '36.g1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9557, -1, 8014, -1], 'generators': [1, 74, 144], 'label': '288.571.18.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51640909
    {'ambient': '288.571', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.90180', 'aut_weyl_index': 4, 'centralizer': '72.a1', 'complements': ['144.c1', '144.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.e1', '6.h1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [8245, 602, 7037, 1580], 'generators': [73, 96, 8, 2, 12, 144], 'label': '288.571.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51640910
    {'ambient': '288.571', 'aut_centralizer_order': 48, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.c1', '9.a1'], 'contains': ['36.a1', '36.d1', '36.g1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9208, -1, 6804, -1], 'generators': [3, 72], 'label': '288.571.18.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51640911
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.27', 'aut_weyl_index': 144, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '9.a1'], 'contains': ['36.c1', '36.d1', '36.e1', '36.h1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8189, -1, 3288, -1], 'generators': [1, 2, 156, 144], 'label': '288.571.18.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.c1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640912
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.27', 'aut_weyl_index': 144, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.g1', '9.a1'], 'contains': ['36.a1', '36.e1', '36.f1', '36.i1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4798, -1, 6163, -1], 'generators': [2, 72, 156], 'label': '288.571.18.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51640913
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.27', 'aut_weyl_index': 144, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '9.a1'], 'contains': ['36.e1', '36.g1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9937, -1, 7052, -1], 'generators': [73, 2], 'label': '288.571.18.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.e1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51640914
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.a1', 'complements': ['12.q1', '12.p1', '12.e1'], 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.a1', '12.e1', '12.g1'], 'contains': ['48.b1', '48.g1', '72.b1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7536, 5000, 4331, 5655], 'generators': [3, 12, 8], 'label': '288.571.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['48.b1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '144.144', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640915
    {'ambient': '288.571', 'aut_centralizer_order': 1152, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '12.a1', '12.b1', '12.c1', '12.h1', '12.i1', '12.k1', '12.m1'], 'contains': ['48.a1', '48.b1', '48.c1', '72.a1'], 'core': '24.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7314, 6078, 5232, 6678], 'generators': [156, 144, 104], 'label': '288.571.24.b1', 'mobius_quo': -2, 'mobius_sub': 24, 'normal_closure': '24.b1', 'normal_contained_in': ['8.b1', '12.a1', '12.b1', '12.c1'], 'normal_contains': ['48.a1', '48.b1', '48.c1', '72.a1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '72.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640916
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.d1', '12.f1', '12.h1'], 'contains': ['48.a1', '48.f1', '72.b1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7024, -1, 4103, -1], 'generators': [3, 12, 104], 'label': '288.571.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.c1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640917
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '12.g1', '12.h1'], 'contains': ['48.b1', '48.f1', '72.b2'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5869, -1, 3326, -1], 'generators': [3, 156, 104], 'label': '288.571.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.d1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640918
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '12.a1', '12.f1'], 'contains': ['48.a1', '48.g1', '72.b2'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5404, -1, 3097, -1], 'generators': [3, 156, 8], 'label': '288.571.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '24.e1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640919
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '12.f1', '12.i1'], 'contains': ['48.a1', '48.h1', '72.c1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4412, -1, 1828, -1], 'generators': [2, 12, 104], 'label': '288.571.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.f1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640920
    {'ambient': '288.571', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 12, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '6.d1', '6.e1', '6.f1', '6.h1', '9.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8507, -1, 6385, -1], 'generators': [1, 104, 144, 2, 72, 156], 'label': '288.571.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640921
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '12.g1', '12.i1'], 'contains': ['48.b1', '48.h1', '72.c1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5213, -1, 1986, -1], 'generators': [2, 12, 8], 'label': '288.571.24.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.g1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640922
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '12.j1'], 'contains': ['48.d1', '48.i1', '72.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1422, -1, 2302, -1], 'generators': [2, 12, 96], 'label': '288.571.24.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '24.h1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640923
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '12.d1', '12.k1'], 'contains': ['48.a1', '48.j1', '72.d1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6625, -1, 7564, -1], 'generators': [74, 12, 104], 'label': '288.571.24.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.i1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640924
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '12.e1', '12.k1'], 'contains': ['48.b1', '48.j1', '72.d1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [6783, -1, 7722, -1], 'generators': [74, 12, 8], 'label': '288.571.24.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.j1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640925
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '12.l1'], 'contains': ['48.d1', '48.k1', '72.d1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3061, -1, 7406, -1], 'generators': [74, 12, 96], 'label': '288.571.24.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '24.k1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640926
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.g1', '12.e1', '12.m1'], 'contains': ['48.b1', '72.e1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8831, -1, 8710, -1], 'generators': [75, 104, 156], 'label': '288.571.24.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.l1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640927
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '24.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.g1', '12.c1', '12.d1'], 'contains': ['48.a1', '72.e1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8477, -1, 8348, -1], 'generators': [75, 156, 8], 'label': '288.571.24.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.m1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640928
    {'ambient': '288.571', 'aut_centralizer_order': 576, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.j1', '12.l1', '12.n1'], 'contains': ['48.d1', '48.e1', '72.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [943, -1, 5723, -1], 'generators': [156, 144, 96], 'label': '288.571.24.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '24.n1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640929
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.h1', '12.h1', '12.o1'], 'contains': ['48.c1', '48.f1', '72.f1'], 'core': '48.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [3444, -1, 2531, -1], 'generators': [3, 144, 104], 'label': '288.571.24.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.o1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640930
    {'ambient': '288.571', 'aut_centralizer_order': 96, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.h1', '12.a1', '12.o1'], 'contains': ['48.c1', '48.g1', '72.f1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [3666, -1, 2759, -1], 'generators': [3, 144, 8], 'label': '288.571.24.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '24.p1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640931
    {'ambient': '288.571', 'aut_centralizer_order': 48, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '24.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.b1', '8.d1', '8.h1', '12.a1', '12.h1'], 'core': '4.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6184, 6650, 3848, 4631], 'generators': [3, 8, 156, 144, 96], 'label': '288.571.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.b1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 51640932
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '12.i1', '12.o1', '12.p1'], 'contains': ['48.c1', '48.h1', '72.g1'], 'core': '48.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [2321, -1, 1670, -1], 'generators': [2, 144, 104], 'label': '288.571.24.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.q1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640933
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '12.j1', '12.q1'], 'contains': ['48.e1', '48.i1', '72.g1'], 'core': '144.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [63, -1, 2144, -1], 'generators': [2, 144, 96], 'label': '288.571.24.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '24.r1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640934
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.i1', '12.k1', '12.p1'], 'contains': ['48.c1', '48.j1', '72.h1'], 'core': '48.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [2168, -1, 6409, -1], 'generators': [74, 144, 104], 'label': '288.571.24.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.s1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640935
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.i1', '12.l1', '12.q1'], 'contains': ['48.e1', '48.k1', '72.h1'], 'core': '144.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [640, -1, 6567, -1], 'generators': [74, 144, 96], 'label': '288.571.24.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '24.t1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51640936
    {'ambient': '288.571', 'aut_centralizer_order': 288, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.j1', '12.b1', '12.p1'], 'contains': ['48.c1', '72.i1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1917, -1, 4986, -1], 'generators': [72, 104, 144], 'label': '288.571.24.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '24.u1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640937
    {'ambient': '288.571', 'aut_centralizer_order': 288, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.j1', '12.n1', '12.q1'], 'contains': ['48.e1', '72.i1'], 'core': '144.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [314, -1, 5478, -1], 'generators': [72, 96, 144], 'label': '288.571.24.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '24.v1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640938
    {'ambient': '288.571', 'aut_centralizer_order': 8, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.k1', '12.f1', '12.g1', '12.o1'], 'contains': ['48.f1', '48.g1', '48.h1', '72.j1'], 'core': '96.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3973, -1, 1033, -1], 'generators': [1, 2, 104], 'label': '288.571.24.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.w1', 'projective_image': '288.571', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51640939
    {'ambient': '288.571', 'aut_centralizer_order': 576, 'aut_label': '32.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.d1', 'complements': ['9.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1'], 'contains': ['96.a1', '96.b1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2701, 2687, 3879, 3745], 'generators': [8, 96], 'label': '288.571.32.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1'], 'normal_contains': ['96.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '288.571', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640940
    {'ambient': '288.571', 'aut_centralizer_order': 576, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '4.d1', 'complements': ['8.k1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.n1', '18.b1', '18.d1'], 'contains': ['72.a1', '72.i1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5132, 7967, 6180, 8646], 'generators': [72, 156], 'label': '288.571.36.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1', 'normal_contained_in': ['12.b1'], 'normal_contains': ['72.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '72.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640941
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.e1', '18.a1'], 'contains': ['72.b1', '72.d1', '72.e1'], 'core': '144.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8658, -1, 8014, -1], 'generators': [1, 74], 'label': '288.571.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.b1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640942
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.889', 'aut_weyl_index': 16, 'centralizer': '72.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.d1', '2.e1'], 'contains': ['8.b1', '8.c1', '8.e1', '12.i1', '12.j1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4111, 913, 2911, 832], 'generators': [2, 96, 156, 144, 8], 'label': '288.571.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.c1', '2.d1', '2.e1'], 'normal_contains': ['8.b1', '8.c1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 51640943
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.f1', '12.g1', '18.c1'], 'contains': ['72.b1', '72.b2', '72.c1', '72.j1'], 'core': '144.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6362, -1, 2928, -1], 'generators': [1, 2, 12], 'label': '288.571.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.c1', 'projective_image': '144.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640944
    {'ambient': '288.571', 'aut_centralizer_order': 192, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '6.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.h1', '18.a1', '18.b1', '18.c1'], 'contains': ['72.a1', '72.b1', '72.b2', '72.f1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8057, -1, 4500, -1], 'generators': [3, 156, 144], 'label': '288.571.36.d1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.d1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640945
    {'ambient': '288.571', 'aut_centralizer_order': 64, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '12.j1', '18.c1', '18.d1', '18.e1'], 'contains': ['72.a1', '72.c1', '72.g1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6025, -1, 3864, -1], 'generators': [2, 156, 144], 'label': '288.571.36.e1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.e1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640946
    {'ambient': '288.571', 'aut_centralizer_order': 64, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '36.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.l1', '18.a1', '18.d1'], 'contains': ['72.a1', '72.d1', '72.h1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5769, -1, 6736, -1], 'generators': [74, 156, 144], 'label': '288.571.36.f1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.f1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640947
    {'ambient': '288.571', 'aut_centralizer_order': 192, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.m1', '18.a1', '18.b1', '18.e1'], 'contains': ['72.a1', '72.e1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9451, -1, 7177, -1], 'generators': [75, 144], 'label': '288.571.36.g1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.g1', 'projective_image': '72.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640948
    {'ambient': '288.571', 'aut_centralizer_order': 16, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '18.c1'], 'contains': ['72.f1', '72.g1', '72.j1'], 'core': '144.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [4819, -1, 1202, -1], 'generators': [1, 2, 144], 'label': '288.571.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.h1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51640949
    {'ambient': '288.571', 'aut_centralizer_order': 32, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.p1', '12.q1', '18.d1'], 'contains': ['72.g1', '72.h1', '72.i1'], 'core': '144.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [1161, -1, 5952, -1], 'generators': [2, 72], 'label': '288.571.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1', 'old_label': '36.i1', 'projective_image': '144.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51640950
    {'ambient': '288.571', 'aut_centralizer_order': 1152, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '24.b1', '24.c1', '24.e1', '24.f1', '24.i1', '24.m1'], 'contains': ['96.a1', '144.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6668, 5374, 4386, 5212], 'generators': [12, 104], 'label': '288.571.48.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': ['16.a1', '24.b1'], 'normal_contains': ['96.a1', '144.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '144.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640951
    {'ambient': '288.571', 'aut_centralizer_order': 1152, 'aut_label': '48.b1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '24.a1', '24.b1', '24.d1', '24.g1', '24.j1', '24.l1'], 'contains': ['96.a1', '144.a1'], 'core': '48.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7075, 4492, 4544, 5920], 'generators': [12, 8], 'label': '288.571.48.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': ['16.a1', '24.a1', '24.b1'], 'normal_contains': ['96.a1', '144.a1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '144.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.6', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51640952
    {'ambient': '288.571', 'aut_centralizer_order': 1152, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '24.b1', '24.o1', '24.p1', '24.q1', '24.s1', '24.u1'], 'contains': ['96.a1', '144.b1'], 'core': '48.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [2288, 3403, 4048, 4503], 'generators': [144, 104], 'label': '288.571.48.c1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': ['16.b1', '24.b1'], 'normal_contains': ['96.a1', '144.b1'], 'normalizer': '1.a1', 'old_label': '48.c1', 'projective_image': '144.154', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.8', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}