Abstract group data - 224.98

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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': 2, 'aut_exponent': 168, 'aut_gen_orders': [28, 12, 12, 28, 24, 12], 'aut_gens': [[1, 2, 112], [179, 30, 168], [111, 206, 168], [223, 190, 168], [213, 170, 112], [131, 122, 168], [181, 38, 168]], 'aut_group': '10752.cc', 'aut_hash': 8389095923206392224, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10752, 'aut_permdeg': 112, 'aut_perms': [171086972584438360580307852314708670785098599131239204028007282254503095925768633986045530559305148204181422290549773693453078637319394360386163098396851110562687401078196701983280938, 141631846107046487433312820952973208110799663840727044636460105950244221166324344696805437821758666487957919629432802468769364574924299683672923071118960063653135687110806145421498432, 94978248338732118461762519348314757170489666273164774905270428545696428916812452484400278170405444500563451355923342743891894496727206738949879167473285534121404776396727620580769699, 35897119001695964408764846501892713368194447823666380618302342867801223934189640419368257648498778361563072119205187664603066104196108824007155817633970293080141441117104377498377627, 11033061031999831054178658001692784860329855854512707642323712623842349863681169932465803994065811496893748828529656134287551734025102499730417510372874236306587583985814525472877134, 157194376771193328133041169144002584124058865413013527168683612917560550170822850818707524004529209115387237322271440387301268982428884564341199000559934943064418457329597114488407798], 'aut_phi_ratio': 112.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 28, 4, 1], [4, 2, 1, 2], [7, 2, 3, 1], [8, 2, 4, 1], [14, 2, 3, 1], [14, 2, 6, 1], [28, 2, 6, 2], [56, 2, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{28}.(C_6\\times D_4^2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': 336, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 28, 4], [4, 2, 2], [7, 2, 3], [8, 2, 4], [14, 2, 9], [28, 2, 12], [56, 2, 24]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '56.5', 'commutator_count': 1, 'commutator_label': '28.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 98, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['112.6', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 28, 1, 4], [4, 2, 1, 2], [7, 2, 3, 1], [8, 2, 2, 2], [14, 2, 3, 3], [28, 2, 6, 2], [56, 2, 12, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 336, 'exponent': 56, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '56.12', 'hash': 98, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 28, 'inner_gen_orders': [2, 28, 1], 'inner_gens': [[1, 110, 112], [5, 2, 112], [1, 2, 112]], 'inner_hash': 5, 'inner_nilpotent': False, 'inner_order': 56, 'inner_split': None, 'inner_tex': 'D_{28}', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 54]], 'label': '224.98', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, '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': 'C2*D56', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 13, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 62, 'number_divisions': 20, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 76, 'number_subgroups': 494, 'old_label': None, 'order': 224, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 115], [4, 4], [7, 6], [8, 8], [14, 18], [28, 24], [56, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [4, 6, 6, 12, 12], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 198, 168], [15, 94, 168], [1, 174, 112], [15, 206, 112], [1, 178, 168]], 'outer_group': '192.1410', 'outer_hash': 1410, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 48, 'outer_perms': [2630981903594817342696368115697239433965821120039091152967479, 6060459908520279212390579308843339682525696519722900326676447, 5030992199043138030334593593094803832231214001050443004613016, 9782932590955441526998159541377511013371223066289359724044112, 8466218886948651137904170443289232484072296077444432517596736], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 2], [6, 4], [12, 2], [24, 2]], 'representations': {'PC': {'code': 62135312172863081559338910, 'gens': [1, 2, 6], 'pres': [6, -2, -2, -2, -2, -7, -2, 1321, 31, 1946, 50, 2499, 69, 2884]}, 'GLZN': {'d': 2, 'p': 56, 'gens': [176009, 176401, 177185, 2634255, 4744517, 176065]}, 'Perm': {'d': 17, 'gens': [1313941311055, 375930, 378576, 24393, 13050, 23550632582400]}}, 'schur_multiplier': [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': 'C_2\\times D_{56}', 'transitive_degree': 112, '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: 98200148
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 98, 'group_order': 224, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 98200159
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 98, 'group_order': 224, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 112, 'size': 1}
  • id: 98200170
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 98, 'group_order': 224, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 168, 'size': 1}
  • id: 98200181
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 98, 'group_order': 224, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 56, 'size': 1}
  • id: 98200192
    {'aut_label': '2D', 'centralizer': '28.c1.a1', 'counter': 5, 'group_counter': 98, 'group_order': 224, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 147, 'size': 28}
  • id: 98200203
    {'aut_label': '2D', 'centralizer': '28.c1.b1', 'counter': 6, 'group_counter': 98, 'group_order': 224, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 157, 'size': 28}
  • id: 98200207
    {'aut_label': '2D', 'centralizer': '28.c1.b1', 'counter': 7, 'group_counter': 98, 'group_order': 224, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 25, 'size': 28}
  • id: 98200208
    {'aut_label': '2D', 'centralizer': '28.c1.a1', 'counter': 8, 'group_counter': 98, 'group_order': 224, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 19, 'size': 28}
  • id: 98200209
    {'aut_label': '4A', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 98, 'group_order': 224, 'label': '4A', 'order': 4, 'powers': [4, 9, 9], 'representative': 140, 'size': 2}
  • id: 98200149
    {'aut_label': '4B', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 98, 'group_order': 224, 'label': '4B', 'order': 4, 'powers': [4, 10, 10], 'representative': 28, 'size': 2}
  • id: 98200150
    {'aut_label': '7A1', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 98, 'group_order': 224, 'label': '7A1', 'order': 7, 'powers': [12, 13, 1], 'representative': 32, 'size': 2}
  • id: 98200151
    {'aut_label': '7A1', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 98, 'group_order': 224, 'label': '7A2', 'order': 7, 'powers': [13, 11, 1], 'representative': 64, 'size': 2}
  • id: 98200152
    {'aut_label': '7A1', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 98, 'group_order': 224, 'label': '7A3', 'order': 7, 'powers': [11, 12, 1], 'representative': 96, 'size': 2}
  • id: 98200153
    {'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 98, 'group_order': 224, 'label': '8A1', 'order': 8, 'powers': [10, 15, 14], 'representative': 14, 'size': 2}
  • id: 98200154
    {'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 15, 'group_counter': 98, 'group_order': 224, 'label': '8A3', 'order': 8, 'powers': [10, 14, 15], 'representative': 42, 'size': 2}
  • id: 98200155
    {'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 98, 'group_order': 224, 'label': '8B1', 'order': 8, 'powers': [10, 17, 16], 'representative': 126, 'size': 2}
  • id: 98200156
    {'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 17, 'group_counter': 98, 'group_order': 224, 'label': '8B3', 'order': 8, 'powers': [10, 16, 17], 'representative': 154, 'size': 2}
  • id: 98200157
    {'aut_label': '14A1', 'centralizer': '2.b1.a1', 'counter': 18, 'group_counter': 98, 'group_order': 224, 'label': '14A1', 'order': 14, 'powers': [11, 19, 2], 'representative': 128, 'size': 2}
  • id: 98200158
    {'aut_label': '14A1', 'centralizer': '2.b1.a1', 'counter': 19, 'group_counter': 98, 'group_order': 224, 'label': '14A3', 'order': 14, 'powers': [13, 20, 2], 'representative': 160, 'size': 2}
  • id: 98200160
    {'aut_label': '14A1', 'centralizer': '2.b1.a1', 'counter': 20, 'group_counter': 98, 'group_order': 224, 'label': '14A5', 'order': 14, 'powers': [12, 18, 2], 'representative': 144, 'size': 2}
  • id: 98200161
    {'aut_label': '14A1', 'centralizer': '2.b1.a1', 'counter': 21, 'group_counter': 98, 'group_order': 224, 'label': '14B1', 'order': 14, 'powers': [13, 22, 3], 'representative': 120, 'size': 2}
  • id: 98200162
    {'aut_label': '14A1', 'centralizer': '2.b1.a1', 'counter': 22, 'group_counter': 98, 'group_order': 224, 'label': '14B3', 'order': 14, 'powers': [12, 23, 3], 'representative': 136, 'size': 2}
  • id: 98200163
    {'aut_label': '14A1', 'centralizer': '2.b1.a1', 'counter': 23, 'group_counter': 98, 'group_order': 224, 'label': '14B5', 'order': 14, 'powers': [11, 21, 3], 'representative': 152, 'size': 2}
  • id: 98200164
    {'aut_label': '14C1', 'centralizer': '2.b1.a1', 'counter': 24, 'group_counter': 98, 'group_order': 224, 'label': '14C1', 'order': 14, 'powers': [13, 25, 4], 'representative': 8, 'size': 2}
  • id: 98200165
    {'aut_label': '14C1', 'centralizer': '2.b1.a1', 'counter': 25, 'group_counter': 98, 'group_order': 224, 'label': '14C3', 'order': 14, 'powers': [12, 26, 4], 'representative': 24, 'size': 2}
  • id: 98200166
    {'aut_label': '14C1', 'centralizer': '2.b1.a1', 'counter': 26, 'group_counter': 98, 'group_order': 224, 'label': '14C5', 'order': 14, 'powers': [11, 24, 4], 'representative': 40, 'size': 2}
  • id: 98200167
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 27, 'group_counter': 98, 'group_order': 224, 'label': '28A1', 'order': 28, 'powers': [24, 28, 9], 'representative': 116, 'size': 2}
  • id: 98200168
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 28, 'group_counter': 98, 'group_order': 224, 'label': '28A3', 'order': 28, 'powers': [25, 30, 9], 'representative': 124, 'size': 2}
  • id: 98200169
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 29, 'group_counter': 98, 'group_order': 224, 'label': '28A5', 'order': 28, 'powers': [26, 32, 9], 'representative': 132, 'size': 2}
  • id: 98200171
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 30, 'group_counter': 98, 'group_order': 224, 'label': '28A9', 'order': 28, 'powers': [26, 27, 9], 'representative': 148, 'size': 2}
  • id: 98200172
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 31, 'group_counter': 98, 'group_order': 224, 'label': '28A11', 'order': 28, 'powers': [25, 29, 9], 'representative': 180, 'size': 2}
  • id: 98200173
    {'aut_label': '28A1', 'centralizer': '2.b1.a1', 'counter': 32, 'group_counter': 98, 'group_order': 224, 'label': '28A13', 'order': 28, 'powers': [24, 31, 9], 'representative': 164, 'size': 2}
  • id: 98200174
    {'aut_label': '28B1', 'centralizer': '2.b1.a1', 'counter': 33, 'group_counter': 98, 'group_order': 224, 'label': '28B1', 'order': 28, 'powers': [24, 34, 10], 'representative': 4, 'size': 2}
  • id: 98200175
    {'aut_label': '28B1', 'centralizer': '2.b1.a1', 'counter': 34, 'group_counter': 98, 'group_order': 224, 'label': '28B3', 'order': 28, 'powers': [25, 36, 10], 'representative': 12, 'size': 2}
  • id: 98200176
    {'aut_label': '28B1', 'centralizer': '2.b1.a1', 'counter': 35, 'group_counter': 98, 'group_order': 224, 'label': '28B5', 'order': 28, 'powers': [26, 38, 10], 'representative': 20, 'size': 2}
  • id: 98200177
    {'aut_label': '28B1', 'centralizer': '2.b1.a1', 'counter': 36, 'group_counter': 98, 'group_order': 224, 'label': '28B9', 'order': 28, 'powers': [26, 33, 10], 'representative': 36, 'size': 2}
  • id: 98200178
    {'aut_label': '28B1', 'centralizer': '2.b1.a1', 'counter': 37, 'group_counter': 98, 'group_order': 224, 'label': '28B11', 'order': 28, 'powers': [25, 35, 10], 'representative': 44, 'size': 2}
  • id: 98200179
    {'aut_label': '28B1', 'centralizer': '2.b1.a1', 'counter': 38, 'group_counter': 98, 'group_order': 224, 'label': '28B13', 'order': 28, 'powers': [24, 37, 10], 'representative': 52, 'size': 2}
  • id: 98200180
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 39, 'group_counter': 98, 'group_order': 224, 'label': '56A1', 'order': 56, 'powers': [33, 40, 14], 'representative': 2, 'size': 2}
  • id: 98200182
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 40, 'group_counter': 98, 'group_order': 224, 'label': '56A3', 'order': 56, 'powers': [34, 42, 15], 'representative': 6, 'size': 2}
  • id: 98200183
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 41, 'group_counter': 98, 'group_order': 224, 'label': '56A5', 'order': 56, 'powers': [35, 45, 15], 'representative': 10, 'size': 2}
  • id: 98200184
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 42, 'group_counter': 98, 'group_order': 224, 'label': '56A9', 'order': 56, 'powers': [36, 50, 14], 'representative': 18, 'size': 2}
  • id: 98200185
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 43, 'group_counter': 98, 'group_order': 224, 'label': '56A11', 'order': 56, 'powers': [37, 48, 15], 'representative': 22, 'size': 2}
  • id: 98200186
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 44, 'group_counter': 98, 'group_order': 224, 'label': '56A13', 'order': 56, 'powers': [38, 46, 15], 'representative': 26, 'size': 2}
  • id: 98200187
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 45, 'group_counter': 98, 'group_order': 224, 'label': '56A15', 'order': 56, 'powers': [38, 43, 14], 'representative': 82, 'size': 2}
  • id: 98200188
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 46, 'group_counter': 98, 'group_order': 224, 'label': '56A17', 'order': 56, 'powers': [37, 41, 14], 'representative': 34, 'size': 2}
  • id: 98200189
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 47, 'group_counter': 98, 'group_order': 224, 'label': '56A19', 'order': 56, 'powers': [36, 39, 15], 'representative': 38, 'size': 2}
  • id: 98200190
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 48, 'group_counter': 98, 'group_order': 224, 'label': '56A23', 'order': 56, 'powers': [35, 44, 14], 'representative': 66, 'size': 2}
  • id: 98200191
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 49, 'group_counter': 98, 'group_order': 224, 'label': '56A25', 'order': 56, 'powers': [34, 47, 14], 'representative': 50, 'size': 2}
  • id: 98200193
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 50, 'group_counter': 98, 'group_order': 224, 'label': '56A27', 'order': 56, 'powers': [33, 49, 15], 'representative': 58, 'size': 2}
  • id: 98200194
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 51, 'group_counter': 98, 'group_order': 224, 'label': '56B1', 'order': 56, 'powers': [33, 52, 16], 'representative': 114, 'size': 2}
  • id: 98200195
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 52, 'group_counter': 98, 'group_order': 224, 'label': '56B3', 'order': 56, 'powers': [34, 54, 17], 'representative': 118, 'size': 2}
  • id: 98200196
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 53, 'group_counter': 98, 'group_order': 224, 'label': '56B5', 'order': 56, 'powers': [35, 57, 17], 'representative': 122, 'size': 2}
  • id: 98200197
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 54, 'group_counter': 98, 'group_order': 224, 'label': '56B9', 'order': 56, 'powers': [36, 62, 16], 'representative': 130, 'size': 2}
  • id: 98200198
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 55, 'group_counter': 98, 'group_order': 224, 'label': '56B11', 'order': 56, 'powers': [37, 60, 17], 'representative': 134, 'size': 2}
  • id: 98200199
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 56, 'group_counter': 98, 'group_order': 224, 'label': '56B13', 'order': 56, 'powers': [38, 58, 17], 'representative': 138, 'size': 2}
  • id: 98200200
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 57, 'group_counter': 98, 'group_order': 224, 'label': '56B15', 'order': 56, 'powers': [38, 55, 16], 'representative': 194, 'size': 2}
  • id: 98200201
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 58, 'group_counter': 98, 'group_order': 224, 'label': '56B17', 'order': 56, 'powers': [37, 53, 16], 'representative': 146, 'size': 2}
  • id: 98200202
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 59, 'group_counter': 98, 'group_order': 224, 'label': '56B19', 'order': 56, 'powers': [36, 51, 17], 'representative': 150, 'size': 2}
  • id: 98200204
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 60, 'group_counter': 98, 'group_order': 224, 'label': '56B23', 'order': 56, 'powers': [35, 56, 16], 'representative': 178, 'size': 2}
  • id: 98200205
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 61, 'group_counter': 98, 'group_order': 224, 'label': '56B25', 'order': 56, 'powers': [34, 59, 16], 'representative': 162, 'size': 2}
  • id: 98200206
    {'aut_label': '56A1', 'centralizer': '2.b1.a1', 'counter': 62, 'group_counter': 98, 'group_order': 224, 'label': '56B27', 'order': 56, 'powers': [33, 61, 17], 'representative': 170, 'size': 2}
• 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: 270995
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 271006
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 271008
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 271009
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 271010
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.1e', '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, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 271011
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.1f', '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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 271012
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.1g', '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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 271013
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.1h', '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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 271014
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 2, 2, 2, 0, 0, 0, 0, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 270996
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, -2, -2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 270997
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2c', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, -4, -4, -4, 4, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 270998
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2d', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, -4, -4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 270999
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2e', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, 6, 6, -1, -1, -1, 6, 6, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 271000
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2f', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, 0, 0, -6, 6, -1, -1, -1, -6, 6, 6, -6, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 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: 271001
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2g', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, 0, 0, -6, 6, -1, -1, -1, 6, -6, -6, 6, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -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: 271002
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2h', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, 6, 6, -1, -1, -1, -6, -6, -6, -6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 271003
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2i', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 0, 0, 0, 0, 12, -12, -2, -2, -2, 0, 0, 0, 0, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 271004
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2j', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 0, 0, -12, -12, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 271005
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2k', 'multiplicity': 12, 'nt': [56, 0], 'qdim': 24, 'qvalues': [24, -24, 24, -24, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 4, 4, 4, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 271007
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '224.98', 'group_order': 224, 'image': None, 'label': '224.98.2l', 'multiplicity': 12, 'nt': [56, 0], 'qdim': 24, 'qvalues': [24, 24, -24, -24, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, -4, -4, 4, 4, 4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 392862
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 224, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 224, 'label': '224.98.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 392873
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 224, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.d1', 'kernel_order': 112, 'label': '224.98.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 392884
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 224, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.c1', 'kernel_order': 112, 'label': '224.98.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 392895
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 224, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.b1', 'kernel_order': 112, 'label': '224.98.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 392906
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 224, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 112, 'label': '224.98.1e', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 392917
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 224, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 112, 'label': '224.98.1f', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 392921
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 224, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 112, 'label': '224.98.1g', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 392922
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 224, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 112, 'label': '224.98.1h', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 392923
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 56, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 28, 'label': '224.98.2a', '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]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 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]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 392863
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 56, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 28, 'label': '224.98.2b', '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]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 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]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 392864
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 28, 'counter': 11, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.b1', 'kernel_order': 14, 'label': '224.98.2c1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-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]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 392865
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 28, 'counter': 12, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.b1', 'kernel_order': 14, 'label': '224.98.2c2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-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]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 392866
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 28, 'counter': 13, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.a1', 'kernel_order': 14, 'label': '224.98.2d1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[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]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 392867
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 28, 'counter': 14, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.a1', 'kernel_order': 14, 'label': '224.98.2d2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[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]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 392868
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 15, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 16, 'label': '224.98.2e1', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 392869
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 16, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 16, 'label': '224.98.2e2', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 392870
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 17, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 16, 'label': '224.98.2e3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 392871
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 18, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 8, 'label': '224.98.2f1', 'nt': [14, 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]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 392872
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 19, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 8, 'label': '224.98.2f2', 'nt': [14, 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]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 392874
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 20, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 8, 'label': '224.98.2f3', 'nt': [14, 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]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 392875
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 21, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.b1', 'kernel_order': 8, 'label': '224.98.2g1', 'nt': [14, 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]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 392876
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 22, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.b1', 'kernel_order': 8, 'label': '224.98.2g2', 'nt': [14, 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]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 392877
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 23, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.b1', 'kernel_order': 8, 'label': '224.98.2g3', 'nt': [14, 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]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 392878
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 24, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 8, 'label': '224.98.2h1', 'nt': [14, 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]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 392879
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 25, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 8, 'label': '224.98.2h2', 'nt': [14, 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]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 392880
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 16, 'counter': 26, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 8, 'label': '224.98.2h3', 'nt': [14, 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]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 392881
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 27, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 4, 'label': '224.98.2i1', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 392882
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 28, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 4, 'label': '224.98.2i2', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 392883
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 4, 'label': '224.98.2i3', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]]]}
  • id: 392885
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 4, 'label': '224.98.2i4', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]]]}
  • id: 392886
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 4, 'label': '224.98.2i5', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]]]}
  • id: 392887
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 4, 'label': '224.98.2i6', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]]]}
  • id: 392888
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 33, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 4, 'label': '224.98.2j1', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 392889
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 4, 'label': '224.98.2j2', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 392890
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 35, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 4, 'label': '224.98.2j3', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]]]}
  • id: 392891
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 36, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 4, 'label': '224.98.2j4', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]]]}
  • id: 392892
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 37, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 4, 'label': '224.98.2j5', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]]]}
  • id: 392893
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 8, 'counter': 38, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 4, 'label': '224.98.2j6', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]]]}
  • id: 392894
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 39, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k1', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 8], [-1, -8]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[1, 3], [1, -3]], [[-1, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[1, 13], [1, -13]], [[-1, 13], [-1, -13]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 13], [1, -13]], [[1, 5], [1, -5]]]}
  • id: 392904
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 48, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k10', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 12], [-1, -12]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[1, 5], [1, -5]], [[1, 11], [1, -11]]]}
  • id: 392905
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 49, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k11', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 12], [-1, -12]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 13], [-1, -13]], [[1, 11], [1, -11]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 13], [-1, -13]], [[-1, 9], [-1, -9]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[1, 13], [1, -13]], [[1, 9], [1, -9]], [[-1, 9], [-1, -9]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]]]}
  • id: 392907
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 50, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k12', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 12], [-1, -12]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[-1, 5], [-1, -5]], [[-1, 11], [-1, -11]]]}
  • id: 392896
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 40, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k2', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 8], [-1, -8]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[1, 11], [1, -11]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]]]}
  • id: 392897
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 41, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k3', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 8], [-1, -8]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[-1, 3], [-1, -3]], [[1, 13], [1, -13]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[-1, 13], [-1, -13]], [[1, 13], [1, -13]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 13], [-1, -13]], [[-1, 5], [-1, -5]]]}
  • id: 392898
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 42, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k4', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 8], [-1, -8]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 8], [1, -8]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 11], [1, -11]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[1, 1], [1, -1]], [[1, 9], [1, -9]]]}
  • id: 392899
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 43, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k5', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 9], [-1, -9]], [[-1, 11], [-1, -11]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 9], [1, -9]], [[1, 11], [1, -11]], [[-1, 11], [-1, -11]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[1, 11], [1, -11]], [[1, 13], [1, -13]]]}
  • id: 392900
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 44, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k6', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[-1, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 392901
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 45, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k7', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 9], [1, -9]], [[1, 11], [1, -11]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 9], [-1, -9]], [[-1, 11], [-1, -11]], [[1, 11], [1, -11]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[-1, 13], [-1, -13]]]}
  • id: 392902
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 46, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k8', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]]]}
  • id: 392903
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 47, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.b1', 'kernel_order': 2, 'label': '224.98.2k9', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 12], [-1, -12]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 13], [1, -13]], [[-1, 11], [-1, -11]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 13], [1, -13]], [[1, 9], [1, -9]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[-1, 13], [-1, -13]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[1, 3], [1, -3]]]}
  • id: 392908
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 51, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l1', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 8], [-1, -8]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[-1, 3], [-1, -3]], [[1, 13], [1, -13]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[1, 13], [1, -13]], [[-1, 13], [-1, -13]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 13], [-1, -13]], [[-1, 5], [-1, -5]]]}
  • id: 392918
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 60, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l10', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[-1, 11], [-1, -11]]]}
  • id: 392919
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 61, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l11', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 13], [-1, -13]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 13], [1, -13]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[1, 13], [1, -13]], [[1, 9], [1, -9]], [[-1, 9], [-1, -9]], [[1, 3], [1, -3]], [[-1, 13], [-1, -13]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[1, 3], [1, -3]]]}
  • id: 392920
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 62, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l12', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 11], [1, -11]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[1, 11], [1, -11]]]}
  • id: 392909
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 52, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l2', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 8], [-1, -8]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 11], [-1, -11]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 9], [1, -9]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[1, 9], [1, -9]]]}
  • id: 392910
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 53, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l3', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 8], [-1, -8]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[1, 3], [1, -3]], [[-1, 13], [-1, -13]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[-1, 13], [-1, -13]], [[1, 13], [1, -13]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[1, 5], [1, -5]]]}
  • id: 392911
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 54, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l4', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 8], [-1, -8]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[-1, 2], [-1, -2]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[1, 11], [1, -11]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 11], [1, -11]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]]]}
  • id: 392912
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 55, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l5', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 9], [1, -9]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 9], [1, -9]], [[1, 11], [1, -11]], [[-1, 11], [-1, -11]], [[-1, 13], [-1, -13]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[-1, 11], [-1, -11]], [[-1, 13], [-1, -13]]]}
  • id: 392913
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 56, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l6', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[-1, 13], [-1, -13]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[1, 13], [1, -13]], [[-1, 11], [-1, -11]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]]]}
  • id: 392914
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 57, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l7', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 9], [-1, -9]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 9], [-1, -9]], [[-1, 11], [-1, -11]], [[1, 11], [1, -11]], [[1, 13], [1, -13]], [[1, 9], [1, -9]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[1, 11], [1, -11]], [[1, 13], [1, -13]]]}
  • id: 392915
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 58, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l8', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[1, 11], [1, -11]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 392916
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 4, 'counter': 59, 'cyclotomic_n': 56, 'dim': 2, 'faithful': False, 'field': [1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1], 'group': '224.98', 'group_counter': 98, 'group_order': 224, 'image': None, 'image_isoclass': '112.6', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 2, 'label': '224.98.2l9', 'nt': [56, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[1, 13], [1, -13]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 13], [-1, -13]], [[-1, 9], [-1, -9]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[-1, 13], [-1, -13]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]], [[1, 13], [1, -13]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[-1, 3], [-1, -3]]]}
• 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: 20971625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 224, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 14, 'label': '224.98.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.98', 'subgroup_hash': 98, 'subgroup_order': 224, 'subgroup_tex': 'C_2\\times D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 20971636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.29', 'subgroup_hash': 29, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.29', 'subgroup_hash': 29, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971658
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 112, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.22', 'subgroup_hash': 22, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 20971669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '224.98.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.6', 'subgroup_hash': 6, 'subgroup_order': 112, 'subgroup_tex': 'D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 20971680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '224.98.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.6', 'subgroup_hash': 6, 'subgroup_order': 112, 'subgroup_tex': 'D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 20971691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '224.98.2.c1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.6', 'subgroup_hash': 6, 'subgroup_order': 112, 'subgroup_tex': 'D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 20971699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '224.98.2.c1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.6', 'subgroup_hash': 6, 'subgroup_order': 112, 'subgroup_tex': 'D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 20971700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 56, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.4.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.4.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971630
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 14, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 20971631
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 20971632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '224.98.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 2}
  • id: 20971638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 28, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971639
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 28, 'counter': 22, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971640
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 28, 'counter': 23, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, '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', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 20971641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971643
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.8.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.8.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.8.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.8.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971650
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 20971651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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: 20971652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.14.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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: 20971653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 20971654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.14.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 20971655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.14.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 20971656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.14.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 20971657
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 39, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971659
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 40, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.16.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971660
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 14, 'counter': 41, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, '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': ['L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 20971661
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 7, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 20971662
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 7, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.16.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 20971663
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 7, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.16.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 20971664
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 7, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.16.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 20971665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, '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: 20971666
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 47, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 20971667
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.28.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 20971668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 20971670
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.28.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 20971671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 20971672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.28.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 20971673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 20971674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.28.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 20971675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.28.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 20971676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.28.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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: 20971677
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 7, 'counter': 57, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '224.98.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_8', 'simple': True, 'solvable': True, 'special_labels': ['L3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 20971678
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': True, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '224.98.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 20971679
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 4, 'counter': 59, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 20971681
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 4, 'counter': 60, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 20971682
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 20971683
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.56.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 20971684
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.56.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 20971685
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.56.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 20971686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 20971687
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.56.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 20971688
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.56.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 20971689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '224.98.56.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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: 20971690
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': True, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '224.98.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{56}', 'simple': True, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 20971692
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': True, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '224.98.112.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '112.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{56}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 20971693
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': True, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 2, 'counter': 71, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '224.98.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '112.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{28}', '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: 20971694
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '224.98.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, '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: 20971695
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '224.98.112.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, '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: 20971696
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '224.98.112.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, '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: 20971697
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '224.98.112.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, '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: 20971698
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '224.98', 'ambient_counter': 98, 'ambient_order': 224, 'ambient_tex': 'C_2\\times D_{56}', 'central': True, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 1, 'counter': 76, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '224.98.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '224.98', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 98, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{56}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D2', 'C6'], '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: 20971625
    {'ambient': '224.98', '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': '56.a1.a1', 'complements': ['224.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.c1.c1', '2.c1.d1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 16, 112, 84, 14, 56], 'label': '224.98.1.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.c1.c1', '2.c1.d1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '56.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971626
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': ['56.d1.b1', '56.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.c1.b1'], 'contains': ['8.c1.a1', '8.e1.a1', '28.e1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [115, 56, 16, 84], 'label': '224.98.4.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.c1.b1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971627
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': ['56.d1.a1', '56.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.c1.c1'], 'contains': ['8.c1.a1', '8.e1.b1', '28.e1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [113, 56, 16, 84], 'label': '224.98.4.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.c1.c1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971628
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': ['56.d1.a1', '56.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.c1.d1'], 'contains': ['8.c1.a1', '8.e1.c1', '28.e1.c1'], 'core': '4.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 56, 16, 84], 'label': '224.98.4.b1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.c1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.c1.d1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.c1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.c1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971629
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': ['56.d1.b1', '56.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.c1', '2.c1.d1'], 'contains': ['8.c1.a1', '8.e1.d1', '28.e1.d1'], 'core': '4.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 56, 16, 84], 'label': '224.98.4.b1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.d1', 'normal_contained_in': ['2.a1.a1', '2.c1.c1', '2.c1.d1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.d1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.d1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971630
    {'ambient': '224.98', 'aut_centralizer_order': 224, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 448, 'centralizer': '2.b1.a1', 'complements': ['56.d1.b1', '56.d1.d1', '56.d1.a1', '56.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.d1'], 'contains': ['8.c1.a1', '28.b1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [14, 28, 56, 16], 'label': '224.98.4.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.d1'], 'normal_contains': ['8.c1.a1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971631
    {'ambient': '224.98', 'aut_centralizer_order': 224, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 448, 'centralizer': '2.b1.a1', 'complements': ['56.d1.b1', '56.d1.d1', '56.d1.a1', '56.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.b1', '2.c1.c1'], 'contains': ['8.c1.a1', '28.b1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [126, 28, 56, 16], 'label': '224.98.4.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.b1.a1', '2.c1.b1', '2.c1.c1'], 'normal_contains': ['8.c1.a1', '28.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971632
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.c1', '8.e1.a1', '8.e1.d1', '28.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 112, 16, 56], 'label': '224.98.4.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '56.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 20971633
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.a1.a1', '8.d1.b1', '8.d1.d1', '8.e1.b1', '8.e1.c1', '28.c1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 112, 16, 56], 'label': '224.98.4.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.d1.b1', 'projective_image': '56.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 20971634
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.e1.d1', '28.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 56, 16, 196], 'label': '224.98.4.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 20971635
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '336.125', 'aut_weyl_index': 32, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.b1.a1', '8.e1.b1', '8.e1.c1', '28.d1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 56, 16, 196], 'label': '224.98.4.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.e1.b1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 20971636
    {'ambient': '224.98', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11444', 'aut_weyl_index': 8, 'centralizer': '56.a1.a1', 'complements': ['112.c1.c1', '112.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.d1', '4.d1.a1', '4.e1.a1', '14.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 112, 56, 84, 16], 'label': '224.98.2.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.b1.d1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '56.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971637
    {'ambient': '224.98', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '256.16870', 'aut_weyl_index': 42, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.b1.b1', '14.c1.a1', '14.c1.b1', '14.c1.c1', '14.c1.d1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 14, 112], 'label': '224.98.7.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '56.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971638
    {'ambient': '224.98', 'aut_centralizer_order': 896, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 896, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.d1.b1'], 'contains': ['16.a1.a1', '16.a1.b1', '16.b1.a1', '56.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [56, 16, 112], 'label': '224.98.8.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1', '16.a1.a1', '16.a1.b1', '56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '56.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971639
    {'ambient': '224.98', 'aut_centralizer_order': 896, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 896, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.e1.a1', '4.e1.b1'], 'contains': ['16.b1.a1', '56.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [196, 56, 16], 'label': '224.98.8.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1', '56.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971640
    {'ambient': '224.98', 'aut_centralizer_order': 896, 'aut_label': '8.c1', 'aut_quo_index': 21, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 896, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.b1.c1', '4.b1.d1', '4.c1.a1', '4.c1.b1'], 'contains': ['16.b1.a1', '56.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [84, 56, 16], 'label': '224.98.8.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.b1.c1', '4.b1.d1', '4.c1.b1', '4.c1.a1'], 'normal_contains': ['16.b1.a1', '56.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971641
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '84.7', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.c1.d1', '56.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [3, 16, 112], 'label': '224.98.8.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.d1.a1', 'projective_image': '112.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 20971642
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '84.7', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1'], 'contains': ['16.a1.a1', '16.c1.b1', '16.c1.c1', '56.d1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 16, 112], 'label': '224.98.8.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.b1', 'old_label': '8.d1.b1', 'projective_image': '112.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 20971643
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '84.7', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.a1.b1', '16.c1.a1', '16.c1.d1', '56.d1.c1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [3, 16, 168], 'label': '224.98.8.d1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.d1.c1', 'projective_image': '112.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.c1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 20971644
    {'ambient': '224.98', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '84.7', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1'], 'contains': ['16.a1.b1', '16.c1.b1', '16.c1.c1', '56.d1.d1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 16, 168], 'label': '224.98.8.d1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.b1', 'old_label': '8.d1.d1', 'projective_image': '112.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.d1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 20971645
    {'ambient': '224.98', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '84.7', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '56.e1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [115, 16, 56], 'label': '224.98.8.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 20971646
    {'ambient': '224.98', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '84.7', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.d1.b1', '4.e1.b1'], 'contains': ['16.b1.a1', '16.c1.b1', '56.e1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [113, 16, 56], 'label': '224.98.8.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.e1.b1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 20971647
    {'ambient': '224.98', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11444', 'aut_weyl_index': 8, 'centralizer': '56.a1.a1', 'complements': ['112.c1.d1', '112.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '4.b1.c1', '4.d1.b1', '4.e1.b1', '14.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 112, 56, 84, 16], 'label': '224.98.2.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '56.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971648
    {'ambient': '224.98', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '84.7', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.c1', '4.d1.b1', '4.e1.b1'], 'contains': ['16.b1.a1', '16.c1.c1', '56.e1.c1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 16, 56], 'label': '224.98.8.e1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.e1.c1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.c1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 20971649
    {'ambient': '224.98', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '84.7', 'aut_weyl_index': 128, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.d1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.b1.a1', '16.c1.d1', '56.e1.d1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 16, 56], 'label': '224.98.8.e1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.d1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.d1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 20971650
    {'ambient': '224.98', 'aut_centralizer_order': 672, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 672, 'centralizer': '2.b1.a1', 'complements': ['16.c1.c1', '16.c1.b1', '16.c1.d1', '16.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.b1.a1', '28.b1.b1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [14, 112], 'label': '224.98.14.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['28.a1.a1', '28.b1.b1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '56.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971651
    {'ambient': '224.98', 'aut_centralizer_order': 24, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.49', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.c1.a1', '28.d1.a1', '28.e1.a1', '28.e1.d1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [3, 84, 112], 'label': '224.98.14.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': '56.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971652
    {'ambient': '224.98', 'aut_centralizer_order': 24, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.49', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.c1.b1', '28.d1.b1', '28.e1.b1', '28.e1.c1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 84, 112], 'label': '224.98.14.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.b1', 'projective_image': '56.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971653
    {'ambient': '224.98', 'aut_centralizer_order': 12, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '32.43', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.e1.a1', '28.e1.b1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [113, 14], 'label': '224.98.14.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971654
    {'ambient': '224.98', 'aut_centralizer_order': 12, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '32.43', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '7.a1.a1'], 'contains': ['28.b1.b1', '28.e1.a1', '28.e1.c1'], 'core': '28.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 126], 'label': '224.98.14.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.b1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971655
    {'ambient': '224.98', 'aut_centralizer_order': 12, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '32.43', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.c1', '7.a1.a1'], 'contains': ['28.b1.b1', '28.e1.b1', '28.e1.d1'], 'core': '28.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [113, 126], 'label': '224.98.14.c1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.c1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971656
    {'ambient': '224.98', 'aut_centralizer_order': 12, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '32.43', 'aut_weyl_index': 336, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.d1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.e1.c1', '28.e1.d1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 14], 'label': '224.98.14.c1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.d1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971657
    {'ambient': '224.98', 'aut_centralizer_order': 896, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '2.b1.a1', 'complements': ['14.c1.d1', '14.c1.a1', '14.c1.b1', '14.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['32.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [112, 16], 'label': '224.98.16.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '112.6', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971658
    {'ambient': '224.98', 'aut_centralizer_order': 112, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.221', 'aut_weyl_index': 112, 'centralizer': '2.b1.a1', 'complements': ['112.c1.c1', '112.c1.b1', '112.c1.d1', '112.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.c1.b1', '14.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [14, 16, 28, 112, 56], 'label': '224.98.2.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.b1', '4.c1.a1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '56.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971659
    {'ambient': '224.98', 'aut_centralizer_order': 896, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '2.b1.a1', 'complements': ['14.c1.d1', '14.c1.a1', '14.c1.b1', '14.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.c1', '8.d1.d1'], 'contains': ['32.a1.a1', '112.a1.b1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168, 16], 'label': '224.98.16.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '112.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.b1', 'projective_image': '112.6', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971660
    {'ambient': '224.98', 'aut_centralizer_order': 1792, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.e1.a1', '8.e1.b1', '8.e1.c1', '8.e1.d1'], 'contains': ['32.a1.a1', '112.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [56, 16], 'label': '224.98.16.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.a1', '8.b1.a1'], 'normal_contains': ['32.a1.a1', '112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971661
    {'ambient': '224.98', 'aut_centralizer_order': 16, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '42.1', 'aut_weyl_index': 256, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.d1.c1', '8.e1.a1'], 'contains': ['32.a1.a1', '112.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [115, 16], 'label': '224.98.16.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.c1.a1', 'projective_image': '224.98', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 20971662
    {'ambient': '224.98', 'aut_centralizer_order': 16, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '42.1', 'aut_weyl_index': 256, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.d1.d1', '8.e1.b1'], 'contains': ['32.a1.a1', '112.c1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [113, 16], 'label': '224.98.16.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.b1', 'old_label': '16.c1.b1', 'projective_image': '224.98', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 20971663
    {'ambient': '224.98', 'aut_centralizer_order': 16, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '42.1', 'aut_weyl_index': 256, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.d1.d1', '8.e1.c1'], 'contains': ['32.a1.a1', '112.c1.c1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 16], 'label': '224.98.16.c1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.b1', 'old_label': '16.c1.c1', 'projective_image': '224.98', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.c1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 20971664
    {'ambient': '224.98', 'aut_centralizer_order': 16, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '42.1', 'aut_weyl_index': 256, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.d1.c1', '8.e1.d1'], 'contains': ['32.a1.a1', '112.c1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [3, 16], 'label': '224.98.16.c1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.c1.d1', 'projective_image': '224.98', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.d1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 20971665
    {'ambient': '224.98', 'aut_centralizer_order': 2688, 'aut_label': '28.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.a1', '14.b1.a1', '14.b1.b1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.c1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [84, 112], 'label': '224.98.28.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.a1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '56.c1.a1', '56.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '56.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971666
    {'ambient': '224.98', 'aut_centralizer_order': 1344, 'aut_label': '28.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': ['8.d1.b1', '8.d1.d1', '8.d1.a1', '8.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.a1.a1', '14.c1.a1', '14.c1.d1'], 'contains': ['56.c1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [14], 'label': '224.98.28.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.a1', 'normal_contained_in': ['4.c1.a1', '14.a1.a1'], 'normal_contains': ['56.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.b1.a1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971667
    {'ambient': '224.98', 'aut_centralizer_order': 1344, 'aut_label': '28.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '2.b1.a1', 'complements': ['8.d1.b1', '8.d1.d1', '8.d1.a1', '8.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '14.a1.a1', '14.c1.b1', '14.c1.c1'], 'contains': ['56.c1.a1'], 'core': '28.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [126], 'label': '224.98.28.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.b1', 'normal_contained_in': ['4.c1.b1', '14.a1.a1'], 'normal_contains': ['56.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.b1.b1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '28.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971668
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.b1.a1'], 'contains': ['56.a1.a1', '56.d1.a1', '56.d1.c1', '56.e1.a1', '56.e1.d1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 56, 112], 'label': '224.98.28.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.c1.a1', 'projective_image': '56.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971669
    {'ambient': '224.98', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '1344.6795', 'aut_weyl_index': 8, 'centralizer': '56.a1.a1', 'complements': ['112.a1.a1', '112.a1.b1', '112.c1.c1', '112.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.c1.a1', '14.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [113, 84, 56, 14, 16], 'label': '224.98.2.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.b1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '112.29', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971670
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '28.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '14.b1.b1'], 'contains': ['56.a1.a1', '56.d1.b1', '56.d1.d1', '56.e1.b1', '56.e1.c1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 56, 112], 'label': '224.98.28.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.b1', 'old_label': '28.c1.b1', 'projective_image': '56.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971671
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.b1.a1'], 'contains': ['56.b1.a1', '56.e1.a1', '56.e1.d1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 196], 'label': '224.98.28.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.d1.a1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 20971672
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '14.b1.b1'], 'contains': ['56.b1.a1', '56.e1.b1', '56.e1.c1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 196], 'label': '224.98.28.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.b1', 'old_label': '28.d1.b1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 20971673
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.b1.a1', '14.c1.a1', '14.c1.b1'], 'contains': ['56.c1.a1', '56.e1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [115, 84], 'label': '224.98.28.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.a1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971674
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '14.b1.b1', '14.c1.a1', '14.c1.c1'], 'contains': ['56.c1.a1', '56.e1.b1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [113, 84], 'label': '224.98.28.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.b1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971675
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.c1', '14.b1.b1', '14.c1.b1', '14.c1.d1'], 'contains': ['56.c1.a1', '56.e1.c1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 84], 'label': '224.98.28.e1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.c1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971676
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.d1', '14.b1.a1', '14.c1.c1', '14.c1.d1'], 'contains': ['56.c1.a1', '56.e1.d1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [3, 84], 'label': '224.98.28.e1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.d1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 20971677
    {'ambient': '224.98', 'aut_centralizer_order': 1792, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.a1.b1', '16.b1.a1', '16.c1.a1', '16.c1.b1', '16.c1.c1', '16.c1.d1'], 'contains': ['224.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16], 'label': '224.98.32.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.b1.a1', '16.a1.a1', '16.a1.b1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '224.98', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971678
    {'ambient': '224.98', 'aut_centralizer_order': 5376, 'aut_label': '56.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1', '28.c1.a1', '28.c1.b1'], 'contains': ['112.a1.a1', '112.a1.b1', '112.b1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [56, 112], 'label': '224.98.56.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': ['8.a1.a1', '28.a1.a1'], 'normal_contains': ['112.b1.a1', '112.a1.a1', '112.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '56.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '56.5', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971679
    {'ambient': '224.98', 'aut_centralizer_order': 5376, 'aut_label': '56.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.a1.a1', '28.d1.a1', '28.d1.b1'], 'contains': ['112.b1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [196], 'label': '224.98.56.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.b1.a1', 'normal_contained_in': ['8.b1.a1', '28.a1.a1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.b1.a1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.2', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971680
    {'ambient': '224.98', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '1344.6795', 'aut_weyl_index': 8, 'centralizer': '56.a1.a1', 'complements': ['112.a1.a1', '112.a1.b1', '112.c1.b1', '112.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.c1', '4.c1.b1', '14.c1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 84, 56, 126, 16], 'label': '224.98.2.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.c1', '4.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '112.29', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971681
    {'ambient': '224.98', 'aut_centralizer_order': 5376, 'aut_label': '56.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.a1.a1', '28.b1.a1', '28.b1.b1', '28.e1.a1', '28.e1.b1', '28.e1.c1', '28.e1.d1'], 'contains': ['112.b1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [84], 'label': '224.98.56.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.c1.a1', 'normal_contained_in': ['8.c1.a1', '28.a1.a1', '28.b1.b1', '28.b1.a1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.c1.a1', 'projective_image': '112.29', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.4', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971682
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '28.c1.a1'], 'contains': ['112.a1.a1', '112.c1.a1', '112.c1.d1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [3, 112], 'label': '224.98.56.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1.a1', 'old_label': '56.d1.a1', 'projective_image': '112.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971683
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '28.c1.b1'], 'contains': ['112.a1.a1', '112.c1.b1', '112.c1.c1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [1, 112], 'label': '224.98.56.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1.b1', 'old_label': '56.d1.b1', 'projective_image': '112.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971684
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.c1', '28.c1.a1'], 'contains': ['112.a1.b1', '112.c1.a1', '112.c1.d1'], 'core': '112.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [3, 168], 'label': '224.98.56.d1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1.a1', 'old_label': '56.d1.c1', 'projective_image': '112.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971685
    {'ambient': '224.98', 'aut_centralizer_order': 48, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.d1', '28.c1.b1'], 'contains': ['112.a1.b1', '112.c1.b1', '112.c1.c1'], 'core': '112.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [1, 168], 'label': '224.98.56.d1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1.b1', 'old_label': '56.d1.d1', 'projective_image': '112.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971686
    {'ambient': '224.98', 'aut_centralizer_order': 96, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '28.c1.a1', '28.d1.a1', '28.e1.a1'], 'contains': ['112.b1.a1', '112.c1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [115, 56], 'label': '224.98.56.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.e1.a1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971687
    {'ambient': '224.98', 'aut_centralizer_order': 96, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '28.c1.b1', '28.d1.b1', '28.e1.b1'], 'contains': ['112.b1.a1', '112.c1.b1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [113, 56], 'label': '224.98.56.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.b1', 'old_label': '56.e1.b1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971688
    {'ambient': '224.98', 'aut_centralizer_order': 96, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.c1', '28.c1.b1', '28.d1.b1', '28.e1.c1'], 'contains': ['112.b1.a1', '112.c1.c1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 56], 'label': '224.98.56.e1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.b1', 'old_label': '56.e1.c1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971689
    {'ambient': '224.98', 'aut_centralizer_order': 96, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.d1', '28.c1.a1', '28.d1.a1', '28.e1.d1'], 'contains': ['112.b1.a1', '112.c1.d1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 56], 'label': '224.98.56.e1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.e1.d1', 'projective_image': '112.29', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 20971690
    {'ambient': '224.98', 'aut_centralizer_order': 5376, 'aut_label': '112.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1.a1', 'complements': ['2.c1.d1', '2.c1.a1', '2.c1.b1', '2.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.d1.a1', '56.d1.b1'], 'contains': ['224.a1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [112], 'label': '224.98.112.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.a1.a1', 'normal_contained_in': ['16.a1.a1', '56.a1.a1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '112.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '112.6', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971691
    {'ambient': '224.98', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '1344.6795', 'aut_weyl_index': 8, 'centralizer': '56.a1.a1', 'complements': ['112.a1.a1', '112.a1.b1', '112.c1.c1', '112.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.b1.d1', '4.c1.b1', '14.c1.c1'], 'core': '2.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [113, 84, 56, 126, 16], 'label': '224.98.2.c1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.b1.d1', '4.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.c1', 'projective_image': '112.29', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.c1.c1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971692
    {'ambient': '224.98', 'aut_centralizer_order': 5376, 'aut_label': '112.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1.a1', 'complements': ['2.c1.d1', '2.c1.a1', '2.c1.b1', '2.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.b1', '56.a1.a1', '56.d1.c1', '56.d1.d1'], 'contains': ['224.a1.a1'], 'core': '112.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168], 'label': '224.98.112.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.a1.b1', 'normal_contained_in': ['16.a1.b1', '56.a1.a1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.a1.b1', 'projective_image': '112.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '112.6', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '112.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971693
    {'ambient': '224.98', 'aut_centralizer_order': 10752, 'aut_label': '112.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1', '56.e1.a1', '56.e1.b1', '56.e1.c1', '56.e1.d1'], 'contains': ['224.a1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [56], 'label': '224.98.112.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.b1.a1', 'normal_contained_in': ['16.b1.a1', '56.a1.a1', '56.c1.a1', '56.b1.a1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.b1.a1', 'projective_image': '112.29', 'quotient_action_image': '1.1', 'quotient_action_kernel': '112.29', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971694
    {'ambient': '224.98', 'aut_centralizer_order': 96, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '56.d1.a1', '56.d1.c1', '56.e1.a1'], 'contains': ['224.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [115], 'label': '224.98.112.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1.a1', 'old_label': '112.c1.a1', 'projective_image': '224.98', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971695
    {'ambient': '224.98', 'aut_centralizer_order': 96, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '56.d1.b1', '56.d1.d1', '56.e1.b1'], 'contains': ['224.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [113], 'label': '224.98.112.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1.b1', 'old_label': '112.c1.b1', 'projective_image': '224.98', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971696
    {'ambient': '224.98', 'aut_centralizer_order': 96, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.c1', '56.d1.b1', '56.d1.d1', '56.e1.c1'], 'contains': ['224.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [1], 'label': '224.98.112.c1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1.b1', 'old_label': '112.c1.c1', 'projective_image': '224.98', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971697
    {'ambient': '224.98', 'aut_centralizer_order': 96, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.d1', '56.d1.a1', '56.d1.c1', '56.e1.d1'], 'contains': ['224.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [3], 'label': '224.98.112.c1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1.a1', 'old_label': '112.c1.d1', 'projective_image': '224.98', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971698
    {'ambient': '224.98', 'aut_centralizer_order': None, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '112.a1.a1', '112.a1.b1', '112.b1.a1', '112.c1.a1', '112.c1.b1', '112.c1.c1', '112.c1.d1'], 'contains': [], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '224.98.224.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '224.a1.a1', 'normal_contained_in': ['32.a1.a1', '112.b1.a1', '112.a1.a1', '112.a1.b1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '224.a1.a1', 'projective_image': '224.98', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 20971699
    {'ambient': '224.98', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '1344.6795', 'aut_weyl_index': 8, 'centralizer': '56.a1.a1', 'complements': ['112.a1.a1', '112.a1.b1', '112.c1.b1', '112.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.c1', '4.b1.d1', '4.c1.a1', '14.c1.d1'], 'core': '2.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 84, 56, 14, 16], 'label': '224.98.2.c1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.c1', '4.b1.d1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.d1', 'projective_image': '112.29', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.c1.d1', 'subgroup_fusion': None, 'weyl_group': '56.5'}
  • id: 20971700
    {'ambient': '224.98', 'aut_centralizer_order': 448, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 448, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '28.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [84, 16, 56, 112], 'label': '224.98.4.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.b1.a1', '28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '56.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}