Abstract group data - 512.41229

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2], 'aut_gens': [[20922662476800, 4103606707223, 1314028759703, 4103734078080, 1313901405496, 9709841473896, 4103734094783, 2789792426303, 1313941673647], [20922702768016, 1314028776367, 2789745609600, 2789792409600, 40296376, 6920263514879, 2789792421136, 4103734089616, 1313941673647], [16819142877503, 2789705329920, 127382400, 11536, 2789832694440, 9709881753583, 2789792421136, 4103734089616, 1313941673647], [19608801384383, 4103606718727, 40279680, 1313941680016, 40284840, 6920223235192, 4103734094783, 1313941668480, 1313941673647], [14002566664896, 2789745609607, 2789745614767, 4103734078080, 4103693803560, 8395980353272, 4103734094783, 4103734089616, 1313941673647], [14002653767616, 4103606707223, 2789705323576, 16703, 40296376, 5606362126072, 4103734094783, 2789792426303, 1313941673647], [11212861351679, 4103606712376, 1313988491520, 1313941680016, 1313901405496, 6920223230039, 4103734094783, 4103734089616, 1313941673647], [15316555156423, 4103606712376, 1314028776360, 1313941680016, 1313901400343, 6920223235192, 4103734094783, 2789792426303, 1313941673647], [18133044261136, 4103606707223, 87096376, 4103734078080, 1313901405496, 9709841473896, 4103734094783, 2789792426303, 1313941673647], [20922662488336, 127387560, 4103647003560, 4103734078080, 40291223, 6920223235192, 4103734094783, 2789792426303, 1313941673647], [18133044249600, 2789745603256, 87102727, 4103734078080, 2789832689287, 6920223235192, 4103734094783, 2789792426303, 1313941673647], [19608801372847, 2789745603256, 87096376, 4103734078080, 1313901405496, 9709841473896, 4103734094783, 2789792426303, 1313941673647], [18133044249600, 2789745603256, 2789705318423, 4103734078080, 2789832689287, 6920223235192, 4103734094783, 2789792426303, 1313941673647], [20922662488336, 1313988491527, 1314028759703, 4103734078080, 1313901405496, 6920223235192, 4103734094783, 2789792426303, 1313941673647]], 'aut_group': '262144.n', 'aut_hash': 5987543607828864560, 'aut_nilpotency_class': 6, 'aut_nilpotent': True, 'aut_order': 262144, 'aut_permdeg': 256, 'aut_perms': [803313321780109011834602804331014194281566606155543294235243735230451126662799307630064176886751621835874945211509782012520095463686050118512182641752847238326943078131253576735182483537839602459676876710649283515944150398692716205756850222602831520130229483314775409426267098532369542824991833781266595622367544250447959682959824149958466373430272401080582017050417725122364911401785512273913344674842424414543392401914425724445030052583256256835704844427275587613950419058878309309669754486151136861807397, 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785846370260914543191173320195376718805195826158852416228646513421527107975617457276258624841346168111478805737717724305480435327206822407710573963531630766970101871906503743675272646178434602191358877013275850103960629611193109900862588794951722423430534800547822275937536931352646385175961596754758782693579957011670697054835497442487223564672305742819845501914526632427051321469134907313847823864299899618153654256751628331902619044968351228878660964388571784707373148179310822320788130864703076255887626], 'aut_phi_ratio': 1024.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 2, 4, 1], [2, 4, 4, 1], [2, 4, 8, 1], [2, 4, 16, 1], [2, 16, 1, 1], [4, 8, 4, 1], [4, 16, 1, 1], [4, 16, 4, 1], [8, 32, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^9.D_4^2:D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 8, 'autcentquo_group': None, 'autcentquo_hash': 3482832714989627550, 'autcentquo_nilpotent': True, 'autcentquo_order': 4096, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3.C_2^5.C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 6], [2, 4, 28], [2, 16, 1], [4, 8, 4], [4, 16, 5], [8, 32, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '128.513', 'commutator_count': 1, 'commutator_label': '32.51', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 41229, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 6], [2, 4, 1, 28], [2, 16, 1, 1], [4, 8, 1, 4], [4, 16, 1, 5], [8, 32, 2, 4]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': 168, 'exponent': 8, 'exponents_of_order': [9], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '64.193', 'frattini_quotient': '8.5', 'hash': 41229, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [4, 2, 2, 2, 2, 2, 1, 2, 1], 'inner_gens': [[20922662476800, 127370903, 127387567, 16703, 4103693798407, 9709841473896, 4103734094783, 4103734089616, 1313941673647], [20922662493503, 4103606707223, 1314028759703, 4103734078080, 1313901405496, 5606362120919, 4103734094783, 2789792426303, 1313941673647], [18133084534440, 4103606707223, 1314028759703, 4103734078080, 1313901405496, 6920223230039, 4103734094783, 2789792426303, 1313941673647], [16819183157183, 4103606707223, 1314028759703, 4103734078080, 1313901405496, 9709841473896, 4103734094783, 2789792426303, 1313941673647], [16819183152016, 4103606707223, 1314028759703, 4103734078080, 1313901405496, 8395980359623, 4103734094783, 2789792426303, 1313941673647], [20922662476800, 127387560, 4103647003560, 4103734078080, 40291223, 9709841473896, 4103734094783, 2789792426303, 1313941673647], [20922662476800, 4103606707223, 1314028759703, 4103734078080, 1313901405496, 9709841473896, 4103734094783, 2789792426303, 1313941673647], [19608801372847, 4103606707223, 1314028759703, 4103734078080, 1313901405496, 9709841473896, 4103734094783, 2789792426303, 1313941673647], [20922662476800, 4103606707223, 1314028759703, 4103734078080, 1313901405496, 9709841473896, 4103734094783, 2789792426303, 1313941673647]], 'inner_hash': 513, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': False, 'inner_tex': 'C_2^5:C_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12], [4, 28]], 'label': '512.41229', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^7.C4', 'ngens': 9, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 56, 'number_divisions': 52, 'number_normal_subgroups': 102, 'number_subgroup_autclasses': 348, 'number_subgroup_classes': 8367, 'number_subgroups': 32986, 'old_label': None, 'order': 512, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 143], [4, 112], [8, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 8, 'outer_gen_orders': [4, 4, 4, 4], 'outer_gen_pows': [2789792426303, 6920136150359, 0, 8396027164783], 'outer_gens': [[19608888475560, 87107887, 1313988491520, 4103734083247, 4103693798407, 8395940073599, 2789792421136, 4103734089616, 1313941673647], [16819096054456, 2789705323583, 2789792414760, 4103734083247, 4103693815096, 8395940073599, 2789792421136, 5167, 1313941673647], [15316555161576, 2789745603256, 2789705323576, 16703, 40296376, 5606362120919, 4103734094783, 2789792426303, 1313941673647], [15316468070399, 87096383, 4103734078087, 4103734083247, 2789832705976, 5606321852736, 2789792421136, 5167, 1313941673647]], 'outer_group': '2048.cpg', 'outer_hash': 7841393102724273575, 'outer_nilpotent': True, 'outer_order': 2048, 'outer_permdeg': 20, 'outer_perms': [143460373796904974, 1007568450042634218, 65491042780367400, 1911643007864896209], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5.D_4^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 28]], 'representations': {'PC': {'code': '68597353910820870211159777121238464545255706119', 'gens': [1, 3, 5, 6, 7, 8, 9], 'pres': [9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 586, 5078, 1037, 74, 1443, 3604, 12103, 5776, 2905, 30464, 14273, 7154]}, 'Perm': {'d': 16, 'gens': [20922662476800, 4103606707223, 1314028759703, 4103734078080, 1313901405496, 9709841473896, 4103734094783, 2789792426303, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^7.C_4', 'transitive_degree': 16, '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: 105623679
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 41229, 'group_order': 512, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 105623690
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 41229, 'group_order': 512, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 1313941673647, 'size': 1}
  • id: 105623701
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 41229, 'group_order': 512, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 2789792421136, 'size': 1}
  • id: 105623712
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 41229, 'group_order': 512, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 4103734094783, 'size': 1}
  • id: 105623723
    {'aut_label': '2D', 'centralizer': '2.b1', 'counter': 5, 'group_counter': 41229, 'group_order': 512, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 11536, 'size': 2}
  • id: 105623731
    {'aut_label': '2D', 'centralizer': '2.b1', 'counter': 6, 'group_counter': 41229, 'group_order': 512, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 16703, 'size': 2}
  • id: 105623732
    {'aut_label': '2D', 'centralizer': '2.b1', 'counter': 7, 'group_counter': 41229, 'group_order': 512, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 1313941680016, 'size': 2}
  • id: 105623733
    {'aut_label': '2D', 'centralizer': '2.b1', 'counter': 8, 'group_counter': 41229, 'group_order': 512, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 1313941685183, 'size': 2}
  • id: 105623734
    {'aut_label': '2H', 'centralizer': '2.b1', 'counter': 9, 'group_counter': 41229, 'group_order': 512, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 5167, 'size': 2}
  • id: 105623680
    {'aut_label': '2H', 'centralizer': '2.b1', 'counter': 10, 'group_counter': 41229, 'group_order': 512, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 2789792426303, 'size': 2}
  • id: 105623681
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 11, 'group_counter': 41229, 'group_order': 512, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 7, 'size': 4}
  • id: 105623682
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 12, 'group_counter': 41229, 'group_order': 512, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 11543, 'size': 4}
  • id: 105623683
    {'aut_label': '2L', 'centralizer': '4.c1', 'counter': 13, 'group_counter': 41229, 'group_order': 512, 'label': '2L', 'order': 2, 'powers': [1], 'representative': 40279687, 'size': 4}
  • id: 105623684
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 14, 'group_counter': 41229, 'group_order': 512, 'label': '2M', 'order': 2, 'powers': [1], 'representative': 40284847, 'size': 4}
  • id: 105623685
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 15, 'group_counter': 41229, 'group_order': 512, 'label': '2N', 'order': 2, 'powers': [1], 'representative': 40291216, 'size': 4}
  • id: 105623686
    {'aut_label': '2L', 'centralizer': '4.c1', 'counter': 16, 'group_counter': 41229, 'group_order': 512, 'label': '2O', 'order': 2, 'powers': [1], 'representative': 40291223, 'size': 4}
  • id: 105623687
    {'aut_label': '2L', 'centralizer': '4.c1', 'counter': 17, 'group_counter': 41229, 'group_order': 512, 'label': '2P', 'order': 2, 'powers': [1], 'representative': 40296376, 'size': 4}
  • id: 105623688
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 18, 'group_counter': 41229, 'group_order': 512, 'label': '2Q', 'order': 2, 'powers': [1], 'representative': 40296383, 'size': 4}
  • id: 105623689
    {'aut_label': '2R', 'centralizer': '4.c1', 'counter': 19, 'group_counter': 41229, 'group_order': 512, 'label': '2R', 'order': 2, 'powers': [1], 'representative': 87091216, 'size': 4}
  • id: 105623691
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 20, 'group_counter': 41229, 'group_order': 512, 'label': '2S', 'order': 2, 'powers': [1], 'representative': 87091223, 'size': 4}
  • id: 105623692
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 21, 'group_counter': 41229, 'group_order': 512, 'label': '2T', 'order': 2, 'powers': [1], 'representative': 87096376, 'size': 4}
  • id: 105623693
    {'aut_label': '2R', 'centralizer': '4.c1', 'counter': 22, 'group_counter': 41229, 'group_order': 512, 'label': '2U', 'order': 2, 'powers': [1], 'representative': 87096383, 'size': 4}
  • id: 105623694
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 23, 'group_counter': 41229, 'group_order': 512, 'label': '2V', 'order': 2, 'powers': [1], 'representative': 87102727, 'size': 4}
  • id: 105623695
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 24, 'group_counter': 41229, 'group_order': 512, 'label': '2W', 'order': 2, 'powers': [1], 'representative': 87107880, 'size': 4}
  • id: 105623696
    {'aut_label': '2R', 'centralizer': '4.c1', 'counter': 25, 'group_counter': 41229, 'group_order': 512, 'label': '2X', 'order': 2, 'powers': [1], 'representative': 87107887, 'size': 4}
  • id: 105623697
    {'aut_label': '2R', 'centralizer': '4.c1', 'counter': 26, 'group_counter': 41229, 'group_order': 512, 'label': '2Y', 'order': 2, 'powers': [1], 'representative': 127370903, 'size': 4}
  • id: 105623698
    {'aut_label': '2R', 'centralizer': '4.c1', 'counter': 27, 'group_counter': 41229, 'group_order': 512, 'label': '2Z', 'order': 2, 'powers': [1], 'representative': 127376056, 'size': 4}
  • id: 105623699
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 28, 'group_counter': 41229, 'group_order': 512, 'label': '2AA', 'order': 2, 'powers': [1], 'representative': 127376063, 'size': 4}
  • id: 105623700
    {'aut_label': '2R', 'centralizer': '4.c1', 'counter': 29, 'group_counter': 41229, 'group_order': 512, 'label': '2AB', 'order': 2, 'powers': [1], 'representative': 127382407, 'size': 4}
  • id: 105623702
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 30, 'group_counter': 41229, 'group_order': 512, 'label': '2AC', 'order': 2, 'powers': [1], 'representative': 127387567, 'size': 4}
  • id: 105623703
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 31, 'group_counter': 41229, 'group_order': 512, 'label': '2AD', 'order': 2, 'powers': [1], 'representative': 1313941680023, 'size': 4}
  • id: 105623704
    {'aut_label': '2R', 'centralizer': '4.c1', 'counter': 32, 'group_counter': 41229, 'group_order': 512, 'label': '2AE', 'order': 2, 'powers': [1], 'representative': 1313988485176, 'size': 4}
  • id: 105623705
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 33, 'group_counter': 41229, 'group_order': 512, 'label': '2AF', 'order': 2, 'powers': [1], 'representative': 1313988485183, 'size': 4}
  • id: 105623706
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 34, 'group_counter': 41229, 'group_order': 512, 'label': '2AG', 'order': 2, 'powers': [1], 'representative': 1313988496687, 'size': 4}
  • id: 105623707
    {'aut_label': '2R', 'centralizer': '4.c1', 'counter': 35, 'group_counter': 41229, 'group_order': 512, 'label': '2AH', 'order': 2, 'powers': [1], 'representative': 1314028764863, 'size': 4}
  • id: 105623708
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 36, 'group_counter': 41229, 'group_order': 512, 'label': '2AI', 'order': 2, 'powers': [1], 'representative': 2789792421143, 'size': 4}
  • id: 105623709
    {'aut_label': '2L', 'centralizer': '4.c1', 'counter': 37, 'group_counter': 41229, 'group_order': 512, 'label': '2AJ', 'order': 2, 'powers': [1], 'representative': 2789832700823, 'size': 4}
  • id: 105623710
    {'aut_label': '2J', 'centralizer': '4.c1', 'counter': 38, 'group_counter': 41229, 'group_order': 512, 'label': '2AK', 'order': 2, 'powers': [1], 'representative': 2789832705983, 'size': 4}
  • id: 105623711
    {'aut_label': '2AL', 'centralizer': '16.c1', 'counter': 39, 'group_counter': 41229, 'group_order': 512, 'label': '2AL', 'order': 2, 'powers': [1], 'representative': 5606234750016, 'size': 16}
  • id: 105623713
    {'aut_label': '4A', 'centralizer': '8.r1', 'counter': 40, 'group_counter': 41229, 'group_order': 512, 'label': '4A', 'order': 4, 'powers': [3], 'representative': 9709881742079, 'size': 8}
  • id: 105623714
    {'aut_label': '4A', 'centralizer': '8.r1', 'counter': 41, 'group_counter': 41229, 'group_order': 512, 'label': '4B', 'order': 4, 'powers': [4], 'representative': 6920223230039, 'size': 8}
  • id: 105623715
    {'aut_label': '4A', 'centralizer': '8.r1', 'counter': 42, 'group_counter': 41229, 'group_order': 512, 'label': '4C', 'order': 4, 'powers': [4], 'representative': 8395980353272, 'size': 8}
  • id: 105623716
    {'aut_label': '4A', 'centralizer': '8.r1', 'counter': 43, 'group_counter': 41229, 'group_order': 512, 'label': '4D', 'order': 4, 'powers': [3], 'representative': 5606321846399, 'size': 8}
  • id: 105623717
    {'aut_label': '4E', 'centralizer': '16.r1', 'counter': 44, 'group_counter': 41229, 'group_order': 512, 'label': '4E', 'order': 4, 'powers': [9], 'representative': 5606234750023, 'size': 16}
  • id: 105623718
    {'aut_label': '4E', 'centralizer': '16.r1', 'counter': 45, 'group_counter': 41229, 'group_order': 512, 'label': '4F', 'order': 4, 'powers': [9], 'representative': 5606234761559, 'size': 16}
  • id: 105623719
    {'aut_label': '4G', 'centralizer': '16.e1', 'counter': 46, 'group_counter': 41229, 'group_order': 512, 'label': '4G', 'order': 4, 'powers': [2], 'representative': 5606275029703, 'size': 16}
  • id: 105623720
    {'aut_label': '4E', 'centralizer': '16.r1', 'counter': 47, 'group_counter': 41229, 'group_order': 512, 'label': '4H', 'order': 4, 'powers': [10], 'representative': 5606321841239, 'size': 16}
  • id: 105623721
    {'aut_label': '4E', 'centralizer': '16.r1', 'counter': 48, 'group_counter': 41229, 'group_order': 512, 'label': '4I', 'order': 4, 'powers': [10], 'representative': 5606321852743, 'size': 16}
  • id: 105623722
    {'aut_label': '8A1', 'centralizer': '32.x1', 'counter': 49, 'group_counter': 41229, 'group_order': 512, 'label': '8A1', 'order': 8, 'powers': [40], 'representative': 16819055774783, 'size': 32}
  • id: 105623724
    {'aut_label': '8A1', 'centralizer': '32.x1', 'counter': 50, 'group_counter': 41229, 'group_order': 512, 'label': '8A-1', 'order': 8, 'powers': [40], 'representative': 12526849826496, 'size': 32}
  • id: 105623725
    {'aut_label': '8A1', 'centralizer': '32.x1', 'counter': 51, 'group_counter': 41229, 'group_order': 512, 'label': '8B1', 'order': 8, 'powers': [41], 'representative': 14002653772783, 'size': 32}
  • id: 105623726
    {'aut_label': '8A1', 'centralizer': '32.x1', 'counter': 52, 'group_counter': 41229, 'group_order': 512, 'label': '8B-1', 'order': 8, 'powers': [41], 'representative': 18133084540823, 'size': 32}
  • id: 105623727
    {'aut_label': '8A1', 'centralizer': '32.x1', 'counter': 53, 'group_counter': 41229, 'group_order': 512, 'label': '8C1', 'order': 8, 'powers': [42], 'representative': 19608848195880, 'size': 32}
  • id: 105623728
    {'aut_label': '8A1', 'centralizer': '32.x1', 'counter': 54, 'group_counter': 41229, 'group_order': 512, 'label': '8C-1', 'order': 8, 'powers': [42], 'representative': 15316427785552, 'size': 32}
  • id: 105623729
    {'aut_label': '8A1', 'centralizer': '32.x1', 'counter': 55, 'group_counter': 41229, 'group_order': 512, 'label': '8D1', 'order': 8, 'powers': [43], 'representative': 20922662488343, 'size': 32}
  • id: 105623730
    {'aut_label': '8A1', 'centralizer': '32.x1', 'counter': 56, 'group_counter': 41229, 'group_order': 512, 'label': '8D-1', 'order': 8, 'powers': [43], 'representative': 14002653756119, 'size': 32}
• 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: 3516547
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3516558
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3516569
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3516580
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3516591
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3516595
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3516596
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3516597
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3516598
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, -2, -2, -2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516548
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, -2, -2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, -2, 2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516549
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516550
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516551
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, -2, 0, 0, 0, -2, 0, 2, 2, -2, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 2, 0, -2, 0, 0, -2, 2, 2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516552
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, -2, 0, 0, 0, -2, 0, 2, 2, -2, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 2, 0, -2, 0, 0, 2, -2, -2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516553
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, -2, 2, 2, 2, 0, 2, -2, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, -2, -2, 2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516554
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, -2, 2, 2, 2, 0, 2, -2, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, -2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516555
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 2, -2, 2, -2, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, -2, 2, 0, 0, -2, -2, 2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516556
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 2, -2, 2, -2, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, -2, 2, 0, 0, 2, 2, -2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516557
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 2, 0, 0, 0, 2, 0, -2, 2, 2, -2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, -2, 0, -2, 0, 0, -2, 2, 2, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516559
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 2, 0, 0, 0, 2, 0, -2, 2, 2, -2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, -2, 0, -2, 0, 0, 2, -2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516560
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2i', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, -2, 2, 2, 0, 0, -2, 0, 0, 0, -2, 2, -2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516561
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2j', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, -2, 2, 2, 0, 0, -2, 0, 0, 0, -2, 2, 2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516562
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2k', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -2, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, -2, -2, -2, 0, 0, 2, 0, 0, 0, -2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516563
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.2l', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -2, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, -2, -2, -2, 0, 0, 2, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516564
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4a', 'multiplicity': 1, 'nt': [8, 16], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -4, 0, 0, 4, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516565
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4b', 'multiplicity': 1, 'nt': [8, 16], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516566
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4c', 'multiplicity': 1, 'nt': [8, 16], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516567
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4d', 'multiplicity': 1, 'nt': [8, 16], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -4, 0, 0, 4, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516568
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4e', 'multiplicity': 1, 'nt': [8, 16], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, 0, 0, -4, 0, -4, 0, 0, 0, -4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516570
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4f', 'multiplicity': 1, 'nt': [8, 16], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516571
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4g', 'multiplicity': 1, 'nt': [8, 16], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516572
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4h', 'multiplicity': 1, 'nt': [8, 16], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, 0, 0, -4, 0, 4, 0, 0, 0, 4, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516573
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4i', 'multiplicity': 1, 'nt': [8, 19], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516574
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4j', 'multiplicity': 1, 'nt': [8, 19], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, 4, 4, -4, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516575
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4k', 'multiplicity': 1, 'nt': [8, 19], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516576
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4l', 'multiplicity': 1, 'nt': [8, 19], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516577
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4m', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, -4, 4, 0, 0, -2, -2, -2, 0, 2, 4, 2, 0, -2, 2, 2, -2, 0, 2, 0, -2, 0, 0, 0, 2, 2, -4, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516578
    {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4n', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, -4, 4, 0, 0, -2, 2, 2, 0, 2, -4, 2, 0, -2, 2, -2, 2, 0, -2, 0, 2, 0, 0, 0, -2, 2, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516579
    {'cdim': 4, 'counter': 39, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4o', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, -4, 4, 0, 0, 2, -2, -2, 0, -2, -4, -2, 0, 2, -2, 2, -2, 0, 2, 0, -2, 0, 0, 0, 2, -2, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516581
    {'cdim': 4, 'counter': 40, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4p', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, -4, 4, 0, 0, 2, 2, 2, 0, -2, 4, -2, 0, 2, -2, -2, 2, 0, -2, 0, 2, 0, 0, 0, -2, -2, -4, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516582
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4q', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 4, -4, 0, -4, -2, 2, 2, 0, 2, 0, -2, 0, -2, -2, -2, -2, 0, 2, 4, -2, 0, 0, 0, -2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516583
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4r', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 4, -4, 0, -4, 2, -2, -2, 0, -2, 0, 2, 0, 2, 2, 2, 2, 0, -2, 4, 2, 0, 0, 0, 2, -2, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516584
    {'cdim': 4, 'counter': 43, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4s', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 4, -4, 0, 4, -2, -2, -2, 0, 2, 0, -2, 0, -2, -2, 2, 2, 0, -2, -4, 2, 0, 0, 0, 2, 2, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516585
    {'cdim': 4, 'counter': 44, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4t', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 4, -4, 0, 4, 2, 2, 2, 0, -2, 0, 2, 0, 2, 2, -2, -2, 0, 2, -4, -2, 0, 0, 0, -2, -2, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516586
    {'cdim': 4, 'counter': 45, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4u', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, -2, -2, 2, 4, 2, 0, 2, 0, 2, -2, 2, 2, 0, -2, 0, -2, 0, 0, -4, -2, -2, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516587
    {'cdim': 4, 'counter': 46, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4v', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, -2, 2, -2, -4, 2, 0, 2, 0, 2, -2, -2, -2, 0, 2, 0, 2, 0, 0, 4, 2, -2, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516588
    {'cdim': 4, 'counter': 47, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4w', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 2, -2, 2, -4, -2, 0, -2, 0, -2, 2, 2, 2, 0, -2, 0, -2, 0, 0, 4, -2, 2, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516589
    {'cdim': 4, 'counter': 48, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4x', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 2, 2, -2, 4, -2, 0, -2, 0, -2, 2, -2, -2, 0, 2, 0, 2, 0, 0, -4, 2, 2, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516590
    {'cdim': 4, 'counter': 49, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4y', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, -2, -2, 2, 0, 2, 0, -2, 0, 2, 2, 2, -2, 0, 2, 0, 2, 0, -4, 0, -2, -2, 0, -2, 2, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516592
    {'cdim': 4, 'counter': 50, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4z', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, -2, 2, -2, 0, 2, 0, -2, 0, 2, 2, -2, 2, 0, -2, 0, -2, 0, 4, 0, 2, -2, 0, -2, 2, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516593
    {'cdim': 4, 'counter': 51, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4aa', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 2, -2, 2, 0, -2, 0, 2, 0, -2, -2, 2, -2, 0, 2, 0, 2, 0, 4, 0, -2, 2, 0, 2, -2, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3516594
    {'cdim': 4, 'counter': 52, 'faithful': False, 'group': '512.41229', 'group_order': 512, 'image': None, 'label': '512.41229.4ab', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 2, 2, -2, 0, -2, 0, 2, 0, -2, -2, -2, 2, 0, -2, 0, -2, 0, -4, 0, 2, 2, 0, 2, -2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 5029487
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 512, 'label': '512.41229.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5029498
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 256, 'label': '512.41229.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5029509
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 256, 'label': '512.41229.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5029520
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 256, 'label': '512.41229.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5029531
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 256, 'label': '512.41229.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5029539
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 256, 'label': '512.41229.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5029540
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 256, 'label': '512.41229.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5029541
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 256, 'label': '512.41229.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5029542
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 128, 'label': '512.41229.1i1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5029488
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 128, 'label': '512.41229.1i2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5029489
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 128, 'label': '512.41229.1j1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5029490
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 128, 'label': '512.41229.1j2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5029491
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1', 'kernel_order': 128, 'label': '512.41229.1k1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5029492
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1', 'kernel_order': 128, 'label': '512.41229.1k2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5029493
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1', 'kernel_order': 128, 'label': '512.41229.1l1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 5029494
    {'center': '1.a1', 'center_index': 1, 'center_order': 512, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1', 'kernel_order': 128, 'label': '512.41229.1l2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 5029495
    {'center': '4.b1', 'center_index': 4, 'center_order': 128, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 64, 'label': '512.41229.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029496
    {'center': '4.b1', 'center_index': 4, 'center_order': 128, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 64, 'label': '512.41229.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029497
    {'center': '4.b1', 'center_index': 4, 'center_order': 128, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 64, 'label': '512.41229.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029499
    {'center': '4.b1', 'center_index': 4, 'center_order': 128, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 64, 'label': '512.41229.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029500
    {'center': '4.b1', 'center_index': 4, 'center_order': 128, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 64, 'label': '512.41229.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029501
    {'center': '4.b1', 'center_index': 4, 'center_order': 128, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 64, 'label': '512.41229.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029502
    {'center': '4.b1', 'center_index': 4, 'center_order': 128, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 64, 'label': '512.41229.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029503
    {'center': '4.b1', 'center_index': 4, 'center_order': 128, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 64, 'label': '512.41229.2h', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029504
    {'center': '4.d1', 'center_index': 4, 'center_order': 128, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.g1', 'kernel_order': 64, 'label': '512.41229.2i', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029505
    {'center': '4.d1', 'center_index': 4, 'center_order': 128, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1', 'kernel_order': 64, 'label': '512.41229.2j', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029506
    {'center': '4.d1', 'center_index': 4, 'center_order': 128, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.g1', 'kernel_order': 64, 'label': '512.41229.2k', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029507
    {'center': '4.d1', 'center_index': 4, 'center_order': 128, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1', 'kernel_order': 64, 'label': '512.41229.2l', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029508
    {'center': '16.f1', 'center_index': 16, 'center_order': 32, 'counter': 29, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.7', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1', 'kernel_order': 16, 'label': '512.41229.4a', 'nt': [8, 16], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029537
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 55, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4aa', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029538
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 56, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4ab', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029510
    {'center': '16.f1', 'center_index': 16, 'center_order': 32, 'counter': 30, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.7', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1', 'kernel_order': 16, 'label': '512.41229.4b', 'nt': [8, 16], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029511
    {'center': '16.f1', 'center_index': 16, 'center_order': 32, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.7', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1', 'kernel_order': 16, 'label': '512.41229.4c', 'nt': [8, 16], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029512
    {'center': '16.f1', 'center_index': 16, 'center_order': 32, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.7', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1', 'kernel_order': 16, 'label': '512.41229.4d', 'nt': [8, 16], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029513
    {'center': '16.f1', 'center_index': 16, 'center_order': 32, 'counter': 33, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.7', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1', 'kernel_order': 16, 'label': '512.41229.4e', 'nt': [8, 16], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029514
    {'center': '16.f1', 'center_index': 16, 'center_order': 32, 'counter': 34, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.7', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1', 'kernel_order': 16, 'label': '512.41229.4f', 'nt': [8, 16], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029515
    {'center': '16.f1', 'center_index': 16, 'center_order': 32, 'counter': 35, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.7', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1', 'kernel_order': 16, 'label': '512.41229.4g', 'nt': [8, 16], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029516
    {'center': '16.f1', 'center_index': 16, 'center_order': 32, 'counter': 36, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.7', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1', 'kernel_order': 16, 'label': '512.41229.4h', 'nt': [8, 16], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029517
    {'center': '16.b1', 'center_index': 16, 'center_order': 32, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.6', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 16, 'label': '512.41229.4i', 'nt': [8, 19], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029518
    {'center': '16.b1', 'center_index': 16, 'center_order': 32, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.6', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 16, 'label': '512.41229.4j', 'nt': [8, 19], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029519
    {'center': '16.b1', 'center_index': 16, 'center_order': 32, 'counter': 39, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.6', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 16, 'label': '512.41229.4k', 'nt': [8, 19], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029521
    {'center': '16.b1', 'center_index': 16, 'center_order': 32, 'counter': 40, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '32.6', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 16, 'label': '512.41229.4l', 'nt': [8, 19], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029522
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 41, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4m', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029523
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 42, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4n', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029524
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4o', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029525
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 44, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4p', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029526
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4q', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029527
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4r', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029528
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 47, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4s', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029529
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 48, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4t', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029530
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 49, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4u', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029532
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 50, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4v', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029533
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 51, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4w', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029534
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 52, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4x', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029535
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 53, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4y', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5029536
    {'center': '32.a1', 'center_index': 32, 'center_order': 16, 'counter': 54, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.41229', 'group_counter': 41229, 'group_order': 512, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.d1', 'kernel_order': 8, 'label': '512.41229.4z', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 59121543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 512, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '512.41229.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '512.41229', 'subgroup_hash': 1311698700316408213, 'subgroup_order': 512, 'subgroup_tex': 'C_2^7.C_4', 'supersolvable': True, 'sylow': 2}
  • id: 59121654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 256, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.4487', 'subgroup_hash': 4487, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59121765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 256, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 256, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.1535', 'subgroup_hash': 1535, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 59121869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.194', 'subgroup_hash': 194, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59121555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.515', 'subgroup_hash': 515, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.194', 'subgroup_hash': 194, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59121599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.48', 'subgroup_hash': 48, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59121610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.4.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59121632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59121643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121710
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59121721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.4', 'subgroup_hash': 4, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59121754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59121799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.88', 'subgroup_hash': 88, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59121820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.s2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121826
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59121827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.4', 'subgroup_hash': 4, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59121830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121831
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59121832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121833
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.8.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59121834
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121835
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121838
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121839
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121840
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.j2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.o2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59121855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.p2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59121856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121863
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121864
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59121872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121879
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bo2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bo2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bo3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bo3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121887
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121888
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bp3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121890
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121545
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bq3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121547
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bq4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121551
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121552
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121553
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bv2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121554
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bv3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121556
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121561
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.16.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59121562
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121563
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 16, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.22', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 22, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['U2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121564
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.22', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 22, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121567
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121572
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.j2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121575
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121576
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121578
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121579
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121580
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121581
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121582
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.q2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121584
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121590
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59121591
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121592
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121593
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.z2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121594
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121597
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121598
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121602
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bk2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bk3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121609
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bk4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121611
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121613
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bo2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121619
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121620
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121622
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bq3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.br2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.br3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.br4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.br5', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bs3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bt2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bt3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59121637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bv2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121640
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121641
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121642
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121644
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121649
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121650
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121651
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.ce2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ce2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121652
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.ce3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ce3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121658
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.ci2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ci2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121661
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121662
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cj3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121664
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121670
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121671
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.co2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.32.co3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59121673
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 8, 'counter': 216, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.90', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 90, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 217, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.60', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 60, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4:C_4', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121675
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 218, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.92', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 92, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 219, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.32', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 32, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\wr C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121678
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121679
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121681
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121682
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121683
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121684
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121685
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121687
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.m2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.m2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121691
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121692
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.q2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.q2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121697
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121698
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121701
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.w2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121702
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.w3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121704
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121706
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121707
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.ba2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ba2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121708
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121709
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121712
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121713
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bc3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bc4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121716
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121717
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121718
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.be2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121719
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121720
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121722
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121723
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bi2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121727
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121728
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121729
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121731
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bm3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bm3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121734
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121737
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 274, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.64.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59121738
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121739
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.br2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.br2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121740
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121741
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121742
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bs3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bs3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121744
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121745
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bt2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121746
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121747
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bu2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bu2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bu3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bu3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121749
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121750
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121751
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121752
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121755
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.ca2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ca2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.ca3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ca3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.ca4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ca4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.ca5', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ca5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.cb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121762
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121763
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.cc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121764
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121767
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.cd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.64.cd3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cd3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59121769
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': True, 'central_factor': False, 'centralizer_order': 512, 'characteristic': True, 'core_order': 4, 'counter': 302, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.513', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 513, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5:C_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U3'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121770
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 303, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '128.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.515', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 515, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5.C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121771
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 304, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.41229.128.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '128.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.850', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 850, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121772
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121774
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121775
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121776
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121778
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 310, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.128.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121781
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121782
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121783
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121784
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121785
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121786
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 318, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.128.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121791
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.s2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.s2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121792
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.s3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.s3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121793
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121794
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121795
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121796
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.v2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121797
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.v3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.v3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121798
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121800
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.w2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.w2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121801
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121802
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121803
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.128.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59121804
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121805
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.ba2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.ba2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121806
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.ba3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.ba3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121807
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.ba4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.ba4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121809
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.41229.128.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59121811
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': True, 'central_factor': False, 'centralizer_order': 512, 'characteristic': True, 'core_order': 2, 'counter': 340, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '512.41229.256.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '256.1535', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1535, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^6.C_4', 'simple': True, 'solvable': True, 'special_labels': ['L3'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121812
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': True, 'central_factor': False, 'centralizer_order': 512, 'characteristic': False, 'core_order': 2, 'counter': 341, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '512.41229.256.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '256.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '256.5675', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5675, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^6:C_4', 'simple': True, 'solvable': True, 'special_labels': ['C8'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121813
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 342, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.256.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121814
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 343, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.256.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121815
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.256.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121816
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.256.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121817
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.256.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121818
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.41229.256.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59121819
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.41229', 'ambient_counter': 41229, 'ambient_order': 512, 'ambient_tex': 'C_2^7.C_4', 'central': True, 'central_factor': False, 'centralizer_order': 512, 'characteristic': True, 'core_order': 1, 'counter': 348, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '512.41229.512.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '512.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '512.41229', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1311698700316408213, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 512, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^7.C_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U4', 'L4', 'D2', 'C9'], '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: 59121776
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1', '64.n1', '64.t1', '64.z1'], 'contains': ['256.a1', '256.h1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6573, -1, 6562, -1], 'generators': [5606234766719, 1313941673647], 'label': '512.41229.128.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '128.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121554
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bv3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.p1', '8.bd1'], 'contains': ['32.br2', '32.br3', '32.br4', '32.bv2', '32.bx1', '32.ce3', '32.cm2'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [2876, -1, 2872, -1], 'generators': [4103734078080, 16703, 2789745598096, 2789792426303, 4103606707223], 'label': '512.41229.16.bv3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bv3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121543
    {'ambient': '512.41229', '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': '128.a1', 'complements': ['512.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8049, 6463, 7929, 6584], 'generators': [4103734078080, 1313901388807, 1313901405496, 4103693798407, 20922662476800, 4103606707223, 9709841473896, 1314028759703, 1313941673647], 'label': '512.41229.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121544
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': ['128.bb1'], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.d1', '8.r1', '8.z1'], 'core': '4.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [8349, 4662, 8187, 4749], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 9709841473896, 16819055769623, 1313941673647], 'label': '512.41229.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.d1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121545
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.i1', '8.bd1'], 'contains': ['32.bq1', '32.br1', '32.br4', '32.bs2', '32.ci1', '32.cj2'], 'core': '64.d1', 'coset_action_label': None, 'count': 64, 'diagramx': [1677, -1, 1676, -1], 'generators': [1313901388807, 4103693798407, 4103606707223, 4103646992056, 4103693809943], 'label': '512.41229.16.bq2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bq2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121546
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bq3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.i1', '8.bd1'], 'contains': ['32.bq2', '32.br1', '32.br4', '32.bs2', '32.ci2', '32.cj3'], 'core': '64.d1', 'coset_action_label': None, 'count': 64, 'diagramx': [1758, -1, 1757, -1], 'generators': [1313901388807, 4103693798407, 4103606707223, 4103693809943, 1314028759703], 'label': '512.41229.16.bq3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bq3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121547
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bq4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['8.i1', '8.bd1'], 'contains': ['32.bq3', '32.br2', '32.br5', '32.bs3', '32.ci1', '32.ci2', '32.cj1', '32.cj2', '32.cj3'], 'core': '256.b1', 'coset_action_label': None, 'count': 256, 'diagramx': [1433, -1, 1432, -1], 'generators': [2789832705976, 1313901388807, 4103693798407, 4103606707223, 1314028759703], 'label': '512.41229.16.bq4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bq4', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq4', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121548
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.k1'], 'contains': ['32.bt2', '32.bu1'], 'core': '64.d1', 'coset_action_label': None, 'count': 64, 'diagramx': [9969, -1, 9953, -1], 'generators': [4103734078080, 16703, 20922662476800, 4103606707223, 9709841473896], 'label': '512.41229.16.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.k1', 'old_label': '16.br1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.br1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121549
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.m1', '8.bc1'], 'contains': ['32.bv1', '32.by1', '32.ca1', '32.cb1', '32.ck1'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [5951, -1, 5942, -1], 'generators': [4103734078080, 16703, 2789792426303, 5606234766719, 1314028759703], 'label': '512.41229.16.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '16.bs1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bs1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121550
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.n1', '8.bc1'], 'contains': ['32.bv1', '32.bz1', '32.ca1', '32.cc1'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [7092, -1, 7081, -1], 'generators': [4103734078080, 16703, 2789792426303, 9709841473896, 2789832689280], 'label': '512.41229.16.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '16.bt1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bt1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121551
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.a1', '8.bd1'], 'contains': ['32.bq1', '32.bq2', '32.bq3', '32.bv1', '32.bv2', '32.bw1', '32.cd1', '32.cd2', '32.cl1', '32.cl2'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [1921, -1, 1919, -1], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 2789832689280], 'label': '512.41229.16.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bu1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bu1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121552
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.p1', '8.bc1', '8.bd1'], 'contains': ['32.br2', '32.br3', '32.br4', '32.bv1', '32.bx1', '32.ce1', '32.cm1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [3202, -1, 3197, -1], 'generators': [4103734078080, 16703, 2789792426303, 4103606707223, 1314028759703], 'label': '512.41229.16.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.bv1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121553
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bv2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.p1', '8.bd1'], 'contains': ['32.br1', '32.br5', '32.bv1', '32.bv2', '32.bx2', '32.ce2', '32.cm1', '32.cm2'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [2591, -1, 2588, -1], 'generators': [4103734078080, 16703, 2789792426303, 87091216, 1314028759703], 'label': '512.41229.16.bv2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bv2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121555
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['8.f1', '8.m1', '8.n1', '8.p1', '8.q1', '8.u1', '8.bc1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [6296, -1, 6287, -1], 'generators': [16703, 4103734078080, 2789792426303, 4103606707223, 9709841473896, 1314028759703, 1313941673647], 'label': '512.41229.4.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121556
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.b1', '8.bd1'], 'contains': ['32.bs1', '32.bs2', '32.bs3', '32.bw1', '32.bx1', '32.bx2', '32.cf1', '32.cn1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [3513, -1, 3507, -1], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 4103606707223], 'label': '512.41229.16.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bw1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bw1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121557
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.f1', '8.bc1'], 'contains': ['32.bt1', '32.bt2', '32.bt3', '32.bx1', '32.by1', '32.bz1', '32.cg1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [8360, -1, 8347, -1], 'generators': [4103734078080, 16703, 2789792426303, 4103606707223, 9709841473896], 'label': '512.41229.16.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '16.bx1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bx1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121558
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.q1', '8.bc1'], 'contains': ['32.bx1', '32.ca1', '32.ch1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [6668, -1, 6657, -1], 'generators': [8396067455999, 4103734078080, 16703, 2789792426303, 4103606707223], 'label': '512.41229.16.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '16.by1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.by1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121559
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['8.u1', '8.bc1'], 'contains': ['32.cb1', '32.cc1', '32.ce1', '32.cg1', '32.ch1'], 'core': '256.b1', 'coset_action_label': None, 'count': 256, 'diagramx': [6488, -1, 6478, -1], 'generators': [2789792426303, 4103606707223, 4103734094783, 9709841473896, 1314028759703], 'label': '512.41229.16.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '16.bz1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bz1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121560
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['8.w1', '8.bd1'], 'contains': ['32.cd1', '32.cd2', '32.ce1', '32.ce2', '32.ce3', '32.cf1', '32.ci1', '32.ci2', '32.co1', '32.co2', '32.co3'], 'core': '256.b1', 'coset_action_label': None, 'count': 256, 'diagramx': [1271, -1, 1270, -1], 'generators': [2789832705976, 1313901388807, 2789792426303, 4103606707223, 1314028759703], 'label': '512.41229.16.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.ca1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ca1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121561
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 256, 'contained_in': ['8.bb1', '8.bd1'], 'contains': ['32.cj1', '32.cj2', '32.cj3', '32.cl1', '32.cl2', '32.cm1', '32.cm2', '32.cn1', '32.co1', '32.co2', '32.co3'], 'core': '512.a1', 'coset_action_label': '16T925', 'count': 1024, 'diagramx': [844, -1, 843, -1], 'generators': [4103734078080, 1313901388807, 4103693798407, 4103606707223, 1314028759703], 'label': '512.41229.16.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.cb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cb1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121562
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['16.b1', '16.j2', '16.k1', '16.n2', '16.o2'], 'contains': ['64.a1', '64.d1', '64.g1', '64.m1', '64.bc1', '64.bc2'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7101, 3481, 7090, 3545], 'generators': [2789792409600, 4103734094783, 87091216, 1313941673647], 'label': '512.41229.32.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.b1'], 'normal_contains': ['64.a1', '64.d1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121563
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.q1', '16.r1'], 'contains': ['64.a1', '64.b1', '64.p1', '64.bf1'], 'core': '32.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7183, 4149, 7171, 4226], 'generators': [4103734078080, 16703, 2789792426303, 1313941673647], 'label': '512.41229.32.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1'], 'normal_contains': ['64.a1', '64.b1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121564
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.f1', '16.g1', '16.h1', '16.v1', '16.x1', '16.y1', '16.z1'], 'contains': ['64.b1', '64.c1', '64.f1', '64.r1', '64.bh1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5218, 6316, 5211, 6434], 'generators': [2789832705976, 1313901388807, 2789792426303, 1313941673647], 'label': '512.41229.32.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': ['16.a1', '16.f1', '16.g1', '16.h1'], 'normal_contains': ['64.b1', '64.c1'], 'normalizer': '1.a1', 'old_label': '32.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121565
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '16.g1', '16.t1', '16.ba1', '16.bb1', '16.bd1'], 'contains': ['64.b1', '64.i1', '64.bk1'], 'core': '32.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [8029, 5282, 8016, 5380], 'generators': [2789792426303, 4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.32.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': ['16.d1', '16.g1'], 'normal_contains': ['64.b1'], 'normalizer': '1.a1', 'old_label': '32.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121566
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['8.g1', '8.n1', '8.o1', '8.p1', '8.q1', '8.v1'], 'core': '8.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [6019, -1, 6010, -1], 'generators': [16703, 4103734078080, 2789792426303, 2789705335087, 9709841473896, 1314028759703, 1313941673647], 'label': '512.41229.4.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121567
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': ['16.br1'], 'conjugacy_class_count': 8, 'contained_in': ['16.f1', '16.bj1', '16.bo1', '16.bp1'], 'contains': ['64.c1', '64.q1', '64.w1', '64.ca1'], 'core': '32.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [1982, 7971, 1979, 8111], 'generators': [2789832705976, 4103693815096, 2789832689280, 1313941673647], 'label': '512.41229.32.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': ['16.f1'], 'normal_contains': ['64.c1'], 'normalizer': '1.a1', 'old_label': '32.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121568
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.i1', '16.j1', '16.j2', '16.q1'], 'contains': ['64.a1', '64.e1', '64.k1', '64.ba1', '64.ba2'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3283, -1, 3278, -1], 'generators': [2789792409600, 4103734094783, 2789832689280, 1313941673647], 'label': '512.41229.32.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121569
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.i1', '16.k1', '16.l1', '16.m1'], 'contains': ['64.a1', '64.f1', '64.l1', '64.bb1', '64.bb2'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5457, -1, 5448, -1], 'generators': [2789832705976, 1313901388807, 4103693798407, 1313941673647], 'label': '512.41229.32.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121570
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '16.j1', '16.k1', '16.n1', '16.o1'], 'contains': ['64.a1', '64.g1', '64.m2', '64.bc3', '64.bc4'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7019, -1, 7009, -1], 'generators': [2789792409600, 4103606707223, 4103734094783, 1313941673647], 'label': '512.41229.32.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121571
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '16.l1', '16.n1', '16.n2'], 'contains': ['64.a1', '64.h1', '64.n1', '64.bd1', '64.bd2'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8683, -1, 8670, -1], 'generators': [2789792409600, 4103734094783, 5606234766719, 1313941673647], 'label': '512.41229.32.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121572
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.m1', '16.n1', '16.o2', '16.p2'], 'contains': ['64.a1', '64.i1', '64.be1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9074, -1, 9059, -1], 'generators': [2789792409600, 4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.32.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121573
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.j2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.m1', '16.n2', '16.o1', '16.p1'], 'contains': ['64.a1', '64.i1', '64.be2'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9500, -1, 9486, -1], 'generators': [6920263521216, 2789792409600, 4103734094783, 1313941673647], 'label': '512.41229.32.j2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.j2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121574
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '16.l1', '16.o1', '16.o2'], 'contains': ['64.a1', '64.j1', '64.o1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8452, -1, 8439, -1], 'generators': [8396067450839, 2789792409600, 4103734094783, 1313941673647], 'label': '512.41229.32.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121575
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.f1', '16.q1', '16.s1', '16.t1', '16.u1', '16.v1', '16.w1'], 'contains': ['64.b1', '64.e1', '64.q1', '64.q2', '64.bg1', '64.bg2'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3689, -1, 3683, -1], 'generators': [2789792426303, 4103734094783, 2789832689280, 1313941673647], 'label': '512.41229.32.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121576
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '16.w1', '16.x1', '16.ba1', '16.bb1', '16.bc1'], 'contains': ['64.b1', '64.g1', '64.s1', '64.bi1', '64.bi2'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6826, -1, 6815, -1], 'generators': [2789792426303, 4103606707223, 4103734094783, 1313941673647], 'label': '512.41229.32.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121577
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['8.f1', '8.k1', '8.r1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [9028, -1, 8801, -1], 'generators': [16703, 4103734078080, 2789792426303, 20922662476800, 4103606707223, 9709841473896, 1313941673647], 'label': '512.41229.4.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121578
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '16.s1', '16.y1', '16.ba1'], 'contains': ['64.b1', '64.h1', '64.t1', '64.bj1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7557, -1, 7545, -1], 'generators': [2789792426303, 4103734094783, 5606234766719, 1313941673647], 'label': '512.41229.32.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121579
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.h1', '16.r1', '16.s1', '16.t1', '16.u1', '16.z1', '16.bc1'], 'contains': ['64.b1', '64.u1', '64.bl1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [6221, -1, 6211, -1], 'generators': [2789792426303, 6920263526376, 4103734094783, 1313941673647], 'label': '512.41229.32.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121580
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '16.u1', '16.y1', '16.bb1'], 'contains': ['64.b1', '64.j1', '64.v1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7301, -1, 7290, -1], 'generators': [6920136150359, 2789792426303, 4103734094783, 1313941673647], 'label': '512.41229.32.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121581
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.f1', '16.i1', '16.be1'], 'contains': ['64.e1', '64.f1', '64.w1', '64.w2', '64.bm1', '64.bm2'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1901, -1, 1898, -1], 'generators': [4103693815096, 4103734094783, 2789832689280, 1313941673647], 'label': '512.41229.32.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121582
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.q2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.i1', '16.v1', '16.be1'], 'contains': ['64.e1', '64.f1', '64.w3', '64.bm3'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1820, -1, 1817, -1], 'generators': [4103693798407, 4103734094783, 2789832689280, 1313941673647], 'label': '512.41229.32.q2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.q2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121583
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.j1', '16.j2', '16.w1', '16.be1'], 'contains': ['64.e1', '64.g1', '64.x1', '64.bn1', '64.bn2'], 'core': '128.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3039, -1, 3034, -1], 'generators': [4103606707223, 4103734094783, 1314028759703, 1313941673647], 'label': '512.41229.32.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121584
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.k1', '16.x1', '16.be1', '16.bf1'], 'contains': ['64.f1', '64.g1', '64.y1', '64.bo1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5137, -1, 5129, -1], 'generators': [4103693798407, 4103606707223, 4103734094783, 1313941673647], 'label': '512.41229.32.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121585
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.l1', '16.y1', '16.bf1'], 'contains': ['64.f1', '64.h1', '64.j1', '64.z1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7665, -1, 7653, -1], 'generators': [4103693798407, 4103734094783, 5606234766719, 1313941673647], 'label': '512.41229.32.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '32.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121586
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.g1', '16.m1', '16.bf1'], 'contains': ['64.f1', '64.i1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8163, -1, 8150, -1], 'generators': [4103693798407, 4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.32.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '32.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121587
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.n1', '16.n2', '16.ba1', '16.bf1'], 'contains': ['64.g1', '64.h1', '64.i1', '64.bp1'], 'core': '128.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [8928, -1, 8914, -1], 'generators': [4103606707223, 4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.32.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '32.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121588
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['8.g1', '8.l1', '8.r1'], 'core': '8.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [8707, -1, 8558, -1], 'generators': [16703, 4103734078080, 2789792426303, 20922662476800, 2789705335087, 9709841473896, 1313941673647], 'label': '512.41229.4.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121589
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.o1', '16.o2', '16.bb1', '16.bf1'], 'contains': ['64.g1', '64.i1', '64.j1'], 'core': '128.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [8586, -1, 8573, -1], 'generators': [4103734094783, 87091216, 9709841473896, 1313941673647], 'label': '512.41229.32.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '32.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121590
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.x1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.p1', '16.p2', '16.bd1'], 'contains': ['64.i1', '64.bq1'], 'core': '128.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [9646, -1, 9632, -1], 'generators': [18132957169920, 6920223246696, 4103734094783, 1313941673647], 'label': '512.41229.32.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1', 'old_label': '32.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121591
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.i1', '16.bg1', '16.bj1', '16.bj2'], 'contains': ['64.k1', '64.l1', '64.w1', '64.w2', '64.w3', '64.br1', '64.br2'], 'core': '256.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [1251, -1, 1249, -1], 'generators': [4103734078080, 4103693798407, 2789832689280, 1313941673647], 'label': '512.41229.32.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121592
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.j1', '16.bg1', '16.bk1'], 'contains': ['64.k1', '64.m2', '64.x1', '64.bs1'], 'core': '256.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [2308, -1, 2304, -1], 'generators': [4103734078080, 87091216, 1314028759703, 1313941673647], 'label': '512.41229.32.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121593
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.z2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.j2', '16.bg1', '16.bk1'], 'contains': ['64.k1', '64.m1', '64.x1', '64.bs2', '64.bs3'], 'core': '256.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [2389, -1, 2385, -1], 'generators': [4103734078080, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.32.z2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.z2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121594
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.k1', '16.bg1', '16.bl1'], 'contains': ['64.l1', '64.m1', '64.m2', '64.y1', '64.bt1', '64.bt2'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3933, -1, 3927, -1], 'generators': [4103734078080, 4103693798407, 4103606707223, 1313941673647], 'label': '512.41229.32.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ba1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121595
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.l1', '16.bm1'], 'contains': ['64.l1', '64.n1', '64.o1', '64.z1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [7447, -1, 7436, -1], 'generators': [4103734078080, 4103693798407, 5606234766719, 1313941673647], 'label': '512.41229.32.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '32.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bb1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121596
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.q1', '16.bh1', '16.bi1', '16.bj1', '16.bk1'], 'contains': ['64.k1', '64.p1', '64.q1', '64.bu1', '64.bu2'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [3446, -1, 3440, -1], 'generators': [4103734078080, 2789792409600, 2789832689280, 1313941673647], 'label': '512.41229.32.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121597
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.q1', '16.bj2', '16.bk1'], 'contains': ['64.k1', '64.p1', '64.q2', '64.bu3'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [2795, -1, 2791, -1], 'generators': [4103734078080, 2789792426303, 2789832689280, 1313941673647], 'label': '512.41229.32.bc2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bc2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121598
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '16.bj1', '16.bj2', '16.bl1', '16.bm1', '16.bn1'], 'contains': ['64.c1', '64.l1', '64.p1', '64.r1', '64.bv1'], 'core': '64.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [4421, -1, 4414, -1], 'generators': [4103734078080, 1313901388807, 4103693798407, 1313941673647], 'label': '512.41229.32.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121599
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.a1'], 'contains': ['8.h1', '8.z1'], 'core': '8.h1', 'coset_action_label': None, 'count': 16, 'diagramx': [8049, -1, 7929, -1], 'generators': [1313901388807, 2789832705976, 2789792426303, 20922662476800, 9709841473896, 2789832689280, 1313941673647], 'label': '512.41229.4.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121600
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.b1', '16.bk1', '16.bl1'], 'contains': ['64.m1', '64.m2', '64.p1', '64.s1', '64.bw1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4502, -1, 4495, -1], 'generators': [4103734078080, 2789792409600, 4103606707223, 1313941673647], 'label': '512.41229.32.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121601
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '16.bh1', '16.bm1'], 'contains': ['64.n1', '64.p1', '64.t1', '64.bx1'], 'core': '128.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [6102, -1, 6092, -1], 'generators': [4103734078080, 2789792409600, 5606234766719, 1313941673647], 'label': '512.41229.32.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121602
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.r1', '16.bh1', '16.bi1', '16.bn1'], 'contains': ['64.p1', '64.u1', '64.by1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [5338, -1, 5329, -1], 'generators': [4103734078080, 2789792426303, 6920263526376, 1313941673647], 'label': '512.41229.32.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121603
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '16.bi1', '16.bm1'], 'contains': ['64.o1', '64.p1', '64.v1'], 'core': '128.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5983, -1, 5974, -1], 'generators': [4103734078080, 8396067450839, 2789792409600, 1313941673647], 'label': '512.41229.32.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bh1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121604
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.s1', '16.bh1', '16.bo1', '16.bo2', '16.bo3'], 'contains': ['64.q1', '64.t1', '64.u1', '64.bz1'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [5028, -1, 5021, -1], 'generators': [2789792426303, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.32.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bi1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121605
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.u1', '16.bi1', '16.bo1', '16.bo2', '16.bo3'], 'contains': ['64.q1', '64.u1', '64.v1'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [4904, -1, 4897, -1], 'generators': [2789792426303, 5606275041239, 1314028759703, 1313941673647], 'label': '512.41229.32.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121606
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.f1', '16.bj1', '16.bo2', '16.bp2'], 'contains': ['64.c1', '64.q1', '64.w2', '64.ca2'], 'core': '64.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [2063, -1, 2060, -1], 'generators': [2789832705976, 1313901388800, 4103693815096, 1313941673647], 'label': '512.41229.32.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.bk1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121607
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bk2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.f1', '16.bj2', '16.bp3'], 'contains': ['64.q2', '64.r1', '64.w1', '64.w2', '64.ca3'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [1576, -1, 1574, -1], 'generators': [2789832705976, 2789792426303, 2789832689280, 1313941673647], 'label': '512.41229.32.bk2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bk2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121608
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bk3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.v1', '16.bj1', '16.bo3', '16.bp3'], 'contains': ['64.q1', '64.r1', '64.w3', '64.ca4'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [1657, -1, 1655, -1], 'generators': [4103693798407, 2789832689287, 2789832689280, 1313941673647], 'label': '512.41229.32.bk3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.bk3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121609
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bk4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.v1', '16.bj2', '16.bp1', '16.bp2'], 'contains': ['64.c1', '64.q2', '64.w3', '64.ca5'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [925, -1, 924, -1], 'generators': [2789792426303, 2789832689287, 2789832689280, 1313941673647], 'label': '512.41229.32.bk4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bk4', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk4', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121610
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.b1'], 'contains': ['8.h1', '8.s1', '8.s2', '8.t1', '8.u1', '8.v1', '8.w1', '8.x1', '8.y1'], 'core': '8.h1', 'coset_action_label': None, 'count': 16, 'diagramx': [5764, -1, 5756, -1], 'generators': [1313901388807, 2789832705976, 2789792426303, 4103606707223, 9709841473896, 1314028759703, 1313941673647], 'label': '512.41229.4.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121611
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.w1', '16.bk1', '16.bp1', '16.bp2', '16.bp3'], 'contains': ['64.q1', '64.q2', '64.s1', '64.x1', '64.cb1', '64.cb2'], 'core': '128.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [1738, -1, 1736, -1], 'generators': [1313941668480, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.32.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121612
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.x1', '16.bl1', '16.bp1', '16.bp2'], 'contains': ['64.c1', '64.s1', '64.y1', '64.cc1'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [3608, -1, 3602, -1], 'generators': [2789792426303, 4103606707223, 2789832689287, 1313941673647], 'label': '512.41229.32.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121613
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.x1', '16.bl1', '16.bp3'], 'contains': ['64.r1', '64.s1', '64.y1', '64.cc2'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [3852, -1, 3846, -1], 'generators': [4103693798407, 4103606707223, 2789832689287, 1313941673647], 'label': '512.41229.32.bm2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bm2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121614
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.y1', '16.bm1', '16.bo1', '16.bo2'], 'contains': ['64.c1', '64.t1', '64.v1', '64.z1'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [5702, -1, 5693, -1], 'generators': [2789792426303, 2789832689287, 5606234766719, 1313941673647], 'label': '512.41229.32.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121615
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.y1', '16.bm1', '16.bo3'], 'contains': ['64.r1', '64.t1', '64.v1', '64.z1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [5838, -1, 5828, -1], 'generators': [4103693798407, 2789832689287, 5606234766719, 1313941673647], 'label': '512.41229.32.bn2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bn2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121616
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.h1', '16.bn1', '16.bo3'], 'contains': ['64.r1', '64.u1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4793, -1, 4785, -1], 'generators': [2789832705976, 2789792426303, 6920263526376, 1313941673647], 'label': '512.41229.32.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bo1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121617
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bo2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.z1', '16.bn1', '16.bo1', '16.bo2'], 'contains': ['64.c1', '64.u1'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [4680, -1, 4673, -1], 'generators': [2789792426303, 6920263526376, 2789832689287, 1313941673647], 'label': '512.41229.32.bo2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bo2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121618
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['16.be1', '16.bg1', '16.bp1', '16.bp3'], 'contains': ['64.w1', '64.w3', '64.x1', '64.y1', '64.cd1', '64.cd2'], 'core': '256.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [195, -1, 194, -1], 'generators': [127370903, 40279687, 1314028759703, 1313941673647], 'label': '512.41229.32.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bp1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121619
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['16.be1', '16.bg1', '16.bp2', '16.bp3'], 'contains': ['64.w2', '64.w3', '64.x1', '64.y1', '64.cd3'], 'core': '256.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [601, -1, 600, -1], 'generators': [40279687, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.32.bp2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bp2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121620
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.i1', '16.bq1', '16.bq2', '16.bu1'], 'contains': ['64.ba1', '64.bb1', '64.bm1', '64.bm3', '64.br1'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [1170, -1, 1168, -1], 'generators': [1313901388807, 4103693798407, 40284847, 4103693809943], 'label': '512.41229.32.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bq1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121621
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '16.f1', '16.i1', '16.q1', '16.v1', '16.bj1', '16.bj2', '16.bu1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2165, 8632, 2162, 8792], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 2789832689280, 1313941673647], 'label': '512.41229.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '16.f1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121622
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.i1', '16.bq1', '16.bq3', '16.bu1'], 'contains': ['64.ba1', '64.bb1', '64.bm2', '64.bm3', '64.br2'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [1495, -1, 1492, -1], 'generators': [1313901388807, 4103693798407, 4103693809943, 2789832689280], 'label': '512.41229.32.bq2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bq2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121623
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bq3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.i1', '16.bq4', '16.bu1'], 'contains': ['64.ba2', '64.bb2', '64.bm1', '64.bm2', '64.bm3', '64.br1', '64.br2'], 'core': '256.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [1088, -1, 1087, -1], 'generators': [2789832705976, 1313901388807, 4103693798407, 2789832689280], 'label': '512.41229.32.bq3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bq3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121624
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.j1', '16.bq1', '16.bq2', '16.bq3', '16.bv2'], 'contains': ['64.ba1', '64.bc3', '64.bn1', '64.bs1'], 'core': '128.c1', 'coset_action_label': None, 'count': 128, 'diagramx': [2551, -1, 2547, -1], 'generators': [2789792421136, 2789792409600, 4103606707223, 1314028759703], 'label': '512.41229.32.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.br1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121625
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.br2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.j1', '16.bq4', '16.bv1', '16.bv3'], 'contains': ['64.ba2', '64.bc4', '64.bn2', '64.bs1'], 'core': '256.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [2957, -1, 2953, -1], 'generators': [2789792409600, 4103606707223, 4103734094783, 1314028759703], 'label': '512.41229.32.br2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.br2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121626
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.br3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.j2', '16.bq1', '16.bv1', '16.bv3'], 'contains': ['64.ba1', '64.bc1', '64.bn2', '64.bs2'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [3202, -1, 3197, -1], 'generators': [2789792421136, 2789705323583, 2789792409600, 1314028759703], 'label': '512.41229.32.br3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.br3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121627
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.br4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.j2', '16.bq2', '16.bq3', '16.bv1', '16.bv3'], 'contains': ['64.d1', '64.ba1', '64.bn2', '64.bs3'], 'core': '64.d1', 'coset_action_label': None, 'count': 64, 'diagramx': [3121, -1, 3115, -1], 'generators': [2789705318416, 2789792421136, 2789792409600, 1314028759703], 'label': '512.41229.32.br4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.br4', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br4', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121628
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.br5', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.j2', '16.bq4', '16.bv2'], 'contains': ['64.ba2', '64.bc2', '64.bn1', '64.bs2', '64.bs3'], 'core': '256.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [2633, -1, 2629, -1], 'generators': [2789705318416, 2789792409600, 4103734094783, 1314028759703], 'label': '512.41229.32.br5', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.br5', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br5', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121629
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.k1', '16.bq1', '16.bw1'], 'contains': ['64.bb1', '64.bc1', '64.bc3', '64.bo1', '64.bt1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [4340, -1, 4333, -1], 'generators': [1313901388807, 1313988485176, 4103693798407, 4103693809943], 'label': '512.41229.32.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bs1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121630
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bs2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.k1', '16.bq2', '16.bq3', '16.bw1'], 'contains': ['64.d1', '64.bb1', '64.bc3', '64.bo1', '64.bt2'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [4177, -1, 4170, -1], 'generators': [1313901388807, 4103693798407, 4103606707223, 4103693809943], 'label': '512.41229.32.bs2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bs2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121631
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bs3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.k1', '16.bq4', '16.bw1'], 'contains': ['64.bb2', '64.bc2', '64.bc4', '64.bo1', '64.bt1', '64.bt2'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [4095, -1, 4089, -1], 'generators': [2789832705976, 1313901388807, 4103693798407, 4103606707223], 'label': '512.41229.32.bs3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bs3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121632
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.b1', '16.k1', '16.x1', '16.bl1', '16.bw1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4505, 3260, 4498, 3321], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 4103606707223, 1313941673647], 'label': '512.41229.8.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': ['4.c1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.b1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121633
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.n1', '16.bx1'], 'contains': ['64.bc4', '64.bd1', '64.be1', '64.bp1'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [8792, -1, 8778, -1], 'generators': [2789792409600, 4103606707223, 4103734094783, 9709841473896], 'label': '512.41229.32.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '32.bt1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121634
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bt2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.n2', '16.br1', '16.bx1'], 'contains': ['64.d1', '64.bd2', '64.be2', '64.bp1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [9354, -1, 9340, -1], 'generators': [2789705318416, 2789792421136, 9709881753583, 2789792409600], 'label': '512.41229.32.bt2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '32.bt2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121635
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bt3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.n2', '16.bx1'], 'contains': ['64.bc1', '64.bd2', '64.be2', '64.bp1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [9220, -1, 9205, -1], 'generators': [2789792421136, 2789705323583, 9709881753583, 2789792409600], 'label': '512.41229.32.bt3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '32.bt3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121636
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.i1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.p1', '16.br1'], 'contains': ['64.be2', '64.bq1'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [9783, -1, 9768, -1], 'generators': [4103734078080, 16703, 9709841473896, 16819055769623], 'label': '512.41229.32.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.k1', 'old_label': '32.bu1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121637
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.q1', '16.bs1', '16.bt1', '16.bu1', '16.bv1', '16.bv2'], 'contains': ['64.ba1', '64.ba2', '64.bf1', '64.bg1', '64.bu1', '64.bu3'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [3770, -1, 3765, -1], 'generators': [4103734078080, 16703, 2789792426303, 2789832689280], 'label': '512.41229.32.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.bv1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121638
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bv2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.q1', '16.bu1', '16.bv2', '16.bv3'], 'contains': ['64.ba1', '64.ba2', '64.bf1', '64.bg2', '64.bu2', '64.bu3'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [2876, -1, 2872, -1], 'generators': [4103734078080, 16703, 1313941668487, 2789792426303], 'label': '512.41229.32.bv2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bv2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121639
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '16.bu1', '16.bw1'], 'contains': ['64.bb1', '64.bb2', '64.bf1', '64.bh1', '64.bv1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [4259, -1, 4252, -1], 'generators': [4103734078080, 1313901388807, 1313901405496, 4103693798407], 'label': '512.41229.32.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bw1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bw1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121640
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.b1', '16.bv1', '16.bv3', '16.bw1', '16.bx1', '16.by1'], 'contains': ['64.d1', '64.bc1', '64.bc4', '64.bf1', '64.bi1', '64.bw1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [6588, -1, 6577, -1], 'generators': [4103734078080, 16703, 2789792426303, 4103606707223], 'label': '512.41229.32.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.bx1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121641
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bx2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.b1', '16.bv2', '16.bw1'], 'contains': ['64.bc2', '64.bc3', '64.bf1', '64.bi2', '64.bw1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [4583, -1, 4576, -1], 'generators': [4103734078080, 16703, 2789792426303, 87091216], 'label': '512.41229.32.bx2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bx2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121642
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '16.bs1', '16.bx1'], 'contains': ['64.bd1', '64.bd2', '64.bf1', '64.bj1', '64.bx1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [7774, -1, 7762, -1], 'generators': [4103734078080, 16703, 2789792426303, 5606234766719], 'label': '512.41229.32.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.by1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.by1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121643
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.d1'], 'contains': ['16.a1', '16.c1', '16.e1', '16.l1', '16.y1', '16.bm1'], 'core': '8.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7154, 4239, 7131, 4317], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 5606234766719, 1313941673647], 'label': '512.41229.8.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': ['4.a1', '4.d1'], 'normal_contains': ['16.a1', '16.c1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121644
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '16.bt1', '16.bx1'], 'contains': ['64.be1', '64.be2', '64.bf1', '64.bk1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [8296, -1, 8283, -1], 'generators': [4103734078080, 16703, 2789792426303, 9709841473896], 'label': '512.41229.32.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.bz1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bz1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121645
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.r1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.r1', '16.bs1', '16.bt1', '16.by1'], 'contains': ['64.bf1', '64.bl1', '64.by1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [6706, -1, 6696, -1], 'generators': [4103734078080, 16703, 2789792426303, 6920263526376], 'label': '512.41229.32.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.ca1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ca1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121646
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.s1', '16.bs1', '16.bz1'], 'contains': ['64.bg1', '64.bj1', '64.bl1', '64.bz1'], 'core': '256.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [6367, -1, 6357, -1], 'generators': [2789792426303, 4103734094783, 5606234766719, 1314028759703], 'label': '512.41229.32.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.cb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cb1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121647
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.t1', '16.bt1', '16.bz1'], 'contains': ['64.bg1', '64.bk1', '64.bl1'], 'core': '256.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [6923, -1, 6912, -1], 'generators': [2789792426303, 4103734094783, 9709841473896, 2789832689280], 'label': '512.41229.32.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.cc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cc1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121648
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.f1', '16.bu1', '16.ca1'], 'contains': ['64.bg1', '64.bg2', '64.bh1', '64.bm1', '64.bm2', '64.ca1', '64.ca2', '64.ca3'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [1332, -1, 1330, -1], 'generators': [2789832705976, 1313901388807, 2789792426303, 2789832689280], 'label': '512.41229.32.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cd1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121649
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.v1', '16.bu1', '16.ca1'], 'contains': ['64.bg1', '64.bg2', '64.bh1', '64.bm3', '64.ca4', '64.ca5'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [1414, -1, 1411, -1], 'generators': [1313901405496, 4103693798407, 2789832689287, 2789832689280], 'label': '512.41229.32.cd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cd2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cd2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121650
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.w1', '16.bv1', '16.bz1', '16.ca1'], 'contains': ['64.bg1', '64.bi1', '64.bn2', '64.cb1'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [3364, -1, 3359, -1], 'generators': [2789792426303, 4103606707223, 4103734094783, 1314028759703], 'label': '512.41229.32.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.ce1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ce1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121651
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.ce2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.w1', '16.bv2', '16.ca1'], 'contains': ['64.bg1', '64.bg2', '64.bi2', '64.bn1', '64.cb1', '64.cb2'], 'core': '256.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [2470, -1, 2466, -1], 'generators': [2789705318416, 2789792426303, 4103734094783, 1314028759703], 'label': '512.41229.32.ce2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.ce2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ce2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121652
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.ce3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.w1', '16.bv3', '16.ca1'], 'contains': ['64.bg2', '64.bi1', '64.bn2', '64.cb2'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [2714, -1, 2710, -1], 'generators': [127370896, 2789792426303, 4103606707223, 4103734094783], 'label': '512.41229.32.ce3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.ce3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ce3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121653
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.x1', '16.bw1', '16.ca1'], 'contains': ['64.bh1', '64.bi1', '64.bi2', '64.bo1', '64.cc1', '64.cc2'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [4014, -1, 4008, -1], 'generators': [2789832705976, 1313901388807, 2789792426303, 4103606707223], 'label': '512.41229.32.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cf1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121654
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': ['256.e1', '256.g1', '256.h1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.f1', '4.k1'], 'core': '2.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8049, 7596, 7929, 7737], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 20922662476800, 9709841473896, 2789832689280, 1313941673647], 'label': '512.41229.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121655
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.d1', '4.f1'], 'contains': ['16.a1', '16.d1', '16.g1', '16.m1'], 'core': '8.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7692, 5738, 7655, 5845], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 9709841473896, 1313941673647], 'label': '512.41229.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.b1', '4.d1', '4.f1'], 'normal_contains': ['16.a1', '16.d1', '16.g1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121656
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.ba1', '16.bx1', '16.bz1'], 'contains': ['64.bi1', '64.bj1', '64.bk1', '64.bp1'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [7883, -1, 7871, -1], 'generators': [2789792426303, 4103606707223, 4103734094783, 9709841473896], 'label': '512.41229.32.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.cg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cg1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121657
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.bc1', '16.by1', '16.bz1'], 'contains': ['64.bi1', '64.bl1'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [6490, -1, 6480, -1], 'generators': [8396067455999, 2789792426303, 4103606707223, 4103734094783], 'label': '512.41229.32.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.ch1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ch1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121658
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['16.be1', '16.bq1', '16.bq2', '16.bq4', '16.ca1'], 'contains': ['64.bm1', '64.bm3', '64.bn1', '64.bn2', '64.bo1', '64.cd1', '64.cd3'], 'core': '256.b1', 'coset_action_label': None, 'count': 512, 'diagramx': [682, -1, 681, -1], 'generators': [127370896, 4103693798407, 4103606707223, 4103734094783], 'label': '512.41229.32.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.ci1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ci1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121659
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.ci2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['16.be1', '16.bq1', '16.bq3', '16.bq4', '16.ca1'], 'contains': ['64.bm2', '64.bm3', '64.bn1', '64.bn2', '64.bo1', '64.cd2', '64.cd3'], 'core': '256.b1', 'coset_action_label': None, 'count': 512, 'diagramx': [763, -1, 762, -1], 'generators': [4103693798407, 4103606707223, 4103734094783, 1314028759703], 'label': '512.41229.32.ci2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.ci2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ci2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121660
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 512, 'contained_in': ['16.bg1', '16.bq1', '16.bq4', '16.cb1'], 'contains': ['64.br1', '64.br2', '64.bs1', '64.bs2', '64.bt1', '64.cd1', '64.cd2', '64.cd3'], 'core': '512.a1', 'coset_action_label': '32T10603', 'count': 2048, 'diagramx': [276, -1, 275, -1], 'generators': [2789705318416, 4103734078080, 4103693798407, 1314028759703], 'label': '512.41229.32.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121661
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 256, 'contained_in': ['16.bg1', '16.bq2', '16.bq4', '16.cb1'], 'contains': ['64.br1', '64.bs1', '64.bs3', '64.bt2', '64.cd1', '64.cd3'], 'core': '512.a1', 'coset_action_label': '32T10608', 'count': 1024, 'diagramx': [438, -1, 437, -1], 'generators': [4103734078080, 127370896, 4103693798407, 4103606707223], 'label': '512.41229.32.cj2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cj2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121662
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cj3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 256, 'contained_in': ['16.bg1', '16.bq3', '16.bq4', '16.cb1'], 'contains': ['64.br2', '64.bs1', '64.bs3', '64.bt2', '64.cd2', '64.cd3'], 'core': '512.a1', 'coset_action_label': '32T10606', 'count': 1024, 'diagramx': [519, -1, 519, -1], 'generators': [4103734078080, 4103693798407, 4103606707223, 1314028759703], 'label': '512.41229.32.cj3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cj3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121663
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.bh1', '16.bs1'], 'contains': ['64.bu1', '64.bx1', '64.by1', '64.bz1'], 'core': '512.a1', 'coset_action_label': '32T17725', 'count': 256, 'diagramx': [5566, -1, 5557, -1], 'generators': [4103734078080, 2789792426303, 5606234766719, 1314028759703], 'label': '512.41229.32.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '32.ck1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ck1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121664
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['16.bj1', '16.bu1', '16.cb1'], 'contains': ['64.br1', '64.br2', '64.bu1', '64.bu2', '64.bv1', '64.ca1', '64.ca2', '64.ca4'], 'core': '512.a1', 'coset_action_label': '32T10611', 'count': 256, 'diagramx': [1007, -1, 1005, -1], 'generators': [4103734078080, 1313901388807, 4103693798407, 2789832689280], 'label': '512.41229.32.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cl1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121665
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cl2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['16.bj2', '16.bu1', '16.cb1'], 'contains': ['64.br1', '64.br2', '64.bu3', '64.bv1', '64.ca3', '64.ca5'], 'core': '512.a1', 'coset_action_label': '32T10602', 'count': 256, 'diagramx': [844, -1, 843, -1], 'generators': [4103734078080, 1313901388807, 2789792426303, 2789832689280], 'label': '512.41229.32.cl2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cl2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cl2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121666
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.b1', '4.e1'], 'contains': ['16.a1', '16.h1', '16.r1', '16.z1', '16.bn1'], 'core': '8.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [4896, 7442, 4889, 7580], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 6920263526376, 1313941673647], 'label': '512.41229.8.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1', '4.b1', '4.e1'], 'normal_contains': ['16.a1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121667
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['16.bk1', '16.bv1', '16.bv2', '16.cb1'], 'contains': ['64.bs1', '64.bs2', '64.bs3', '64.bu1', '64.bu3', '64.bw1', '64.cb1'], 'core': '512.a1', 'coset_action_label': '32T10607', 'count': 512, 'diagramx': [2227, -1, 2223, -1], 'generators': [4103734078080, 2789792409600, 4103606707223, 1314028759703], 'label': '512.41229.32.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cm1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121668
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['16.bk1', '16.bv2', '16.bv3', '16.cb1'], 'contains': ['64.bs1', '64.bs2', '64.bs3', '64.bu2', '64.bu3', '64.bw1', '64.cb2'], 'core': '512.a1', 'coset_action_label': '32T10609', 'count': 512, 'diagramx': [2145, -1, 2142, -1], 'generators': [2789705318416, 4103734078080, 2789792409600, 1314028759703], 'label': '512.41229.32.cm2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cm2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cm2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121669
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['16.bl1', '16.bw1', '16.cb1'], 'contains': ['64.bt1', '64.bt2', '64.bv1', '64.bw1', '64.cc1', '64.cc2'], 'core': '512.a1', 'coset_action_label': '32T10605', 'count': 256, 'diagramx': [3527, -1, 3521, -1], 'generators': [4103734078080, 1313901388807, 4103693798407, 4103606707223], 'label': '512.41229.32.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.cn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cn1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121670
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['16.bp1', '16.ca1', '16.cb1'], 'contains': ['64.ca1', '64.ca5', '64.cb1', '64.cb2', '64.cc1', '64.cd1', '64.cd2'], 'core': '512.a1', 'coset_action_label': '32T10601', 'count': 512, 'diagramx': [112, -1, 113, -1], 'generators': [127370896, 2789792426303, 4103606707223, 2789832689287], 'label': '512.41229.32.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.co1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121671
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.co2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['16.bp2', '16.ca1', '16.cb1'], 'contains': ['64.ca2', '64.ca5', '64.cb1', '64.cb2', '64.cc1', '64.cd3'], 'core': '512.a1', 'coset_action_label': '32T10610', 'count': 512, 'diagramx': [357, -1, 356, -1], 'generators': [2789792426303, 4103606707223, 2789832689287, 1314028759703], 'label': '512.41229.32.co2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.co2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121672
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '32.co3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 256, 'contained_in': ['16.bp3', '16.ca1', '16.cb1'], 'contains': ['64.ca3', '64.ca4', '64.cb1', '64.cb2', '64.cc2', '64.cd1', '64.cd2', '64.cd3'], 'core': '512.a1', 'coset_action_label': '32T10604', 'count': 1024, 'diagramx': [31, -1, 32, -1], 'generators': [4103693798407, 4103606707223, 2789832689287, 1314028759703], 'label': '512.41229.32.co3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.co3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121692
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.e1', '32.l1', '32.bc1', '32.bi1', '32.bj1', '32.bk1', '32.bk3', '32.bl1'], 'contains': ['128.b1', '128.e1', '128.v1', '128.v2'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [3121, -1, 3115, -1], 'generators': [1313941668480, 2789832689280, 1313941673647], 'label': '512.41229.64.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.q1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121673
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '32.b1', '32.f1', '32.g1', '32.h1', '32.i1', '32.j1', '32.j2', '32.k1'], 'contains': ['128.a1', '128.c1', '128.d1', '128.j1'], 'core': '64.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7060, 4149, 7049, 4226], 'generators': [2789792409600, 4103734094783, 1313941673647], 'label': '512.41229.64.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1'], 'normal_contains': ['128.a1', '128.c1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121674
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1', '32.c1', '32.d1', '32.l1', '32.m1', '32.n1', '32.o1', '32.p1'], 'contains': ['128.a1', '128.b1', '128.k1'], 'core': '64.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6494, 5282, 6484, 5380], 'generators': [2789792426303, 4103734094783, 1313941673647], 'label': '512.41229.64.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': ['32.b1', '32.c1', '32.d1'], 'normal_contains': ['128.a1', '128.b1'], 'normalizer': '1.a1', 'old_label': '64.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121675
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['32.c1', '32.e1', '32.bd1', '32.bk1', '32.bk4', '32.bm1', '32.bn1', '32.bo2'], 'contains': ['128.b1', '128.f1', '128.w1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [4177, 6316, 4170, 6434], 'generators': [2789792426303, 2789832689287, 1313941673647], 'label': '512.41229.64.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1', 'normal_contained_in': ['32.c1', '32.e1'], 'normal_contains': ['128.b1'], 'normalizer': '1.a1', 'old_label': '64.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121676
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['32.a1', '32.br4', '32.bs2', '32.bt2', '32.bx1'], 'contains': ['128.c1', '128.n1', '128.s1'], 'core': '64.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [6169, 3481, 6160, 3545], 'generators': [2789705318416, 2789792421136, 2789792409600], 'label': '512.41229.64.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.d1', 'normal_contained_in': ['32.a1'], 'normal_contains': ['128.c1'], 'normalizer': '1.a1', 'old_label': '64.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121677
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '4.g1', '4.i1'], 'contains': ['16.b1', '16.c1', '16.d1', '16.n1', '16.n2', '16.ba1', '16.bx1'], 'core': '8.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [8082, 570, 8044, 581], 'generators': [4103734078080, 16703, 2789792426303, 4103606707223, 9709841473896, 1313941673647], 'label': '512.41229.8.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': ['4.d1'], 'normal_contains': ['16.b1', '16.c1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121678
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.f1', '32.l1', '32.q1', '32.q2', '32.r1'], 'contains': ['128.a1', '128.e1', '128.l1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3283, -1, 3278, -1], 'generators': [4103734094783, 2789832689280, 1313941673647], 'label': '512.41229.64.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121679
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.c1', '32.g1', '32.q1', '32.q2', '32.s1', '32.t1', '32.u1'], 'contains': ['128.a1', '128.f1', '128.m1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5287, -1, 5279, -1], 'generators': [4103693798407, 4103734094783, 1313941673647], 'label': '512.41229.64.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121680
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.a1', '32.h1', '32.m1', '32.r1', '32.s1', '32.v1', '32.w1'], 'contains': ['128.a1', '128.g1', '128.n1', '128.n2'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6413, -1, 6403, -1], 'generators': [4103606707223, 4103734094783, 1313941673647], 'label': '512.41229.64.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121681
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1', '32.n1', '32.t1', '32.v1'], 'contains': ['128.a1', '128.h1', '128.o1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7672, -1, 7660, -1], 'generators': [4103734094783, 5606234766719, 1313941673647], 'label': '512.41229.64.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '64.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121682
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.d1', '32.j1', '32.j2', '32.u1', '32.v1', '32.w1', '32.x1'], 'contains': ['128.a1', '128.p1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8879, -1, 8710, -1], 'generators': [4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.64.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '64.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121683
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1', '32.p1', '32.t1', '32.w1'], 'contains': ['128.a1', '128.i1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7565, -1, 7552, -1], 'generators': [8396067450839, 4103734094783, 1313941673647], 'label': '512.41229.64.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '64.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121684
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.f1', '32.y1', '32.z1', '32.z2', '32.bc1', '32.bc2'], 'contains': ['128.d1', '128.e1', '128.q1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [2795, -1, 2791, -1], 'generators': [4103734078080, 2789832689280, 1313941673647], 'label': '512.41229.64.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121685
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.g1', '32.y1', '32.ba1', '32.bb1', '32.bd1'], 'contains': ['128.d1', '128.f1', '128.r1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4583, -1, 4576, -1], 'generators': [4103734078080, 4103693798407, 1313941673647], 'label': '512.41229.64.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121686
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.a1', '32.z2', '32.ba1', '32.be1'], 'contains': ['128.d1', '128.g1', '128.s1', '128.s2'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4746, -1, 4738, -1], 'generators': [4103734078080, 4103606707223, 1313941673647], 'label': '512.41229.64.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121687
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.m2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.h1', '32.z1', '32.ba1', '32.be1'], 'contains': ['128.d1', '128.g1', '128.s3'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4665, -1, 4657, -1], 'generators': [4103734078080, 87091216, 1313941673647], 'label': '512.41229.64.m2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.m2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121688
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '4.h1', '4.j1'], 'contains': ['16.b1', '16.d1', '16.e1', '16.o1', '16.o2', '16.bb1'], 'core': '8.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [7900, 2070, 7862, 2109], 'generators': [4103734078080, 16703, 2789792426303, 2789705335087, 9709841473896, 1313941673647], 'label': '512.41229.8.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': ['4.d1'], 'normal_contains': ['16.b1', '16.d1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121689
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.i1', '32.bb1', '32.bf1'], 'contains': ['128.d1', '128.h1', '128.t1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6782, -1, 6771, -1], 'generators': [4103734078080, 5606234766719, 1313941673647], 'label': '512.41229.64.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '64.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121690
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.k1', '32.bb1', '32.bh1'], 'contains': ['128.d1', '128.i1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6674, -1, 6663, -1], 'generators': [4103734078080, 8396067450839, 1313941673647], 'label': '512.41229.64.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '64.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121691
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.b1', '32.bc1', '32.bc2', '32.bd1', '32.be1', '32.bf1', '32.bg1', '32.bh1'], 'contains': ['128.b1', '128.d1', '128.u1'], 'core': '128.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5071, -1, 5063, -1], 'generators': [4103734078080, 2789792409600, 1313941673647], 'label': '512.41229.64.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121693
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.q2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.l1', '32.bc2', '32.bk2', '32.bk4', '32.bl1'], 'contains': ['128.b1', '128.e1', '128.v3'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [2308, -1, 2304, -1], 'generators': [2789792426303, 2789832689280, 1313941673647], 'label': '512.41229.64.q2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.q2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.q2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121694
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.c1', '32.bd1', '32.bk2', '32.bk3', '32.bm2', '32.bn2', '32.bo1'], 'contains': ['128.b1', '128.f1', '128.w2'], 'core': '128.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4340, -1, 4333, -1], 'generators': [4103693798407, 2789832689287, 1313941673647], 'label': '512.41229.64.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.r1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121695
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.m1', '32.be1', '32.bl1', '32.bm1', '32.bm2'], 'contains': ['128.b1', '128.g1', '128.x1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4502, -1, 4495, -1], 'generators': [1313941668480, 4103606707223, 1313941673647], 'label': '512.41229.64.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.s1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121696
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.n1', '32.bf1', '32.bi1', '32.bn1', '32.bn2'], 'contains': ['128.b1', '128.h1', '128.y1'], 'core': '128.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5791, -1, 5782, -1], 'generators': [1313941668480, 5606234766719, 1313941673647], 'label': '512.41229.64.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.t1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121697
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.o1', '32.bg1', '32.bi1', '32.bj1', '32.bo1', '32.bo2'], 'contains': ['128.b1', '128.z1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [5179, -1, 5171, -1], 'generators': [2789792426303, 6920263526376, 1313941673647], 'label': '512.41229.64.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.u1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121698
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.p1', '32.bh1', '32.bj1', '32.bn1', '32.bn2'], 'contains': ['128.b1', '128.i1'], 'core': '128.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5683, -1, 5674, -1], 'generators': [9709928559959, 1313941668480, 1313941673647], 'label': '512.41229.64.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121699
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['4.b1', '4.k1', '4.l1'], 'contains': ['16.f1', '16.g1', '16.h1', '16.t1'], 'core': '8.h1', 'coset_action_label': None, 'count': 8, 'diagramx': [5891, 9430, 5883, 9605], 'generators': [2789832705976, 1313901388807, 2789792426303, 9709841473896, 2789832689280, 1313941673647], 'label': '512.41229.8.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.f1', '16.g1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121700
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.e1', '32.q1', '32.y1', '32.bk2', '32.bp1'], 'contains': ['128.e1', '128.f1', '128.ba1', '128.ba2'], 'core': '256.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1738, -1, 1736, -1], 'generators': [1313901388800, 40279687, 1313941673647], 'label': '512.41229.64.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121701
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.w2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.q1', '32.y1', '32.bk1', '32.bk2', '32.bp2'], 'contains': ['128.e1', '128.f1', '128.ba3'], 'core': '256.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1820, -1, 1817, -1], 'generators': [40279687, 2789832689280, 1313941673647], 'label': '512.41229.64.w2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.w2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121702
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.w3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.q2', '32.y1', '32.bk3', '32.bk4', '32.bp1', '32.bp2'], 'contains': ['128.e1', '128.f1', '128.ba4'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [1170, -1, 1168, -1], 'generators': [2789832689287, 2789832689280, 1313941673647], 'label': '512.41229.64.w3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.w3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121703
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['32.r1', '32.z1', '32.z2', '32.bl1', '32.bp1', '32.bp2'], 'contains': ['128.e1', '128.g1', '128.bb1'], 'core': '256.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [2145, -1, 2142, -1], 'generators': [4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.64.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.x1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121704
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.s1', '32.ba1', '32.bm1', '32.bm2', '32.bp1', '32.bp2'], 'contains': ['128.f1', '128.g1', '128.bc1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3527, -1, 3521, -1], 'generators': [40279687, 4103606707223, 1313941673647], 'label': '512.41229.64.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.y1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121705
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.t1', '32.bb1', '32.bn1', '32.bn2'], 'contains': ['128.f1', '128.h1', '128.i1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [6570, -1, 6560, -1], 'generators': [40279687, 5606234766719, 1313941673647], 'label': '512.41229.64.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '64.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.z1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121706
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.f1', '32.bq1', '32.bq2', '32.br1', '32.br3', '32.br4', '32.bv1', '32.bv2'], 'contains': ['128.c1', '128.l1', '128.q1'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [2957, -1, 2953, -1], 'generators': [2789792421136, 2789792409600, 2789832689280], 'label': '512.41229.64.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121707
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.ba2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.f1', '32.bq3', '32.br2', '32.br5', '32.bv1', '32.bv2'], 'contains': ['128.j1', '128.l1', '128.q1'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [3202, -1, 3197, -1], 'generators': [2789792409600, 4103734094783, 2789832689280], 'label': '512.41229.64.ba2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.ba2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121708
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.g1', '32.bq1', '32.bq2', '32.bs1', '32.bs2', '32.bw1'], 'contains': ['128.c1', '128.m1', '128.r1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [4095, -1, 4089, -1], 'generators': [1313901388807, 4103693798407, 4103693809943], 'label': '512.41229.64.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121709
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.g1', '32.bq3', '32.bs3', '32.bw1'], 'contains': ['128.j1', '128.m1', '128.r1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4259, -1, 4252, -1], 'generators': [2789832705976, 1313901388807, 4103693798407], 'label': '512.41229.64.bb2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bb2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121710
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.c1'], 'contains': ['16.i1', '16.j1', '16.j2', '16.k1', '16.be1', '16.bg1', '16.bq1', '16.bq2', '16.bq3', '16.bq4'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1921, -1, 1919, -1], 'generators': [2789832705976, 1313901388807, 4103693798407, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.8.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121711
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.a1', '32.br3', '32.bs1', '32.bt3', '32.bx1'], 'contains': ['128.c1', '128.n1', '128.s2'], 'core': '128.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [6332, -1, 6322, -1], 'generators': [2789792421136, 2789705323583, 2789792409600], 'label': '512.41229.64.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121712
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.a1', '32.br5', '32.bs3', '32.bx2'], 'contains': ['128.j1', '128.n2', '128.s1', '128.s2'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4989, -1, 4982, -1], 'generators': [2789705318416, 2789792409600, 4103734094783], 'label': '512.41229.64.bc2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bc2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121713
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bc3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.h1', '32.br1', '32.bs1', '32.bs2', '32.bx2'], 'contains': ['128.c1', '128.n2', '128.s3'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [4908, -1, 4901, -1], 'generators': [2789792421136, 2789792409600, 4103606707223], 'label': '512.41229.64.bc3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bc3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121714
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bc4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.h1', '32.br2', '32.bs3', '32.bt1', '32.bx1'], 'contains': ['128.j1', '128.n1', '128.s3'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [6088, -1, 6079, -1], 'generators': [2789792409600, 4103606707223, 4103734094783], 'label': '512.41229.64.bc4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.bc4', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc4', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121715
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.i1', '32.bt1', '32.by1'], 'contains': ['128.j1', '128.o1', '128.t1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [7767, -1, 7755, -1], 'generators': [2789792409600, 4103734094783, 5606234766719], 'label': '512.41229.64.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '64.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121716
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.i1', '32.bt2', '32.bt3', '32.by1'], 'contains': ['128.c1', '128.o1', '128.t1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [8544, -1, 8462, -1], 'generators': [2789792421136, 2789792409600, 5606234766719], 'label': '512.41229.64.bd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '64.bd2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121717
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.j1', '32.bt1', '32.bz1'], 'contains': ['128.j1', '128.p1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [8436, -1, 8354, -1], 'generators': [2789792409600, 4103734094783, 9709841473896], 'label': '512.41229.64.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '64.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121718
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.be2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.j2', '32.bt2', '32.bt3', '32.bu1', '32.bz1'], 'contains': ['128.c1', '128.p1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [9220, -1, 9205, -1], 'generators': [2789792421136, 2789792409600, 9709881748416], 'label': '512.41229.64.be2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '64.be2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121719
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.b1', '32.bv1', '32.bv2', '32.bw1', '32.bx1', '32.bx2', '32.by1', '32.bz1', '32.ca1'], 'contains': ['128.c1', '128.j1', '128.k1', '128.u1'], 'core': '128.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [6250, -1, 6241, -1], 'generators': [4103734078080, 16703, 2789792426303], 'label': '512.41229.64.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bf1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121720
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.l1', '32.bv1', '32.cb1', '32.cc1', '32.cd1', '32.cd2', '32.ce1', '32.ce2'], 'contains': ['128.k1', '128.l1', '128.v1', '128.v3'], 'core': '256.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [3770, -1, 3765, -1], 'generators': [2789792426303, 4103734094783, 2789832689280], 'label': '512.41229.64.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bg1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121721
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1'], 'contains': ['16.k1', '16.l1', '16.m1', '16.n1', '16.n2', '16.o1', '16.o2', '16.bf1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8284, -1, 8246, -1], 'generators': [2789832705976, 1313901388807, 4103693798407, 4103606707223, 9709841473896, 1313941673647], 'label': '512.41229.8.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '8.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121722
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.l1', '32.bv2', '32.cd1', '32.cd2', '32.ce2', '32.ce3'], 'contains': ['128.k1', '128.l1', '128.v2', '128.v3'], 'core': '256.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [2633, -1, 2629, -1], 'generators': [2789792426303, 4103734094783, 4103734078087], 'label': '512.41229.64.bg2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bg2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bg2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121723
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.c1', '32.bw1', '32.cd1', '32.cd2', '32.cf1'], 'contains': ['128.k1', '128.m1', '128.w1', '128.w2'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [3933, -1, 3927, -1], 'generators': [2789832705976, 1313901388807, 2789792426303], 'label': '512.41229.64.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bh1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121724
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.m1', '32.bx1', '32.ce1', '32.ce3', '32.cf1', '32.cg1', '32.ch1'], 'contains': ['128.k1', '128.n1', '128.x1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [5574, -1, 5566, -1], 'generators': [2789792426303, 4103606707223, 4103734094783], 'label': '512.41229.64.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bi1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121725
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bi2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.m1', '32.bx2', '32.ce2', '32.cf1'], 'contains': ['128.k1', '128.n2', '128.x1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4827, -1, 4820, -1], 'generators': [2789705318416, 2789792426303, 4103734094783], 'label': '512.41229.64.bi2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bi2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bi2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121726
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.n1', '32.by1', '32.cb1', '32.cg1'], 'contains': ['128.k1', '128.o1', '128.y1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [6979, -1, 6968, -1], 'generators': [2789792426303, 4103734094783, 5606234766719], 'label': '512.41229.64.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '64.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bj1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121727
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.d1', '32.bz1', '32.cc1', '32.cg1'], 'contains': ['128.k1', '128.p1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [7429, -1, 7418, -1], 'generators': [2789792426303, 4103734094783, 9709841473896], 'label': '512.41229.64.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '64.bk1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bk1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121728
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.r1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.o1', '32.ca1', '32.cb1', '32.cc1', '32.ch1'], 'contains': ['128.k1', '128.z1'], 'core': '256.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [5980, -1, 5971, -1], 'generators': [2789792426303, 6920263526376, 4103734094783], 'label': '512.41229.64.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '64.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bl1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121729
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.q1', '32.bq1', '32.bq3', '32.cd1', '32.ci1'], 'contains': ['128.l1', '128.m1', '128.ba1', '128.ba3'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [1576, -1, 1574, -1], 'generators': [4103693815096, 4103734094783, 4103734078087], 'label': '512.41229.64.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bm1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121730
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.q1', '32.bq2', '32.bq3', '32.cd1', '32.ci2'], 'contains': ['128.l1', '128.m1', '128.ba2', '128.ba3'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [1657, -1, 1655, -1], 'generators': [4103693815096, 4103734094783, 2789832689280], 'label': '512.41229.64.bm2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bm2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bm2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121731
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bm3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.q2', '32.bq1', '32.bq2', '32.bq3', '32.cd2', '32.ci1', '32.ci2'], 'contains': ['128.l1', '128.m1', '128.ba4'], 'core': '256.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [1495, -1, 1492, -1], 'generators': [4103693798407, 4103734094783, 2789832689280], 'label': '512.41229.64.bm3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bm3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bm3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121732
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1'], 'contains': ['16.n2', '16.p1', '16.br1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9605, -1, 9580, -1], 'generators': [4103734078080, 16703, 20922662476800, 4103606707223, 9709841473896, 1313941673647], 'label': '512.41229.8.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '8.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121733
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['32.r1', '32.br1', '32.br5', '32.ce2', '32.ci1', '32.ci2'], 'contains': ['128.l1', '128.n2', '128.bb1'], 'core': '256.b1', 'coset_action_label': None, 'count': 256, 'diagramx': [2470, -1, 2466, -1], 'generators': [4103734094783, 87091216, 1314028759703], 'label': '512.41229.64.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bn1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121734
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['32.r1', '32.br2', '32.br3', '32.br4', '32.ce1', '32.ce3', '32.ci1', '32.ci2'], 'contains': ['128.l1', '128.n1', '128.bb1'], 'core': '256.b1', 'coset_action_label': None, 'count': 256, 'diagramx': [2876, -1, 2872, -1], 'generators': [4103606707223, 4103734094783, 1314028759703], 'label': '512.41229.64.bn2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bn2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bn2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121735
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.s1', '32.bs1', '32.bs2', '32.bs3', '32.cf1', '32.ci1', '32.ci2'], 'contains': ['128.m1', '128.n1', '128.n2', '128.bc1'], 'core': '256.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [4014, -1, 4008, -1], 'generators': [4103693798407, 4103606707223, 4103734094783], 'label': '512.41229.64.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bo1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bo1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121736
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.v1', '32.bt1', '32.bt2', '32.bt3', '32.cg1'], 'contains': ['128.n1', '128.o1', '128.p1'], 'core': '256.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [8776, -1, 8607, -1], 'generators': [4103606707223, 4103734094783, 9709841473896], 'label': '512.41229.64.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '64.bp1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bp1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121737
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.x1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.x1', '32.bu1'], 'contains': ['128.p1'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [9646, -1, 9632, -1], 'generators': [19608888470400, 8395980348119, 4103734094783], 'label': '512.41229.64.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.p1', 'old_label': '64.bq1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bq1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121738
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['32.y1', '32.bq1', '32.bq3', '32.cj1', '32.cj2', '32.cl1', '32.cl2'], 'contains': ['128.q1', '128.r1', '128.ba1', '128.ba3', '128.ba4'], 'core': '512.a1', 'coset_action_label': None, 'count': 512, 'diagramx': [925, -1, 924, -1], 'generators': [4103734078080, 4103693798407, 4103734078087], 'label': '512.41229.64.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.br1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.br1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121739
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.br2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['32.y1', '32.bq2', '32.bq3', '32.cj1', '32.cj3', '32.cl1', '32.cl2'], 'contains': ['128.q1', '128.r1', '128.ba2', '128.ba3', '128.ba4'], 'core': '512.a1', 'coset_action_label': None, 'count': 512, 'diagramx': [1007, -1, 1005, -1], 'generators': [4103734078080, 4103693798407, 2789832689280], 'label': '512.41229.64.br2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.br2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.br2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121740
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 256, 'contained_in': ['32.z1', '32.br1', '32.br2', '32.cj1', '32.cj2', '32.cj3', '32.cm1', '32.cm2'], 'contains': ['128.q1', '128.s3', '128.bb1'], 'core': '512.a1', 'coset_action_label': None, 'count': 1024, 'diagramx': [2063, -1, 2060, -1], 'generators': [4103734078080, 87091216, 1314028759703], 'label': '512.41229.64.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bs1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bs1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121741
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bs2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['32.z2', '32.br3', '32.br5', '32.cj1', '32.cm1', '32.cm2'], 'contains': ['128.q1', '128.s2', '128.bb1'], 'core': '512.a1', 'coset_action_label': None, 'count': 512, 'diagramx': [2389, -1, 2385, -1], 'generators': [4103734078080, 1313988480023, 1314028759703], 'label': '512.41229.64.bs2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bs2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bs2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121742
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bs3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['32.z2', '32.br4', '32.br5', '32.cj2', '32.cj3', '32.cm1', '32.cm2'], 'contains': ['128.q1', '128.s1', '128.bb1'], 'core': '512.a1', 'coset_action_label': None, 'count': 512, 'diagramx': [2227, -1, 2223, -1], 'generators': [4103734078080, 4103606707223, 1314028759703], 'label': '512.41229.64.bs3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bs3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bs3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121743
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.j1'], 'contains': ['16.o2', '16.p2'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8998, -1, 8795, -1], 'generators': [4103646986896, 20922662476800, 2789792409600, 4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.8.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '8.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121744
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['32.ba1', '32.bs1', '32.bs3', '32.cj1', '32.cn1'], 'contains': ['128.r1', '128.s2', '128.s3', '128.bc1'], 'core': '512.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [3852, -1, 3846, -1], 'generators': [2789705318416, 4103734078080, 4103693798407], 'label': '512.41229.64.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bt1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bt1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121745
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bt2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['32.ba1', '32.bs2', '32.bs3', '32.cj2', '32.cj3', '32.cn1'], 'contains': ['128.r1', '128.s1', '128.s3', '128.bc1'], 'core': '512.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [3608, -1, 3602, -1], 'generators': [4103734078080, 4103693798407, 4103606707223], 'label': '512.41229.64.bt2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bt2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bt2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121746
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.bc1', '32.bv1', '32.ck1', '32.cl1', '32.cm1'], 'contains': ['128.q1', '128.u1', '128.v1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3364, -1, 3359, -1], 'generators': [4103734078080, 2789792409600, 2789832689280], 'label': '512.41229.64.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.bu1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bu1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121747
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bu2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.bc1', '32.bv2', '32.cl1', '32.cm2'], 'contains': ['128.q1', '128.u1', '128.v2'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [2551, -1, 2547, -1], 'generators': [4103734078080, 2789792409600, 4103734078087], 'label': '512.41229.64.bu2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bu2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bu2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121748
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bu3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.bc2', '32.bv1', '32.bv2', '32.cl2', '32.cm1', '32.cm2'], 'contains': ['128.q1', '128.u1', '128.v3'], 'core': '512.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [2714, -1, 2710, -1], 'generators': [4103734078080, 2789792426303, 2789832689280], 'label': '512.41229.64.bu3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bu3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bu3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121749
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.bd1', '32.bw1', '32.cl1', '32.cl2', '32.cn1'], 'contains': ['128.r1', '128.u1', '128.w1', '128.w2'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3689, -1, 3683, -1], 'generators': [4103734078080, 1313901388807, 4103693798407], 'label': '512.41229.64.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bv1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bv1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121750
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.be1', '32.bx1', '32.bx2', '32.cm1', '32.cm2', '32.cn1'], 'contains': ['128.s1', '128.s2', '128.s3', '128.u1', '128.x1'], 'core': '512.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [4421, -1, 4414, -1], 'generators': [4103734078080, 2789792409600, 4103606707223], 'label': '512.41229.64.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.bw1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bw1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121751
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.bf1', '32.by1', '32.ck1'], 'contains': ['128.t1', '128.u1', '128.y1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [5872, -1, 5863, -1], 'generators': [4103734078080, 2789792409600, 5606234766719], 'label': '512.41229.64.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '64.bx1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bx1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121752
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.r1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.bg1', '32.ca1', '32.ck1'], 'contains': ['128.u1', '128.z1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [5467, -1, 5458, -1], 'generators': [4103734078080, 2789792426303, 6920263526376], 'label': '512.41229.64.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '64.by1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.by1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121753
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.bi1', '32.cb1', '32.ck1'], 'contains': ['128.v1', '128.y1', '128.z1'], 'core': '512.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [5363, -1, 5355, -1], 'generators': [2789792426303, 5606234766719, 1314028759703], 'label': '512.41229.64.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '64.bz1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bz1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121754
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.g1'], 'contains': ['16.c1', '16.q1', '16.r1', '16.s1', '16.bh1', '16.bs1'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [5645, -1, 5636, -1], 'generators': [4103734078080, 16703, 2789792426303, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.8.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121755
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.e1', '32.cd1', '32.cl1', '32.co1'], 'contains': ['128.v1', '128.v2', '128.w1', '128.ba1', '128.ba2'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [1251, -1, 1249, -1], 'generators': [2789832705976, 4103693815096, 2789832689280], 'label': '512.41229.64.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.ca1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ca1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121756
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.ca2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.bk1', '32.cd1', '32.cl1', '32.co2'], 'contains': ['128.v1', '128.v2', '128.w1', '128.ba3'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [1332, -1, 1330, -1], 'generators': [2789832705976, 40279680, 4103693815096], 'label': '512.41229.64.ca2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.ca2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ca2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121757
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.ca3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.bk2', '32.cd1', '32.cl2', '32.co3'], 'contains': ['128.v3', '128.w2', '128.ba1', '128.ba2', '128.ba3'], 'core': '512.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [1088, -1, 1087, -1], 'generators': [2789832705976, 2789792426303, 2789832689280], 'label': '512.41229.64.ca3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.ca3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ca3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121758
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.ca4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.bk3', '32.cd2', '32.cl1', '32.co3'], 'contains': ['128.v1', '128.v2', '128.w2', '128.ba4'], 'core': '512.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [1414, -1, 1411, -1], 'generators': [4103693798407, 2789832689287, 2789832689280], 'label': '512.41229.64.ca4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.ca4', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ca4', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121759
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.ca5', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.bk4', '32.cd2', '32.cl2', '32.co1', '32.co2'], 'contains': ['128.v3', '128.w1', '128.ba4'], 'core': '512.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [844, -1, 843, -1], 'generators': [2789792426303, 2789832689287, 2789832689280], 'label': '512.41229.64.ca5', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.ca5', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ca5', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121760
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['32.bl1', '32.ce1', '32.ce2', '32.cm1', '32.co1', '32.co2', '32.co3'], 'contains': ['128.v1', '128.v3', '128.x1', '128.bb1'], 'core': '512.a1', 'coset_action_label': None, 'count': 512, 'diagramx': [1982, -1, 1979, -1], 'generators': [1313941668480, 4103606707223, 1314028759703], 'label': '512.41229.64.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.cb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cb1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121761
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.cb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['32.bl1', '32.ce2', '32.ce3', '32.cm2', '32.co1', '32.co2', '32.co3'], 'contains': ['128.v2', '128.v3', '128.x1', '128.bb1'], 'core': '512.a1', 'coset_action_label': None, 'count': 512, 'diagramx': [1901, -1, 1898, -1], 'generators': [1313941668480, 87091216, 1314028759703], 'label': '512.41229.64.cb2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.cb2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cb2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121762
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.bm1', '32.cf1', '32.cn1', '32.co1', '32.co2'], 'contains': ['128.w1', '128.x1', '128.bc1'], 'core': '512.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [3039, -1, 3034, -1], 'generators': [2789792426303, 4103606707223, 2789832689287], 'label': '512.41229.64.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.cc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cc1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121763
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.cc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.bm2', '32.cf1', '32.cn1', '32.co3'], 'contains': ['128.w2', '128.x1', '128.bc1'], 'core': '512.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [3446, -1, 3440, -1], 'generators': [4103693798407, 4103606707223, 2789832689287], 'label': '512.41229.64.cc2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.cc2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cc2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121764
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 256, 'contained_in': ['32.bp1', '32.ci1', '32.cj1', '32.cj2', '32.co1', '32.co3'], 'contains': ['128.ba1', '128.ba4', '128.bb1', '128.bc1'], 'core': '512.a1', 'coset_action_label': None, 'count': 1024, 'diagramx': [478, -1, 457, -1], 'generators': [40279687, 1313988480023, 1314028759703], 'label': '512.41229.64.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.cd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cd1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121765
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.g1', '4.h1', '4.l1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5907, 6463, 5898, 6584], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 4103606707223, 9709841473896, 1314028759703, 1313941673647], 'label': '512.41229.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121766
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.g1', '4.h1'], 'contains': ['16.d1', '16.q1', '16.r1', '16.t1', '16.bt1'], 'core': '16.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [6617, -1, 6607, -1], 'generators': [4103734078080, 16703, 2789792426303, 9709841473896, 2789832689280, 1313941673647], 'label': '512.41229.8.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121767
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.cd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 256, 'contained_in': ['32.bp1', '32.ci2', '32.cj1', '32.cj3', '32.co1', '32.co3'], 'contains': ['128.ba2', '128.ba4', '128.bb1', '128.bc1'], 'core': '512.a1', 'coset_action_label': None, 'count': 1024, 'diagramx': [571, -1, 549, -1], 'generators': [40279687, 87091216, 1314028759703], 'label': '512.41229.64.cd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.cd2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cd2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121768
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '64.cd3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 512, 'contained_in': ['32.bp2', '32.ci1', '32.ci2', '32.cj1', '32.cj2', '32.cj3', '32.co2', '32.co3'], 'contains': ['128.ba3', '128.ba4', '128.bb1', '128.bc1'], 'core': '512.a1', 'coset_action_label': None, 'count': 2048, 'diagramx': [672, -1, 640, -1], 'generators': [40279687, 4103606707223, 1314028759703], 'label': '512.41229.64.cd3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.cd3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cd3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121769
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.e1', '64.f1', '64.g1', '64.h1', '64.i1', '64.j1'], 'contains': ['256.a1', '256.b1'], 'core': '128.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6492, 4728, 6481, 4815], 'generators': [4103734094783, 1313941673647], 'label': '512.41229.128.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '128.a1', 'normal_contained_in': ['64.a1', '64.b1'], 'normal_contains': ['256.a1', '256.b1'], 'normalizer': '1.a1', 'old_label': '128.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121770
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['64.b1', '64.c1', '64.p1', '64.q1', '64.q2', '64.r1', '64.s1', '64.t1', '64.u1', '64.v1'], 'contains': ['256.a1', '256.d1'], 'core': '128.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4908, 5395, 4901, 5496], 'generators': [1313941668480, 1313941673647], 'label': '512.41229.128.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '128.b1', 'normal_contained_in': ['64.b1', '64.c1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121771
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['64.a1', '64.d1', '64.ba1', '64.bb1', '64.bc1', '64.bc3', '64.bd2', '64.be2', '64.bf1'], 'contains': ['256.b1', '256.c1'], 'core': '128.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [6169, 4059, 6160, 4135], 'generators': [2789792421136, 2789792409600], 'label': '512.41229.128.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '128.c1', 'normal_contained_in': ['64.a1', '64.d1'], 'normal_contains': ['256.b1'], 'normalizer': '1.a1', 'old_label': '128.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121772
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '64.k1', '64.l1', '64.m1', '64.m2', '64.n1', '64.o1', '64.p1'], 'contains': ['256.a1', '256.c1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4989, -1, 4982, -1], 'generators': [4103734078080, 1313941673647], 'label': '512.41229.128.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '128.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121773
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['64.e1', '64.k1', '64.q1', '64.q2', '64.w1', '64.w2', '64.w3', '64.x1'], 'contains': ['256.a1', '256.e1'], 'core': '256.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2348, -1, 2345, -1], 'generators': [2789832689280, 1313941673647], 'label': '512.41229.128.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121774
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.c1', '64.f1', '64.l1', '64.r1', '64.w1', '64.w2', '64.w3', '64.y1', '64.z1'], 'contains': ['256.a1', '256.f1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4177, -1, 4170, -1], 'generators': [40279687, 1313941673647], 'label': '512.41229.128.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '128.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121775
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.g1', '64.m1', '64.m2', '64.s1', '64.x1', '64.y1'], 'contains': ['256.a1', '256.g1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4502, -1, 4495, -1], 'generators': [4103606707223, 1313941673647], 'label': '512.41229.128.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121777
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.h1'], 'contains': ['16.e1', '16.q1', '16.r1', '16.u1', '16.bi1'], 'core': '16.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [5463, -1, 5454, -1], 'generators': [4103734078080, 1313941673647, 1314028759703, 2789792426303, 16703, 5606275034856], 'label': '512.41229.8.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121778
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.j1', '64.o1', '64.v1', '64.z1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6416, -1, 6405, -1], 'generators': [8396067450839, 1313941673647], 'label': '512.41229.128.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '128.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121779
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '64.ba2', '64.bb2', '64.bc2', '64.bc4', '64.bd1', '64.be1', '64.bf1'], 'contains': ['256.b1', '256.c1'], 'core': '256.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6088, -1, 6079, -1], 'generators': [2789792409600, 4103734094783], 'label': '512.41229.128.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '128.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121780
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.b1', '64.bf1', '64.bg1', '64.bg2', '64.bh1', '64.bi1', '64.bi2', '64.bj1', '64.bk1', '64.bl1'], 'contains': ['256.b1', '256.d1'], 'core': '256.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5642, -1, 5633, -1], 'generators': [2789792426303, 4103734094783], 'label': '512.41229.128.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '128.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121781
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['64.e1', '64.ba1', '64.ba2', '64.bg1', '64.bg2', '64.bm1', '64.bm2', '64.bm3', '64.bn1', '64.bn2'], 'contains': ['256.b1', '256.e1'], 'core': '256.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [3202, -1, 3197, -1], 'generators': [4103734094783, 2789832689280], 'label': '512.41229.128.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121782
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.f1', '64.bb1', '64.bb2', '64.bh1', '64.bm1', '64.bm2', '64.bm3', '64.bo1'], 'contains': ['256.b1', '256.f1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [3974, -1, 3968, -1], 'generators': [4103693798407, 4103734094783], 'label': '512.41229.128.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.m1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121783
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['64.d1', '64.g1', '64.bc1', '64.bc4', '64.bi1', '64.bn2', '64.bo1', '64.bp1'], 'contains': ['256.b1', '256.g1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [6007, -1, 5997, -1], 'generators': [4103606707223, 4103734094783], 'label': '512.41229.128.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '128.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121784
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.n2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.g1', '64.bc2', '64.bc3', '64.bi2', '64.bn1', '64.bo1'], 'contains': ['256.b1', '256.g1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4827, -1, 4820, -1], 'generators': [4103734094783, 87091216], 'label': '512.41229.128.n2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.n2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121785
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.h1', '64.bd1', '64.bd2', '64.bj1', '64.bp1'], 'contains': ['256.b1', '256.h1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [7672, -1, 7660, -1], 'generators': [4103734094783, 5606234766719], 'label': '512.41229.128.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '128.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.o1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121786
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.i1', '64.be1', '64.be2', '64.bk1', '64.bp1', '64.bq1'], 'contains': ['256.b1'], 'core': '256.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [8776, -1, 8607, -1], 'generators': [4103734094783, 9709841473896], 'label': '512.41229.128.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '128.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.p1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121787
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['64.k1', '64.ba1', '64.ba2', '64.br1', '64.br2', '64.bs1', '64.bs2', '64.bs3', '64.bu1', '64.bu2', '64.bu3'], 'contains': ['256.c1', '256.e1'], 'core': '512.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [2551, -1, 2547, -1], 'generators': [4103734078080, 2789832689280], 'label': '512.41229.128.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.q1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121788
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.g1', '4.h1'], 'contains': ['16.b1', '16.j1', '16.j2', '16.q1', '16.w1', '16.bk1', '16.bv1', '16.bv2', '16.bv3'], 'core': '16.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3080, -1, 3075, -1], 'generators': [4103734078080, 16703, 2789792426303, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.8.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121789
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['64.l1', '64.bb1', '64.bb2', '64.br1', '64.br2', '64.bt1', '64.bt2', '64.bv1'], 'contains': ['256.c1', '256.f1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3770, -1, 3765, -1], 'generators': [4103734078080, 4103693798407], 'label': '512.41229.128.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.r1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121790
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['64.d1', '64.m1', '64.bc2', '64.bs3', '64.bt2', '64.bw1'], 'contains': ['256.c1', '256.g1'], 'core': '512.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4583, -1, 4576, -1], 'generators': [4103734078080, 4103606707223], 'label': '512.41229.128.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.s1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121791
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.s2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['64.m1', '64.bc1', '64.bc2', '64.bs2', '64.bt1', '64.bw1'], 'contains': ['256.c1', '256.g1'], 'core': '512.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4746, -1, 4738, -1], 'generators': [4103734078080, 1313988480023], 'label': '512.41229.128.s2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.s2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.s2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121792
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.s3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['64.m2', '64.bc3', '64.bc4', '64.bs1', '64.bt1', '64.bt2', '64.bw1'], 'contains': ['256.c1', '256.g1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [4421, -1, 4414, -1], 'generators': [4103734078080, 87091216], 'label': '512.41229.128.s3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.s3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.s3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121793
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.n1', '64.bd1', '64.bd2', '64.bx1'], 'contains': ['256.c1', '256.h1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [6719, -1, 6707, -1], 'generators': [4103734078080, 5606234766719], 'label': '512.41229.128.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '128.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.t1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121794
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['64.p1', '64.bf1', '64.bu1', '64.bu2', '64.bu3', '64.bv1', '64.bw1', '64.bx1', '64.by1'], 'contains': ['256.c1', '256.d1'], 'core': '512.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4665, -1, 4657, -1], 'generators': [4103734078080, 2789792409600], 'label': '512.41229.128.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '128.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.u1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121795
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['64.q1', '64.bg1', '64.bu1', '64.bz1', '64.ca1', '64.ca2', '64.ca4', '64.cb1'], 'contains': ['256.d1', '256.e1'], 'core': '512.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3121, -1, 3115, -1], 'generators': [1313941668480, 2789832689280], 'label': '512.41229.128.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '128.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.v1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121796
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.v2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['64.q1', '64.bg2', '64.bu2', '64.ca1', '64.ca2', '64.ca4', '64.cb2'], 'contains': ['256.d1', '256.e1'], 'core': '512.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2186, -1, 2182, -1], 'generators': [1313941668487, 1313941668480], 'label': '512.41229.128.v2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.v2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.v2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121797
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.v3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['64.q2', '64.bg1', '64.bg2', '64.bu3', '64.ca3', '64.ca5', '64.cb1', '64.cb2'], 'contains': ['256.d1', '256.e1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [2267, -1, 2263, -1], 'generators': [2789792426303, 2789832689280], 'label': '512.41229.128.v3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.v3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.v3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121798
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.c1', '64.bh1', '64.bv1', '64.ca1', '64.ca2', '64.ca5', '64.cc1'], 'contains': ['256.d1', '256.f1'], 'core': '512.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3039, -1, 3034, -1], 'generators': [2789792426303, 2789832689287], 'label': '512.41229.128.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.w1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121799
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '4.g1', '4.h1'], 'contains': ['16.b1', '16.r1', '16.bc1', '16.by1'], 'core': '16.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6410, -1, 6400, -1], 'generators': [8396067455999, 4103734078080, 16703, 2789792426303, 4103606707223, 1313941673647], 'label': '512.41229.8.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121800
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.w2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.r1', '64.bh1', '64.bv1', '64.ca3', '64.ca4', '64.cc2'], 'contains': ['256.d1', '256.f1'], 'core': '512.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3567, -1, 3562, -1], 'generators': [4103693798407, 2789832689287], 'label': '512.41229.128.w2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.w2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.w2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121801
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['64.s1', '64.bi1', '64.bi2', '64.bw1', '64.cb1', '64.cb2', '64.cc1', '64.cc2'], 'contains': ['256.d1', '256.g1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [4340, -1, 4333, -1], 'generators': [1313941668480, 4103606707223], 'label': '512.41229.128.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.x1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121802
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.t1', '64.bj1', '64.bx1', '64.bz1'], 'contains': ['256.d1', '256.h1'], 'core': '512.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5832, -1, 5822, -1], 'generators': [1313941668480, 5606234766719], 'label': '512.41229.128.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '128.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.y1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121803
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.u1', '64.bl1', '64.by1', '64.bz1'], 'contains': ['256.d1'], 'core': '512.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5363, -1, 5355, -1], 'generators': [2789792426303, 6920263526376], 'label': '512.41229.128.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '128.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.z1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121804
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['64.w1', '64.bm1', '64.br1', '64.ca1', '64.ca3', '64.cd1'], 'contains': ['256.e1', '256.f1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [1271, -1, 1269, -1], 'generators': [40279687, 40279680], 'label': '512.41229.128.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.ba1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121805
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.ba2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['64.w1', '64.bm2', '64.br2', '64.ca1', '64.ca3', '64.cd2'], 'contains': ['256.e1', '256.f1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [1373, -1, 1431, -1], 'generators': [40279687, 1313941668487], 'label': '512.41229.128.ba2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.ba2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.ba2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121806
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.ba3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['64.w2', '64.bm1', '64.bm2', '64.br1', '64.br2', '64.ca2', '64.ca3', '64.cd3'], 'contains': ['256.e1', '256.f1'], 'core': '512.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [1535, -1, 1553, -1], 'generators': [40279687, 2789832689280], 'label': '512.41229.128.ba3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.ba3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.ba3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121807
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.ba4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['64.w3', '64.bm3', '64.br1', '64.br2', '64.ca4', '64.ca5', '64.cd1', '64.cd2', '64.cd3'], 'contains': ['256.e1', '256.f1'], 'core': '512.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [1007, -1, 1005, -1], 'generators': [2789832689287, 2789832689280], 'label': '512.41229.128.ba4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.ba4', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.ba4', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121808
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 256, 'contained_in': ['64.x1', '64.bn1', '64.bn2', '64.bs1', '64.bs2', '64.bs3', '64.cb1', '64.cb2', '64.cd1', '64.cd2', '64.cd3'], 'contains': ['256.e1', '256.g1'], 'core': '512.a1', 'coset_action_label': None, 'count': 1024, 'diagramx': [2104, -1, 2101, -1], 'generators': [4103606707223, 1314028759703], 'label': '512.41229.128.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.bb1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121809
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '128.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['64.y1', '64.bo1', '64.bt1', '64.bt2', '64.cc1', '64.cc2', '64.cd1', '64.cd2', '64.cd3'], 'contains': ['256.f1', '256.g1'], 'core': '512.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [2957, -1, 2953, -1], 'generators': [40279687, 4103606707223], 'label': '512.41229.128.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '128.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.bc1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121810
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '4.i1', '4.j1'], 'contains': ['16.d1', '16.p1', '16.p2', '16.bd1'], 'core': '16.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [9153, -1, 8950, -1], 'generators': [4103734078080, 16703, 2789792426303, 9709841473896, 16819055769623, 1313941673647], 'label': '512.41229.8.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121811
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['128.a1', '128.b1', '128.d1', '128.e1', '128.f1', '128.g1', '128.h1', '128.i1'], 'contains': ['512.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4908, 5021, 4901, 5114], 'generators': [1313941673647], 'label': '512.41229.256.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '256.a1', 'normal_contained_in': ['128.a1', '128.b1'], 'normal_contains': ['512.a1'], 'normalizer': '1.a1', 'old_label': '256.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121812
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '256.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['128.a1', '128.c1', '128.j1', '128.k1', '128.l1', '128.m1', '128.n1', '128.n2', '128.o1', '128.p1'], 'contains': ['512.a1'], 'core': '256.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6007, 4434, 5997, 4516], 'generators': [4103734094783], 'label': '512.41229.256.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '256.b1', 'normal_contained_in': ['128.a1', '128.c1'], 'normal_contains': ['512.a1'], 'normalizer': '1.a1', 'old_label': '256.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121813
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '256.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['128.c1', '128.d1', '128.j1', '128.q1', '128.r1', '128.s1', '128.s2', '128.s3', '128.t1', '128.u1'], 'contains': ['512.a1'], 'core': '512.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4665, -1, 4657, -1], 'generators': [4103734078080], 'label': '512.41229.256.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '128.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '256.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121814
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '256.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.b1', '128.k1', '128.u1', '128.v1', '128.v2', '128.v3', '128.w1', '128.w2', '128.x1', '128.y1', '128.z1'], 'contains': ['512.a1'], 'core': '512.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4426, -1, 4398, -1], 'generators': [1313941668480], 'label': '512.41229.256.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '128.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '256.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121815
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '256.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['128.e1', '128.l1', '128.q1', '128.v1', '128.v2', '128.v3', '128.ba1', '128.ba2', '128.ba3', '128.ba4', '128.bb1'], 'contains': ['512.a1'], 'core': '512.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [2227, -1, 2223, -1], 'generators': [2789832689280], 'label': '512.41229.256.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '256.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121816
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '256.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['128.f1', '128.m1', '128.r1', '128.w1', '128.w2', '128.ba1', '128.ba2', '128.ba3', '128.ba4', '128.bc1'], 'contains': ['512.a1'], 'core': '512.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3039, -1, 3034, -1], 'generators': [40279687], 'label': '512.41229.256.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '256.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121817
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '256.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['128.g1', '128.n1', '128.n2', '128.s1', '128.s2', '128.s3', '128.x1', '128.bb1', '128.bc1'], 'contains': ['512.a1'], 'core': '512.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4542, -1, 4536, -1], 'generators': [4103606707223], 'label': '512.41229.256.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '256.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121818
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '256.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.h1', '128.o1', '128.t1', '128.y1'], 'contains': ['512.a1'], 'core': '512.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6573, -1, 6562, -1], 'generators': [5606234766719], 'label': '512.41229.256.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '256.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121819
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '512.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['256.a1', '256.b1', '256.c1', '256.d1', '256.e1', '256.f1', '256.g1', '256.h1'], 'contains': [], 'core': '512.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4583, 4728, 4617, 4815], 'generators': [], 'label': '512.41229.512.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '512.a1', 'normal_contained_in': ['256.a1', '256.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '512.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121820
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.l1'], 'contains': ['16.f1', '16.s1', '16.u1', '16.y1', '16.z1', '16.bo1', '16.bo2'], 'core': '16.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [4669, -1, 4662, -1], 'generators': [1313901405496, 4103693798407, 2789832689287, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.8.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121821
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.s2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.l1'], 'contains': ['16.h1', '16.s1', '16.u1', '16.v1', '16.y1', '16.bo3'], 'core': '16.h1', 'coset_action_label': None, 'count': 8, 'diagramx': [5123, -1, 5116, -1], 'generators': [2789832705976, 1313901388807, 2789792426303, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.8.s2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.s2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121822
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.l1'], 'contains': ['16.g1', '16.t1', '16.v1', '16.z1'], 'core': '16.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [5780, -1, 5771, -1], 'generators': [1313901405496, 4103693798407, 2789832689287, 9709841473896, 2789832689280, 1313941673647], 'label': '512.41229.8.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121823
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.g1', '4.l1'], 'contains': ['16.s1', '16.t1', '16.w1', '16.ba1', '16.bc1', '16.bz1'], 'core': '32.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [6183, -1, 6174, -1], 'generators': [2789792426303, 4103606707223, 4103734094783, 9709841473896, 1314028759703, 1313941673647], 'label': '512.41229.8.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121824
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.h1', '4.l1'], 'contains': ['16.t1', '16.u1', '16.w1', '16.bb1', '16.bc1'], 'core': '32.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [6004, -1, 5994, -1], 'generators': [4103646986896, 2789792426303, 4103734094783, 9709841473896, 1314028759703, 1313941673647], 'label': '512.41229.8.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121825
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': ['256.e1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.f1', '4.i1', '4.j1'], 'core': '2.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8349, 4662, 8187, 4749], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 20922662476800, 4103606707223, 9709841473896, 1313941673647], 'label': '512.41229.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121826
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '4.l1'], 'contains': ['16.f1', '16.v1', '16.w1', '16.x1', '16.be1', '16.bp1', '16.bp2', '16.bp3', '16.ca1'], 'core': '16.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [1758, -1, 1757, -1], 'generators': [2789832705976, 1313901388807, 2789792426303, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.8.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121827
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.l1'], 'contains': ['16.g1', '16.x1', '16.y1', '16.ba1', '16.bb1', '16.bf1'], 'core': '16.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [7465, -1, 7428, -1], 'generators': [2789832705976, 1313901388807, 2789792426303, 4103606707223, 9709841473896, 1313941673647], 'label': '512.41229.8.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121828
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.e1', '4.l1'], 'contains': ['16.h1', '16.x1', '16.z1', '16.bc1'], 'core': '16.h1', 'coset_action_label': None, 'count': 8, 'diagramx': [5303, -1, 5295, -1], 'generators': [8396067455999, 2789832705976, 1313901388807, 2789792426303, 4103606707223, 1313941673647], 'label': '512.41229.8.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121829
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.f1', '4.k1'], 'contains': ['16.g1', '16.bd1'], 'core': '16.g1', 'coset_action_label': None, 'count': 16, 'diagramx': [8465, -1, 8425, -1], 'generators': [2789832705976, 1313901388807, 2789792426303, 5606362137576, 16819055769623, 1313941673647], 'label': '512.41229.8.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121830
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.a1'], 'contains': ['16.bh1', '16.bi1', '16.bj1', '16.bm1', '16.bn1', '16.bo1', '16.bo2', '16.bo3'], 'core': '32.e1', 'coset_action_label': None, 'count': 32, 'diagramx': [4170, -1, 4164, -1], 'generators': [4103734078080, 1313901388807, 2789792426303, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.8.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '8.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121831
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.c1'], 'contains': ['16.bg1', '16.bj1', '16.bj2', '16.bk1', '16.bl1', '16.bp1', '16.bp2', '16.bp3', '16.cb1'], 'core': '32.e1', 'coset_action_label': None, 'count': 32, 'diagramx': [1556, -1, 1554, -1], 'generators': [4103734078080, 1313901388807, 4103693798407, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.8.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121832
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.g1'], 'contains': ['16.bs1', '16.bt1', '16.bv1', '16.bx1', '16.by1', '16.bz1'], 'core': '64.d1', 'coset_action_label': None, 'count': 64, 'diagramx': [6844, -1, 6834, -1], 'generators': [4103734078080, 16703, 2789792426303, 4103606707223, 9709841473896, 1314028759703], 'label': '512.41229.8.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '8.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121833
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.c1'], 'contains': ['16.bq1', '16.bq2', '16.bq3', '16.bq4', '16.bu1', '16.bv1', '16.bv2', '16.bv3', '16.bw1', '16.ca1', '16.cb1'], 'core': '64.d1', 'coset_action_label': None, 'count': 64, 'diagramx': [1839, -1, 1838, -1], 'generators': [4103734078080, 1313901388807, 1313901405496, 4103693798407, 4103606707223, 1314028759703], 'label': '512.41229.8.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121834
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1'], 'contains': ['32.b1', '32.c1', '32.g1', '32.bd1', '32.bw1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4804, 5216, 4796, 5313], 'generators': [4103734078080, 1313901388807, 1313901405496, 4103693798407, 1313941673647], 'label': '512.41229.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1'], 'normal_contains': ['32.b1', '32.c1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121835
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.f1', '8.g1', '8.p1', '8.q1'], 'contains': ['32.a1', '32.b1', '32.h1', '32.m1', '32.be1', '32.bx1', '32.bx2'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6801, 1312, 6791, 1337], 'generators': [16703, 4103734078080, 2789792426303, 4103606707223, 1313941673647], 'label': '512.41229.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.b1', '8.f1', '8.g1'], 'normal_contains': ['32.a1', '32.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121836
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['8.a1', '8.c1', '8.e1', '8.m1', '8.o1', '8.s1', '8.s2', '8.ba1'], 'core': '4.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5123, 7662, 5116, 7804], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.4.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['8.a1', '8.c1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121876
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.o1', '8.ba1'], 'contains': ['32.bc1', '32.bg1', '32.bh1', '32.bj1'], 'core': '128.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [4432, -1, 4425, -1], 'generators': [4103734078080, 2789792426303, 5606275041239, 1314028759703, 1313941673647], 'label': '512.41229.16.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121837
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.f1', '8.m1'], 'contains': ['32.b1', '32.i1', '32.n1', '32.bf1', '32.by1'], 'core': '16.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7382, 1981, 7371, 2017], 'generators': [16703, 4103734078080, 2789792426303, 5606234766719, 1313941673647], 'label': '512.41229.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.c1', '8.f1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121838
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '8.f1', '8.g1', '8.n1', '8.r1'], 'contains': ['32.b1', '32.d1', '32.j1', '32.j2', '32.bz1'], 'core': '16.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [8516, 2959, 8503, 3014], 'generators': [16703, 4103734078080, 2789792426303, 9709841473896, 1313941673647], 'label': '512.41229.16.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': ['8.d1', '8.f1', '8.g1'], 'normal_contains': ['32.b1', '32.d1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121839
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.g1', '8.o1'], 'contains': ['32.b1', '32.k1', '32.p1', '32.bh1'], 'core': '16.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [7264, 4239, 7252, 4317], 'generators': [16703, 4103734078080, 5606275034856, 2789792426303, 1313941673647], 'label': '512.41229.16.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': ['8.c1', '8.g1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121840
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.h1', '8.s1', '8.w1'], 'contains': ['32.c1', '32.e1', '32.l1', '32.q1', '32.bk1', '32.bk2', '32.cd1'], 'core': '16.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [2246, 8949, 2244, 9116], 'generators': [1313901388807, 2789832705976, 2789792426303, 2789832689280, 1313941673647], 'label': '512.41229.16.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': ['8.a1', '8.h1'], 'normal_contains': ['32.c1', '32.e1'], 'normalizer': '1.a1', 'old_label': '16.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121841
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '8.h1', '8.t1', '8.x1', '8.z1'], 'contains': ['32.c1', '32.d1', '32.u1'], 'core': '16.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [7516, 6316, 7505, 6434], 'generators': [1313901388807, 2789832705976, 2789792426303, 9709841473896, 1313941673647], 'label': '512.41229.16.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': ['8.d1', '8.h1'], 'normal_contains': ['32.c1', '32.d1'], 'normalizer': '1.a1', 'old_label': '16.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121842
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.e1', '8.h1', '8.s2', '8.y1'], 'contains': ['32.c1', '32.o1', '32.bo1'], 'core': '16.h1', 'coset_action_label': None, 'count': 4, 'diagramx': [5123, 7849, 5116, 7995], 'generators': [1313901388807, 2789832705976, 2789792426303, 6920263526376, 1313941673647], 'label': '512.41229.16.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': ['8.e1', '8.h1'], 'normal_contains': ['32.c1'], 'normalizer': '1.a1', 'old_label': '16.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121843
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.i1'], 'contains': ['32.f1', '32.g1', '32.q1', '32.q2', '32.y1', '32.bq1', '32.bq2', '32.bq3'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2003, -1, 2000, -1], 'generators': [1313901388807, 2789832705976, 4103693798407, 2789832689280, 1313941673647], 'label': '512.41229.16.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121844
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.i1', '8.p1'], 'contains': ['32.f1', '32.h1', '32.r1', '32.z1', '32.br1', '32.br2'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2957, -1, 2953, -1], 'generators': [2789792409600, 4103606707223, 4103734094783, 1314028759703, 1313941673647], 'label': '512.41229.16.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121845
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.j2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.i1', '8.p1'], 'contains': ['32.a1', '32.f1', '32.r1', '32.z2', '32.br3', '32.br4', '32.br5'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3039, -1, 3034, -1], 'generators': [2789792409600, 4103734094783, 87091216, 1314028759703, 1313941673647], 'label': '512.41229.16.j2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.j2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121846
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.i1', '8.j1'], 'contains': ['32.a1', '32.g1', '32.h1', '32.s1', '32.ba1', '32.bs1', '32.bs2', '32.bs3'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4566, -1, 4558, -1], 'generators': [1313901388807, 2789832705976, 4103693798407, 4103606707223, 1313941673647], 'label': '512.41229.16.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121847
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.d1', '8.e1', '8.h1', '8.n1', '8.t1'], 'core': '4.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5907, 8583, 5898, 8742], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 9709841473896, 2789832689280, 1313941673647], 'label': '512.41229.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.d1', '8.e1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121848
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '8.j1'], 'contains': ['32.g1', '32.i1', '32.k1', '32.t1', '32.bb1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7874, -1, 7862, -1], 'generators': [1313901388807, 2789832705976, 4103693798407, 5606234766719, 1313941673647], 'label': '512.41229.16.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121849
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '8.j1'], 'contains': ['32.g1', '32.j1', '32.j2', '32.u1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8689, -1, 8675, -1], 'generators': [1313901388807, 2789832705976, 4103693798407, 9709841473896, 1313941673647], 'label': '512.41229.16.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121850
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '8.j1'], 'contains': ['32.h1', '32.i1', '32.j1', '32.v1', '32.bt1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9232, -1, 9218, -1], 'generators': [2789792409600, 4103606707223, 4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.16.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121851
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.n2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.f1', '8.j1', '8.k1'], 'contains': ['32.a1', '32.i1', '32.j2', '32.v1', '32.bt2', '32.bt3'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9389, -1, 9374, -1], 'generators': [6920263521216, 2789792409600, 4103734094783, 87091216, 1313941673647], 'label': '512.41229.16.n2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.n2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121852
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.g1', '8.j1'], 'contains': ['32.h1', '32.j2', '32.k1', '32.w1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8874, -1, 8861, -1], 'generators': [6920263521216, 2789792409600, 4103606707223, 4103734094783, 1313941673647], 'label': '512.41229.16.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121853
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.o2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.j1', '8.l1'], 'contains': ['32.a1', '32.j1', '32.k1', '32.w1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9061, -1, 9047, -1], 'generators': [2789792409600, 4103734094783, 87091216, 9709841473896, 1313941673647], 'label': '512.41229.16.o2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.o2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121854
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.k1', '8.r1'], 'contains': ['32.j2', '32.x1', '32.bu1'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9802, -1, 9787, -1], 'generators': [16703, 4103734078080, 9709841473896, 16819055769623, 1313941673647], 'label': '512.41229.16.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '16.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121855
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.p2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.l1', '8.r1'], 'contains': ['32.j1', '32.x1'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9635, -1, 9620, -1], 'generators': [2789792409600, 4103734094783, 18132957158416, 9709841473896, 1313941673647], 'label': '512.41229.16.p2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '16.p2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121856
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.m1', '8.n1', '8.o1', '8.p1'], 'contains': ['32.b1', '32.f1', '32.l1', '32.bc1', '32.bc2', '32.bv1', '32.bv2'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3351, -1, 3345, -1], 'generators': [16703, 4103734078080, 2789792426303, 2789832689280, 1313941673647], 'label': '512.41229.16.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121857
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.m1', '8.n1', '8.o1', '8.q1'], 'contains': ['32.b1', '32.o1', '32.bg1', '32.ca1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5794, -1, 5786, -1], 'generators': [16703, 4103734078080, 2789792426303, 6920263526376, 1313941673647], 'label': '512.41229.16.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121858
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['8.a1', '8.b1', '8.i1', '8.p1', '8.w1', '8.bb1', '8.bd1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2043, 6863, 2081, 6990], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.4.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['8.a1', '8.b1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121859
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.m1', '8.s1', '8.s2', '8.u1'], 'contains': ['32.l1', '32.n1', '32.o1', '32.bi1', '32.cb1'], 'core': '64.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [5638, -1, 5629, -1], 'generators': [2789792426303, 4103734094783, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.16.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121860
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.h1', '8.n1', '8.t1', '8.u1', '8.v1'], 'contains': ['32.d1', '32.l1', '32.o1', '32.cc1'], 'core': '32.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [6309, -1, 6299, -1], 'generators': [2789792426303, 4103734094783, 9709841473896, 2789832689280, 1313941673647], 'label': '512.41229.16.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121861
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.o1', '8.s1', '8.s2', '8.v1'], 'contains': ['32.l1', '32.o1', '32.p1', '32.bj1'], 'core': '64.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [5310, -1, 5302, -1], 'generators': [6920136150359, 2789792426303, 4103734094783, 1314028759703, 1313941673647], 'label': '512.41229.16.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121862
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.s2', '8.t1', '8.w1'], 'contains': ['32.c1', '32.l1', '32.q2', '32.bk3', '32.bk4', '32.cd2'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2165, -1, 2162, -1], 'generators': [1313901405496, 4103693798407, 2789832689287, 2789832689280, 1313941673647], 'label': '512.41229.16.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121863
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.p1', '8.u1', '8.v1', '8.w1'], 'contains': ['32.l1', '32.m1', '32.r1', '32.bl1', '32.ce1', '32.ce2', '32.ce3'], 'core': '64.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [3121, -1, 3115, -1], 'generators': [2789792426303, 4103606707223, 4103734094783, 1314028759703, 1313941673647], 'label': '512.41229.16.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121864
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.w1', '8.x1', '8.y1'], 'contains': ['32.c1', '32.m1', '32.s1', '32.bm1', '32.bm2', '32.cf1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [4298, -1, 4291, -1], 'generators': [1313901388807, 2789832705976, 2789792426303, 4103606707223, 1313941673647], 'label': '512.41229.16.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121865
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '8.s1', '8.s2', '8.x1'], 'contains': ['32.c1', '32.n1', '32.p1', '32.t1', '32.bn1', '32.bn2'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [6921, -1, 6910, -1], 'generators': [1313901388807, 2789832705976, 2789792426303, 5606234766719, 1313941673647], 'label': '512.41229.16.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121866
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.s1', '8.t1', '8.y1'], 'contains': ['32.c1', '32.o1', '32.bo2'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [4938, -1, 4930, -1], 'generators': [1313901405496, 4103693798407, 6920263526376, 2789832689287, 1313941673647], 'label': '512.41229.16.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.z1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121867
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.f1', '8.u1', '8.x1'], 'contains': ['32.d1', '32.m1', '32.n1', '32.v1', '32.cg1'], 'core': '32.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [8031, -1, 8018, -1], 'generators': [2789792426303, 4103606707223, 4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.16.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ba1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121868
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.v1', '8.x1'], 'contains': ['32.d1', '32.m1', '32.p1', '32.w1'], 'core': '32.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [7702, -1, 7691, -1], 'generators': [4103646986896, 2789792426303, 4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.16.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bb1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121869
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.c1'], 'contains': ['8.b1', '8.c1', '8.d1', '8.f1', '8.g1', '8.j1', '8.x1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7692, 3260, 7655, 3321], 'generators': [1313901388807, 4103734078080, 1313901405496, 4103693798407, 4103606707223, 9709841473896, 1313941673647], 'label': '512.41229.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.c1'], 'normal_contains': ['8.b1', '8.c1', '8.d1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121870
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.q1', '8.u1', '8.v1', '8.y1'], 'contains': ['32.m1', '32.o1', '32.ch1'], 'core': '64.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [6122, -1, 6113, -1], 'generators': [8396067455999, 2789792426303, 4103606707223, 4103734094783, 1313941673647], 'label': '512.41229.16.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bc1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121871
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.r1', '8.z1'], 'contains': ['32.d1', '32.x1'], 'core': '32.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [9524, -1, 9508, -1], 'generators': [2789792426303, 5606362137576, 4103734094783, 16819055769623, 1313941673647], 'label': '512.41229.16.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bd1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121872
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.i1', '8.w1'], 'contains': ['32.q1', '32.q2', '32.r1', '32.s1', '32.bp1', '32.bp2', '32.ci1', '32.ci2'], 'core': '128.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [1514, -1, 1513, -1], 'generators': [4103693798407, 4103606707223, 4103734094783, 1314028759703, 1313941673647], 'label': '512.41229.16.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121873
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.j1', '8.x1'], 'contains': ['32.s1', '32.t1', '32.u1', '32.v1', '32.w1'], 'core': '128.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [8195, -1, 8182, -1], 'generators': [4103693798407, 4103606707223, 4103734094783, 9709841473896, 1313941673647], 'label': '512.41229.16.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121874
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['8.i1', '8.bb1'], 'contains': ['32.y1', '32.z1', '32.z2', '32.ba1', '32.bp1', '32.bp2', '32.cj1', '32.cj2', '32.cj3'], 'core': '256.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [1190, -1, 1189, -1], 'generators': [4103734078080, 4103693798407, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.16.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121875
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.m1', '8.ba1'], 'contains': ['32.bc1', '32.bf1', '32.bg1', '32.bi1', '32.ck1'], 'core': '128.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [4684, -1, 4677, -1], 'generators': [4103734078080, 2789792426303, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.16.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121877
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.a1', '8.ba1', '8.bb1'], 'contains': ['32.e1', '32.y1', '32.bc1', '32.bd1', '32.bk1', '32.bk3', '32.cl1'], 'core': '32.e1', 'coset_action_label': None, 'count': 16, 'diagramx': [2084, -1, 2081, -1], 'generators': [1313901388807, 4103734078080, 4103693798407, 2789832689280, 1313941673647], 'label': '512.41229.16.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121878
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.bb1'], 'contains': ['32.y1', '32.bc2', '32.bd1', '32.bk2', '32.bk4', '32.cl2'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [1839, -1, 1838, -1], 'generators': [1313901388807, 4103734078080, 2789792426303, 2789832689280, 1313941673647], 'label': '512.41229.16.bj2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bj2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121879
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.p1', '8.bb1'], 'contains': ['32.z1', '32.z2', '32.bc1', '32.bc2', '32.be1', '32.bl1', '32.cm1', '32.cm2'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [2369, -1, 2365, -1], 'generators': [4103734078080, 2789792409600, 4103606707223, 1314028759703, 1313941673647], 'label': '512.41229.16.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bk1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121880
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['8.b1', '8.e1', '8.q1', '8.y1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5303, 6064, 5295, 6177], 'generators': [1313901388807, 4103734078080, 8396067455999, 1313901405496, 4103693798407, 4103606707223, 1313941673647], 'label': '512.41229.4.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['8.b1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121881
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.bb1'], 'contains': ['32.ba1', '32.bd1', '32.be1', '32.bm1', '32.bm2', '32.cn1'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [3432, -1, 3426, -1], 'generators': [1313901388807, 4103734078080, 4103693798407, 4103606707223, 1313941673647], 'label': '512.41229.16.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121882
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '8.ba1'], 'contains': ['32.bb1', '32.bd1', '32.bf1', '32.bh1', '32.bn1', '32.bn2'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [5481, -1, 5473, -1], 'generators': [1313901388807, 4103734078080, 4103693798407, 5606234766719, 1313941673647], 'label': '512.41229.16.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.bm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121883
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.e1', '8.ba1'], 'contains': ['32.bd1', '32.bg1', '32.bo1', '32.bo2'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [3646, -1, 3641, -1], 'generators': [1313901388807, 4103734078080, 2789792426303, 6920263526376, 1313941673647], 'label': '512.41229.16.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.bn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121884
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.s1', '8.ba1'], 'contains': ['32.e1', '32.bi1', '32.bj1', '32.bn1', '32.bo2'], 'core': '32.e1', 'coset_action_label': None, 'count': 32, 'diagramx': [3826, -1, 3820, -1], 'generators': [2789792426303, 2789832689287, 5606234766719, 2789705318423, 1313941673647], 'label': '512.41229.16.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.bo1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bo1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121885
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bo2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.s1', '8.ba1'], 'contains': ['32.bi1', '32.bj1', '32.bk1', '32.bn1', '32.bo2'], 'core': '64.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [3998, -1, 3992, -1], 'generators': [2789792426303, 2789832689287, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.16.bo2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.bo2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bo2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121886
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bo3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.s2', '8.ba1'], 'contains': ['32.bi1', '32.bj1', '32.bk3', '32.bn2', '32.bo1'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [4170, -1, 4164, -1], 'generators': [2789832705976, 2789792426303, 5606234766719, 1314028759703, 1313941673647], 'label': '512.41229.16.bo3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.bo3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bo3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121887
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.w1', '8.bb1'], 'contains': ['32.e1', '32.bk4', '32.bl1', '32.bm1', '32.bp1', '32.co1'], 'core': '32.e1', 'coset_action_label': None, 'count': 32, 'diagramx': [1108, -1, 1107, -1], 'generators': [2789792426303, 4103606707223, 2789832689287, 2789705318423, 1313941673647], 'label': '512.41229.16.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bp1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121888
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.w1', '8.bb1'], 'contains': ['32.bk1', '32.bk4', '32.bl1', '32.bm1', '32.bp2', '32.co2'], 'core': '64.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [1352, -1, 1351, -1], 'generators': [2789792426303, 4103606707223, 2789832689287, 1314028759703, 1313941673647], 'label': '512.41229.16.bp2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bp2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121889
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bp3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.w1', '8.bb1'], 'contains': ['32.bk2', '32.bk3', '32.bl1', '32.bm2', '32.bp1', '32.bp2', '32.co3'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [1027, -1, 1026, -1], 'generators': [4103693798407, 4103606707223, 2789832689287, 1314028759703, 1313941673647], 'label': '512.41229.16.bp3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bp3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp3', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 59121890
    {'ambient': '512.41229', 'aut_centralizer_order': None, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['8.i1', '8.bd1'], 'contains': ['32.bq1', '32.bq2', '32.br1', '32.br3', '32.bs1', '32.ci1', '32.ci2', '32.cj1'], 'core': '128.c1', 'coset_action_label': None, 'count': 128, 'diagramx': [1596, -1, 1594, -1], 'generators': [1313901388807, 1313988485176, 4103693798407, 4103693809943, 1314028759703], 'label': '512.41229.16.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bq1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq1', 'subgroup_fusion': None, 'weyl_group': None}