Abstract group data - 1210.9

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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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1320, 'aut_gen_orders': [10, 3, 11], 'aut_gens': [[1, 10, 110], [371, 590, 1110], [881, 260, 720], [741, 10, 110]], 'aut_group': '1597200.a', 'aut_hash': 6850908737282390520, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1597200, 'aut_permdeg': 121, 'aut_perms': [181417371571402109957089744648082960812450202490043533099430035665760755360654859882367850400826922737746888376991248496065480503511254922045980611594295097209615481387675938261772681142743228385172176, 604137004207147995661123908138992871335302340755979302066281397641123179211935504959854703513203707999267095004377395113273581430762043356269811295530186356012473960537922269553373802223921732455398476, 272895087505728869206623450514951385441982711268812752348306545833885792421619386208846455158591474347173023953167234429157721026201710282981372758541449285904444348962107403796032873448700571333679332], 'aut_phi_ratio': 3630.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [5, 121, 1, 4], [10, 121, 1, 4], [11, 10, 12, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.\\GL(2,11)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '1597200.a', 'autcentquo_hash': 6850908737282390520, 'autcentquo_nilpotent': False, 'autcentquo_order': 1597200, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^2.\\GL(2,11)', 'cc_stats': [[1, 1, 1], [2, 121, 1], [5, 121, 4], [10, 121, 4], [11, 10, 12]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1210.9', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '5.1', '11.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [5, 121, 4, 1], [10, 121, 4, 1], [11, 10, 1, 12]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 868, 'exponent': 110, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1210.9', 'hash': 9, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 11, 11], 'inner_gens': [[1, 70, 770], [51, 10, 110], [551, 10, 110]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 1210, 'inner_split': False, 'inner_tex': 'C_{11}:F_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 10], [10, 12]], 'label': '1210.9', 'linC_count': 66, 'linC_degree': 20, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 66, 'linQ_dim': 20, 'linQ_dim_count': 66, 'linR_count': 66, 'linR_degree': 20, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C11:F11', 'ngens': 4, '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': 11, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 22, 'number_divisions': 16, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 56, 'number_subgroups': 776, 'old_label': None, 'order': 1210, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 121], [5, 484], [10, 484], [11, 120]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 660, 'outer_gen_orders': [10, 3], 'outer_gen_pows': [0, 8], 'outer_gens': [[1, 540, 870], [1, 510, 70]], 'outer_group': '1320.133', 'outer_hash': 133, 'outer_nilpotent': False, 'outer_order': 1320, 'outer_permdeg': 12, 'outer_perms': [140882579, 212246363], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\PGL(2,11)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2], [10, 12]], 'representations': {'PC': {'code': 44299841477537130399, 'gens': [1, 3, 4], 'pres': [4, -2, -5, -11, -11, 8, 842, 306, 12323, 4407]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [2143604792, 295918632, 1071928841, 418103038]}, 'Perm': {'d': 22, 'gens': [2446779061503274421, 5251477993144647812, 4736740, 58410722688808089600]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}:F_{11}', 'transitive_degree': 121, '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: 113326972
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 9, 'group_order': 1210, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 113326983
    {'aut_label': '2A', 'centralizer': '121.a1.a1', 'counter': 2, 'group_counter': 9, 'group_order': 1210, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 385, 'size': 121}
  • id: 113326987
    {'aut_label': '5A1', 'centralizer': '121.a1.a1', 'counter': 3, 'group_counter': 9, 'group_order': 1210, 'label': '5A1', 'order': 5, 'powers': [5, 1, 3], 'representative': 206, 'size': 121}
  • id: 113326988
    {'aut_label': '5A-1', 'centralizer': '121.a1.a1', 'counter': 4, 'group_counter': 9, 'group_order': 1210, 'label': '5A-1', 'order': 5, 'powers': [6, 1, 4], 'representative': 944, 'size': 121}
  • id: 113326989
    {'aut_label': '5A2', 'centralizer': '121.a1.a1', 'counter': 5, 'group_counter': 9, 'group_order': 1210, 'label': '5A2', 'order': 5, 'powers': [4, 1, 5], 'representative': 562, 'size': 121}
  • id: 113326990
    {'aut_label': '5A-2', 'centralizer': '121.a1.a1', 'counter': 6, 'group_counter': 9, 'group_order': 1210, 'label': '5A-2', 'order': 5, 'powers': [3, 1, 6], 'representative': 1128, 'size': 121}
  • id: 113326991
    {'aut_label': '10A1', 'centralizer': '121.a1.a1', 'counter': 7, 'group_counter': 9, 'group_order': 1210, 'label': '10A1', 'order': 10, 'powers': [3, 2, 7], 'representative': 473, 'size': 121}
  • id: 113326992
    {'aut_label': '10A-1', 'centralizer': '121.a1.a1', 'counter': 8, 'group_counter': 9, 'group_order': 1210, 'label': '10A-1', 'order': 10, 'powers': [4, 2, 8], 'representative': 1037, 'size': 121}
  • id: 113326993
    {'aut_label': '10A3', 'centralizer': '121.a1.a1', 'counter': 9, 'group_counter': 9, 'group_order': 1210, 'label': '10A3', 'order': 10, 'powers': [6, 2, 9], 'representative': 769, 'size': 121}
  • id: 113326973
    {'aut_label': '10A-3', 'centralizer': '121.a1.a1', 'counter': 10, 'group_counter': 9, 'group_order': 1210, 'label': '10A-3', 'order': 10, 'powers': [5, 2, 10], 'representative': 291, 'size': 121}
  • id: 113326974
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 11, 'group_counter': 9, 'group_order': 1210, 'label': '11A', 'order': 11, 'powers': [11, 11, 1], 'representative': 110, 'size': 10}
  • id: 113326975
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 12, 'group_counter': 9, 'group_order': 1210, 'label': '11B', 'order': 11, 'powers': [12, 12, 1], 'representative': 10, 'size': 10}
  • id: 113326976
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 13, 'group_counter': 9, 'group_order': 1210, 'label': '11C', 'order': 11, 'powers': [13, 13, 1], 'representative': 120, 'size': 10}
  • id: 113326977
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 14, 'group_counter': 9, 'group_order': 1210, 'label': '11D', 'order': 11, 'powers': [14, 14, 1], 'representative': 230, 'size': 10}
  • id: 113326978
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 15, 'group_counter': 9, 'group_order': 1210, 'label': '11E', 'order': 11, 'powers': [15, 15, 1], 'representative': 130, 'size': 10}
  • id: 113326979
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 16, 'group_counter': 9, 'group_order': 1210, 'label': '11F', 'order': 11, 'powers': [16, 16, 1], 'representative': 340, 'size': 10}
  • id: 113326980
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 17, 'group_counter': 9, 'group_order': 1210, 'label': '11G', 'order': 11, 'powers': [17, 17, 1], 'representative': 140, 'size': 10}
  • id: 113326981
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 18, 'group_counter': 9, 'group_order': 1210, 'label': '11H', 'order': 11, 'powers': [18, 18, 1], 'representative': 350, 'size': 10}
  • id: 113326982
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 19, 'group_counter': 9, 'group_order': 1210, 'label': '11I', 'order': 11, 'powers': [19, 19, 1], 'representative': 250, 'size': 10}
  • id: 113326984
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 20, 'group_counter': 9, 'group_order': 1210, 'label': '11J', 'order': 11, 'powers': [20, 20, 1], 'representative': 560, 'size': 10}
  • id: 113326985
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 21, 'group_counter': 9, 'group_order': 1210, 'label': '11K', 'order': 11, 'powers': [21, 21, 1], 'representative': 160, 'size': 10}
  • id: 113326986
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 22, 'group_counter': 9, 'group_order': 1210, 'label': '11L', 'order': 11, 'powers': [22, 22, 1], 'representative': 1110, 'size': 10}
• 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: 5192625
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.1a', '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], 'schur_index': 1}
  • id: 5192633
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.1b', '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], 'schur_index': 1}
  • id: 5192634
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.1c', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
  • id: 5192635
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.1d', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, -1, -1, -1, -1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
  • id: 5192636
    {'cdim': 10, 'counter': 5, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10a', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10], 'schur_index': 1}
  • id: 5192637
    {'cdim': 10, 'counter': 6, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10b', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, -1], 'schur_index': 1}
  • id: 5192638
    {'cdim': 10, 'counter': 7, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10c', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, -1, -1], 'schur_index': 1}
  • id: 5192639
    {'cdim': 10, 'counter': 8, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10d', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 10, -1, -1, -1], 'schur_index': 1}
  • id: 5192640
    {'cdim': 10, 'counter': 9, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10e', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 10, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5192626
    {'cdim': 10, 'counter': 10, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10f', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 10, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5192627
    {'cdim': 10, 'counter': 11, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10g', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 10, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5192628
    {'cdim': 10, 'counter': 12, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10h', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5192629
    {'cdim': 10, 'counter': 13, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10i', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5192630
    {'cdim': 10, 'counter': 14, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10j', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5192631
    {'cdim': 10, 'counter': 15, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10k', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5192632
    {'cdim': 10, 'counter': 16, 'faithful': False, 'group': '1210.9', 'group_order': 1210, 'image': None, 'label': '1210.9.10l', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], '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: 9601743
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1210, 'label': '1210.9.1a', '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]]]}
  • id: 9601754
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 605, 'label': '1210.9.1b', '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]]]}
  • id: 9601758
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 3, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 242, 'label': '1210.9.1c1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[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: 9601759
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 4, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 242, 'label': '1210.9.1c2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[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: 9601760
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 242, 'label': '1210.9.1c3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 9601761
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 6, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 242, 'label': '1210.9.1c4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 9601762
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 7, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 121, 'label': '1210.9.1d1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[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: 9601763
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 8, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 121, 'label': '1210.9.1d2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[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: 9601764
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 121, 'label': '1210.9.1d3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 9601744
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1210, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 121, 'label': '1210.9.1d4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 9601745
    {'center': '110.a1.f1', 'center_index': 110, 'center_order': 11, 'counter': 11, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.f1', 'kernel_order': 11, 'label': '1210.9.10a', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]]]}
  • id: 9601746
    {'center': '110.a1.b1', 'center_index': 110, 'center_order': 11, 'counter': 12, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.b1', 'kernel_order': 11, 'label': '1210.9.10b', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]]]}
  • id: 9601747
    {'center': '110.a1.j1', 'center_index': 110, 'center_order': 11, 'counter': 13, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.j1', 'kernel_order': 11, 'label': '1210.9.10c', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 9601748
    {'center': '110.a1.d1', 'center_index': 110, 'center_order': 11, 'counter': 14, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.d1', 'kernel_order': 11, 'label': '1210.9.10d', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 9601749
    {'center': '110.a1.c1', 'center_index': 110, 'center_order': 11, 'counter': 15, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.c1', 'kernel_order': 11, 'label': '1210.9.10e', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 9601750
    {'center': '110.a1.a1', 'center_index': 110, 'center_order': 11, 'counter': 16, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.a1', 'kernel_order': 11, 'label': '1210.9.10f', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 9601751
    {'center': '110.a1.l1', 'center_index': 110, 'center_order': 11, 'counter': 17, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.l1', 'kernel_order': 11, 'label': '1210.9.10g', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 9601752
    {'center': '110.a1.k1', 'center_index': 110, 'center_order': 11, 'counter': 18, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.k1', 'kernel_order': 11, 'label': '1210.9.10h', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 9601753
    {'center': '110.a1.i1', 'center_index': 110, 'center_order': 11, 'counter': 19, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.i1', 'kernel_order': 11, 'label': '1210.9.10i', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 9601755
    {'center': '110.a1.h1', 'center_index': 110, 'center_order': 11, 'counter': 20, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.h1', 'kernel_order': 11, 'label': '1210.9.10j', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 9601756
    {'center': '110.a1.e1', 'center_index': 110, 'center_order': 11, 'counter': 21, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.e1', 'kernel_order': 11, 'label': '1210.9.10k', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 9601757
    {'center': '110.a1.g1', 'center_index': 110, 'center_order': 11, 'counter': 22, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1210.9', 'group_counter': 9, 'group_order': 1210, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.g1', 'kernel_order': 11, 'label': '1210.9.10l', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 70214612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1210, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 110, 'label': '1210.9.1.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': '1210.9', 'subgroup_hash': 9, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 605, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 55, 'label': '1210.9.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.4', 'subgroup_hash': 4, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}^2:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 242, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 22, 'label': '1210.9.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '242.4', 'subgroup_hash': 4, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}:D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': True, 'core_order': 121, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 11, 'label': '1210.9.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '121.2', 'subgroup_hash': 2, 'subgroup_order': 121, 'subgroup_tex': 'C_{11}^2', 'supersolvable': True, 'sylow': 11}
  • id: 70214656
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214664
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214665
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214666
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.d1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214667
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.e1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214613
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.f1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214614
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.g1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.g1', '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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214615
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.h1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.h1', '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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214616
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.i1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.i1', '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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214617
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.j1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.j1', '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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214618
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.k1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.k1', '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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214619
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.11.a1.l1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.l1', '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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214620
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214621
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214622
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214624
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214625
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214626
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214627
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.g1', '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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214628
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.h1', '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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214629
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.i1', '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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214630
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.j1', '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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214631
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.k1', '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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214632
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.22.a1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.l1', '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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 70214633
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214635
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214636
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214637
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214638
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214639
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214640
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.g1', '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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214641
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.h1', '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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214642
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.i1', '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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214643
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.j1', '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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214644
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.k1', '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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214646
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.9.55.a1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.l1', '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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214647
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 41, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214648
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 42, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214649
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214650
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 44, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214651
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 45, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214652
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 46, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214653
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 47, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214654
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 48, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214655
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 49, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214657
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 50, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214658
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 51, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214659
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 121, 'characteristic': False, 'core_order': 11, 'counter': 52, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1210.9.110.a1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 70214660
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 10, 'label': '1210.9.121.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '121.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': 121, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 70214661
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '1210.9.242.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '242.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': 242, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 70214662
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '1210.9.605.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.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': 605, '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': 2}
  • id: 70214663
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1210.9', 'ambient_counter': 9, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': True, 'central_factor': False, 'centralizer_order': 1210, 'characteristic': True, 'core_order': 1, 'counter': 56, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1210.9.1210.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1210.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1210.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1210, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}:F_{11}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C4'], '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: 70214612
    {'ambient': '1210.9', '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': '1210.a1.a1', 'complements': ['1210.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '5.a1.a1', '11.a1.a1', '11.a1.b1', '11.a1.c1', '11.a1.d1', '11.a1.e1', '11.a1.f1', '11.a1.g1', '11.a1.h1', '11.a1.i1', '11.a1.j1', '11.a1.k1', '11.a1.l1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3415, 5844, 2802, 4999, 5062, 5037, 5678, 5000], 'generators': [5, 10, 110, 2], 'label': '1210.9.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1210.9', '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': '1210.9'}
  • id: 70214613
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.f1', '55.a1.f1', '121.a1.a1'], 'core': '110.a1.f1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 489, -1, 7965, -1, 4867, -1], 'generators': [5, 340, 2], 'label': '1210.9.11.a1.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.f1', 'old_label': '11.a1.f1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.f1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214614
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.g1', '55.a1.g1', '121.a1.a1'], 'core': '110.a1.g1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 2567, -1, 7965, -1, 4542, -1], 'generators': [5, 450, 2], 'label': '1210.9.11.a1.g1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.g1', 'old_label': '11.a1.g1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.g1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214615
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.h1', '55.a1.h1', '121.a1.a1'], 'core': '110.a1.h1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 1000, -1, 7965, -1, 5518, -1], 'generators': [5, 780, 2], 'label': '1210.9.11.a1.h1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.h1', 'old_label': '11.a1.h1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.h1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214616
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.i1', '55.a1.i1', '121.a1.a1'], 'core': '110.a1.i1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 9654, -1, 7965, -1, 3892, -1], 'generators': [5, 890, 2], 'label': '1210.9.11.a1.i1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.i1', 'old_label': '11.a1.i1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.i1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214617
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.j1', '55.a1.j1', '121.a1.a1'], 'core': '110.a1.j1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 1384, -1, 7965, -1, 7468, -1], 'generators': [5, 560, 2], 'label': '1210.9.11.a1.j1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.j1', 'old_label': '11.a1.j1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.j1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214618
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.k1', '55.a1.k1', '121.a1.a1'], 'core': '110.a1.k1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 3168, -1, 7965, -1, 7143, -1], 'generators': [5, 1000, 2], 'label': '1210.9.11.a1.k1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.k1', 'old_label': '11.a1.k1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.k1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214619
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.l1', '55.a1.l1', '121.a1.a1'], 'core': '110.a1.l1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 8766, -1, 7965, -1, 6818, -1], 'generators': [5, 1110, 2], 'label': '1210.9.11.a1.l1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.l1', 'old_label': '11.a1.l1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.l1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214620
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['110.a1.a1', '242.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 3440, -1, 4343, -1, 633, -1], 'generators': [2, 110], 'label': '1210.9.22.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214621
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.b1'], 'contains': ['110.a1.b1', '242.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 4766, -1, 4343, -1, 3746, -1], 'generators': [2, 10], 'label': '1210.9.22.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '22.a1.b1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214622
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.c1'], 'contains': ['110.a1.c1', '242.a1.a1'], 'core': '110.a1.c1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 8236, -1, 4343, -1, 1967, -1], 'generators': [2, 120], 'label': '1210.9.22.a1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.c1', 'old_label': '22.a1.c1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214623
    {'ambient': '1210.9', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1597200.a', 'aut_weyl_index': 1, 'centralizer': '1210.a1.a1', 'complements': ['605.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '22.a1.a1', '22.a1.b1', '22.a1.c1', '22.a1.d1', '22.a1.e1', '22.a1.f1', '22.a1.g1', '22.a1.h1', '22.a1.i1', '22.a1.j1', '22.a1.k1', '22.a1.l1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6451, 7077, 5755, 5433, 1514, 7724, 3081, 5693], 'generators': [2, 110, 10], 'label': '1210.9.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '1210.9', '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': '1210.9'}
  • id: 70214624
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.d1'], 'contains': ['110.a1.d1', '242.a1.a1'], 'core': '110.a1.d1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 7405, -1, 4343, -1, 3302, -1], 'generators': [2, 230], 'label': '1210.9.22.a1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.d1', 'old_label': '22.a1.d1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214625
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.e1'], 'contains': ['110.a1.e1', '242.a1.a1'], 'core': '110.a1.e1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 6444, -1, 4343, -1, 2857, -1], 'generators': [2, 670], 'label': '1210.9.22.a1.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.e1', 'old_label': '22.a1.e1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.e1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214626
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.f1'], 'contains': ['110.a1.f1', '242.a1.a1'], 'core': '110.a1.f1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 3921, -1, 4343, -1, 1523, -1], 'generators': [2, 340], 'label': '1210.9.22.a1.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.f1', 'old_label': '22.a1.f1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.f1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214627
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.g1'], 'contains': ['110.a1.g1', '242.a1.a1'], 'core': '110.a1.g1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 5480, -1, 4343, -1, 1078, -1], 'generators': [2, 450], 'label': '1210.9.22.a1.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.g1', 'old_label': '22.a1.g1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.g1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214628
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.h1'], 'contains': ['110.a1.h1', '242.a1.a1'], 'core': '110.a1.h1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 4403, -1, 4343, -1, 2412, -1], 'generators': [2, 780], 'label': '1210.9.22.a1.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.h1', 'old_label': '22.a1.h1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.h1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214629
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.i1'], 'contains': ['110.a1.i1', '242.a1.a1'], 'core': '110.a1.i1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 9895, -1, 4343, -1, 189, -1], 'generators': [2, 890], 'label': '1210.9.22.a1.i1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.i1', 'old_label': '22.a1.i1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.i1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214630
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.j1'], 'contains': ['110.a1.j1', '242.a1.a1'], 'core': '110.a1.j1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 5962, -1, 4343, -1, 5080, -1], 'generators': [2, 560], 'label': '1210.9.22.a1.j1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.j1', 'old_label': '22.a1.j1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.j1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214631
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.k1'], 'contains': ['110.a1.k1', '242.a1.a1'], 'core': '110.a1.k1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 6807, -1, 4343, -1, 4636, -1], 'generators': [2, 1000], 'label': '1210.9.22.a1.k1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.k1', 'old_label': '22.a1.k1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.k1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214632
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.l1'], 'contains': ['110.a1.l1', '242.a1.a1'], 'core': '110.a1.l1', 'coset_action_label': None, 'count': 11, 'diagramx': [6154, -1, 9065, -1, 4343, -1, 4191, -1], 'generators': [2, 1110], 'label': '1210.9.22.a1.l1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.l1', 'old_label': '22.a1.l1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.l1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214633
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.a1'], 'contains': ['110.a1.a1', '605.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 172, -1, 6923, -1, 6541, -1], 'generators': [5, 110], 'label': '1210.9.55.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '55.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214634
    {'ambient': '1210.9', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1597200.a', 'aut_weyl_index': 1, 'centralizer': '1210.a1.a1', 'complements': ['242.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '55.a1.a1', '55.a1.b1', '55.a1.c1', '55.a1.d1', '55.a1.e1', '55.a1.f1', '55.a1.g1', '55.a1.h1', '55.a1.i1', '55.a1.j1', '55.a1.k1', '55.a1.l1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3415, 2923, 2403, 4556, 5062, 2388, 7905, 4316], 'generators': [5, 110, 10], 'label': '1210.9.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': '5.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.9'}
  • id: 70214635
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.b1'], 'contains': ['110.a1.b1', '605.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 2005, -1, 6923, -1, 8869, -1], 'generators': [5, 10], 'label': '1210.9.55.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '55.a1.b1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214636
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.c1'], 'contains': ['110.a1.c1', '605.a1.a1'], 'core': '110.a1.c1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 7841, -1, 6923, -1, 7539, -1], 'generators': [5, 120], 'label': '1210.9.55.a1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.c1', 'old_label': '55.a1.c1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214637
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.d1'], 'contains': ['110.a1.d1', '605.a1.a1'], 'core': '110.a1.d1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 3290, -1, 6923, -1, 8537, -1], 'generators': [5, 230], 'label': '1210.9.55.a1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.d1', 'old_label': '55.a1.d1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214638
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.e1'], 'contains': ['110.a1.e1', '605.a1.a1'], 'core': '110.a1.e1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 1615, -1, 6923, -1, 8204, -1], 'generators': [5, 670], 'label': '1210.9.55.a1.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.e1', 'old_label': '55.a1.e1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.e1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214639
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.f1'], 'contains': ['110.a1.f1', '605.a1.a1'], 'core': '110.a1.f1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 562, -1, 6923, -1, 7207, -1], 'generators': [5, 340], 'label': '1210.9.55.a1.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.f1', 'old_label': '55.a1.f1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.f1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214640
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.g1'], 'contains': ['110.a1.g1', '605.a1.a1'], 'core': '110.a1.g1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 2397, -1, 6923, -1, 6874, -1], 'generators': [5, 450], 'label': '1210.9.55.a1.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.g1', 'old_label': '55.a1.g1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.g1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214641
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.h1'], 'contains': ['110.a1.h1', '605.a1.a1'], 'core': '110.a1.h1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 835, -1, 6923, -1, 7872, -1], 'generators': [5, 780], 'label': '1210.9.55.a1.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.h1', 'old_label': '55.a1.h1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.h1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214642
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.i1'], 'contains': ['110.a1.i1', '605.a1.a1'], 'core': '110.a1.i1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 9584, -1, 6923, -1, 6209, -1], 'generators': [5, 890], 'label': '1210.9.55.a1.i1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.i1', 'old_label': '55.a1.i1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.i1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214643
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.j1'], 'contains': ['110.a1.j1', '605.a1.a1'], 'core': '110.a1.j1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 1225, -1, 6923, -1, 9867, -1], 'generators': [5, 560], 'label': '1210.9.55.a1.j1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.j1', 'old_label': '55.a1.j1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.j1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214644
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.k1'], 'contains': ['110.a1.k1', '605.a1.a1'], 'core': '110.a1.k1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 3019, -1, 6923, -1, 9535, -1], 'generators': [5, 1000], 'label': '1210.9.55.a1.k1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.k1', 'old_label': '55.a1.k1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.k1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214645
    {'ambient': '1210.9', 'aut_centralizer_order': 121, 'aut_label': '10.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '13200.a', 'aut_weyl_index': 121, 'centralizer': '10.a1.a1', 'complements': ['121.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['110.a1.a1', '110.a1.b1', '110.a1.c1', '110.a1.d1', '110.a1.e1', '110.a1.f1', '110.a1.g1', '110.a1.h1', '110.a1.i1', '110.a1.j1', '110.a1.k1', '110.a1.l1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8861, 5022, 5380, 4999, 1514, 5037, 5506, 5000], 'generators': [10, 110], 'label': '1210.9.10.a1.a1', 'mobius_quo': 11, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['110.a1.i1', '110.a1.f1', '110.a1.g1', '110.a1.j1', '110.a1.e1', '110.a1.h1', '110.a1.k1', '110.a1.l1', '110.a1.a1', '110.a1.b1', '110.a1.c1', '110.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214646
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.l1'], 'contains': ['110.a1.l1', '605.a1.a1'], 'core': '110.a1.l1', 'coset_action_label': None, 'count': 11, 'diagramx': [3251, -1, 8683, -1, 6923, -1, 9202, -1], 'generators': [5, 1110], 'label': '1210.9.55.a1.l1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.l1', 'old_label': '55.a1.l1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.l1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214647
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.b1', '11.a1.c1', '11.a1.d1', '11.a1.f1', '11.a1.g1', '11.a1.j1', '11.a1.e1', '11.a1.h1', '11.a1.i1', '11.a1.k1', '11.a1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.a1', '55.a1.a1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 3564, 1185, 4343, 5037, 4064, 1185], 'generators': [110], 'label': '1210.9.110.a1.a1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.a1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214648
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.c1', '11.a1.e1', '11.a1.g1', '11.a1.f1', '11.a1.k1', '11.a1.d1', '11.a1.i1', '11.a1.h1', '11.a1.j1', '11.a1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.b1', '55.a1.b1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 4690, 7119, 4343, 5037, 6366, 7119], 'generators': [10], 'label': '1210.9.110.a1.b1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.b1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.b1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214649
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.d1', '11.a1.h1', '11.a1.j1', '11.a1.g1', '11.a1.l1', '11.a1.f1', '11.a1.k1', '11.a1.i1', '11.a1.e1', '11.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.c1', '55.a1.c1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 7903, 3728, 4343, 5037, 5050, 3728], 'generators': [120], 'label': '1210.9.110.a1.c1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.c1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.c1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.c1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214650
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.f1', '11.a1.i1', '11.a1.e1', '11.a1.j1', '11.a1.b1', '11.a1.g1', '11.a1.l1', '11.a1.k1', '11.a1.h1', '11.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.d1', '55.a1.d1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 7094, 6271, 4343, 5037, 6037, 6272], 'generators': [230], 'label': '1210.9.110.a1.d1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.d1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.d1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.d1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214651
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.h1', '11.a1.c1', '11.a1.l1', '11.a1.k1', '11.a1.g1', '11.a1.i1', '11.a1.f1', '11.a1.d1', '11.a1.b1', '11.a1.j1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.e1', '55.a1.e1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 6292, 5424, 4343, 5037, 5708, 5424], 'generators': [670], 'label': '1210.9.110.a1.e1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.e1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.e1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.e1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214652
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.g1', '11.a1.k1', '11.a1.h1', '11.a1.e1', '11.a1.c1', '11.a1.j1', '11.a1.b1', '11.a1.l1', '11.a1.i1', '11.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.f1', '55.a1.f1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 3921, 2880, 4343, 5037, 4722, 2880], 'generators': [340], 'label': '1210.9.110.a1.f1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.f1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.f1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.f1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214653
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.j1', '11.a1.l1', '11.a1.i1', '11.a1.h1', '11.a1.d1', '11.a1.e1', '11.a1.c1', '11.a1.b1', '11.a1.k1', '11.a1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.g1', '55.a1.g1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 4958, 2033, 4343, 5037, 4393, 2033], 'generators': [450], 'label': '1210.9.110.a1.g1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.g1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.g1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.g1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214654
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.i1', '11.a1.d1', '11.a1.b1', '11.a1.l1', '11.a1.j1', '11.a1.k1', '11.a1.g1', '11.a1.f1', '11.a1.c1', '11.a1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.h1', '55.a1.h1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 4190, 4575, 4343, 5037, 5379, 4576], 'generators': [780], 'label': '1210.9.110.a1.h1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.h1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.h1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.h1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214655
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.k1', '11.a1.f1', '11.a1.c1', '11.a1.b1', '11.a1.e1', '11.a1.l1', '11.a1.j1', '11.a1.g1', '11.a1.d1', '11.a1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.i1', '55.a1.i1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.i1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 9584, 337, 4343, 5037, 3735, 337], 'generators': [890], 'label': '1210.9.110.a1.i1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.i1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.i1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.i1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214656
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '55.a1.a1', '121.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 105, -1, 7965, -1, 4217, -1], 'generators': [5, 110, 2], 'label': '1210.9.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214657
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.e1', '11.a1.b1', '11.a1.k1', '11.a1.i1', '11.a1.f1', '11.a1.h1', '11.a1.d1', '11.a1.c1', '11.a1.l1', '11.a1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.j1', '55.a1.j1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.j1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 5591, 9663, 4343, 5037, 7352, 9663], 'generators': [560], 'label': '1210.9.110.a1.j1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.j1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.j1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.j1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214658
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.l1', '11.a1.g1', '11.a1.d1', '11.a1.c1', '11.a1.h1', '11.a1.b1', '11.a1.e1', '11.a1.j1', '11.a1.f1', '11.a1.i1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.k1', '55.a1.k1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.k1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 6826, 8814, 4343, 5037, 7023, 8815], 'generators': [1000], 'label': '1210.9.110.a1.k1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.k1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.k1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.k1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214659
    {'ambient': '1210.9', 'aut_centralizer_order': 13310, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 159720, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1', '11.a1.b1', '11.a1.j1', '11.a1.f1', '11.a1.d1', '11.a1.i1', '11.a1.c1', '11.a1.h1', '11.a1.e1', '11.a1.g1', '11.a1.k1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.l1', '55.a1.l1'], 'contains': ['1210.a1.a1'], 'core': '110.a1.l1', 'coset_action_label': None, 'count': 1, 'diagramx': [7442, 5022, 8808, 7966, 4343, 5037, 6695, 7967], 'generators': [1110], 'label': '1210.9.110.a1.l1', 'mobius_quo': -1, 'mobius_sub': -11, 'normal_closure': '110.a1.l1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.l1', 'projective_image': '1210.9', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.l1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 70214660
    {'ambient': '1210.9', 'aut_centralizer_order': 13200, 'aut_label': '121.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1597200, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1.a1', '11.a1.b1', '11.a1.c1', '11.a1.d1', '11.a1.e1', '11.a1.f1', '11.a1.g1', '11.a1.h1', '11.a1.i1', '11.a1.j1', '11.a1.k1', '11.a1.l1'], 'contains': ['242.a1.a1', '605.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [1271, -1, 2589, -1, 9132, -1, 5876, -1], 'generators': [5, 2], 'label': '1210.9.121.a1.a1', 'mobius_quo': None, 'mobius_sub': 11, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '121.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '121.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70214661
    {'ambient': '1210.9', 'aut_centralizer_order': 13200, 'aut_label': '242.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1597200, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '22.a1.b1', '22.a1.c1', '22.a1.d1', '22.a1.e1', '22.a1.f1', '22.a1.g1', '22.a1.h1', '22.a1.i1', '22.a1.j1', '22.a1.k1', '22.a1.l1', '121.a1.a1'], 'contains': ['1210.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5230, -1, 6011, -1, 6328, -1, 3081, -1], 'generators': [2], 'label': '1210.9.242.a1.a1', 'mobius_quo': None, 'mobius_sub': -11, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '242.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70214662
    {'ambient': '1210.9', 'aut_centralizer_order': 13200, 'aut_label': '605.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1597200, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1.a1', '55.a1.b1', '55.a1.c1', '55.a1.d1', '55.a1.e1', '55.a1.f1', '55.a1.g1', '55.a1.h1', '55.a1.i1', '55.a1.j1', '55.a1.k1', '55.a1.l1', '121.a1.a1'], 'contains': ['1210.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3349, -1, 2473, -1, 8114, -1, 7662, -1], 'generators': [5], 'label': '1210.9.605.a1.a1', 'mobius_quo': None, 'mobius_sub': -11, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70214663
    {'ambient': '1210.9', 'aut_centralizer_order': None, 'aut_label': '1210.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': ['110.a1.a1', '110.a1.b1', '110.a1.c1', '110.a1.d1', '110.a1.e1', '110.a1.f1', '110.a1.g1', '110.a1.h1', '110.a1.i1', '110.a1.j1', '110.a1.k1', '110.a1.l1', '242.a1.a1', '605.a1.a1'], 'contains': [], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5230, 5022, 5324, 4999, 6328, 5037, 5544, 5000], 'generators': [], 'label': '1210.9.1210.a1.a1', 'mobius_quo': 1, 'mobius_sub': 1331, 'normal_closure': '1210.a1.a1', 'normal_contained_in': ['110.a1.i1', '110.a1.f1', '110.a1.g1', '110.a1.j1', '110.a1.e1', '110.a1.h1', '110.a1.k1', '110.a1.l1', '110.a1.a1', '110.a1.b1', '110.a1.c1', '110.a1.d1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1210.a1.a1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 70214664
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.b1', '55.a1.b1', '121.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 2153, -1, 7965, -1, 6493, -1], 'generators': [5, 10, 2], 'label': '1210.9.11.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '11.a1.b1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214665
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.c1', '55.a1.c1', '121.a1.a1'], 'core': '110.a1.c1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 7995, -1, 7965, -1, 5193, -1], 'generators': [5, 120, 2], 'label': '1210.9.11.a1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.c1', 'old_label': '11.a1.c1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214666
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.d1', '55.a1.d1', '121.a1.a1'], 'core': '110.a1.d1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 3434, -1, 7965, -1, 6168, -1], 'generators': [5, 230, 2], 'label': '1210.9.11.a1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.d1', 'old_label': '11.a1.d1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 70214667
    {'ambient': '1210.9', 'aut_centralizer_order': 110, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '110.1', 'aut_weyl_index': 14520, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.e1', '55.a1.e1', '121.a1.a1'], 'core': '110.a1.e1', 'coset_action_label': None, 'count': 11, 'diagramx': [1139, -1, 1768, -1, 7965, -1, 5843, -1], 'generators': [5, 670, 2], 'label': '1210.9.11.a1.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.e1', 'old_label': '11.a1.e1', 'projective_image': '1210.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.e1', 'subgroup_fusion': None, 'weyl_group': '110.1'}