Abstract group data - 256.5716

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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': [4, 4, 8, 2, 4, 4, 2, 2], 'aut_gens': [[1, 4, 8, 16, 64], [27, 4, 204, 148, 192], [93, 132, 76, 20, 96], [247, 36, 108, 84, 224], [1, 132, 136, 48, 192], [217, 132, 40, 48, 64], [229, 4, 168, 176, 64], [161, 4, 136, 16, 64], [165, 4, 40, 48, 64]], 'aut_group': '4096.bug', 'aut_hash': 9041563242884736525, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 128, 'aut_perms': [10209801455126226492113371517477223071429460961166497297706054706610560609317140210852378600503668116788283641096629182683519032523512406385081050732580818614301284064911757551945752177903673085864829737130496426021, 383155289378035986010028477201151409642975312465792175075167109839837739202758499073225348839440429957501976401079111241398673151219120211811792092229610513663864784684450396366571760315349809700493182112903409856894, 14242569543907620463312395042981547047577488825526867790285600649720713963446140648464829958281426326555468533797157433896338062963711921603659736787679589046646702096162340817675718306802051831047427182403630949786, 192851640894542709742352033638656716523199452390898712326459712737696384068722933019703301012641396102256931629669078840882842068013346249203554379712627558960900938236566111615826703165215943744407314706651910405689, 81595523917160931020780583538163899550977142188338776212157790226778036176424878553174942007839969923044108729138130044728172803823214086486989563410968837954413276050596275992396412049229816438933512111889055823234, 233211357523173218673802656095921038068991317404750225101913399930577531890457354035850293406461934080624660063205528999882995219362098209271979216771094601413127346090312342709466868367133238287575557609831048561172, 193681831479196735392979688488292461362337680216433131303081779625332319745564401056532067961447032146138651756771038925312098421233406779718694682903584855154349666154211838657864309034292655050550416942752706122212, 138075766517794546273258119823818717004890115168850690875544833786801371650384283548285912024579119042677114378715769013176100795703628598026894118758590677320376695341688859632535018203682431079051464163671616790565], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 2, 2, 1], [2, 4, 4, 1], [2, 8, 1, 1], [4, 4, 1, 2], [4, 4, 2, 1], [4, 4, 4, 1], [4, 8, 1, 2], [4, 8, 2, 3], [4, 16, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6.D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '512.301469', 'autcentquo_hash': 8840593593888112679, 'autcentquo_nilpotent': True, 'autcentquo_order': 512, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^5.C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 4, 4], [2, 8, 1], [4, 4, 8], [4, 8, 8], [4, 16, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '128.514', 'commutator_count': 1, 'commutator_label': '16.10', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5716, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 4, 1, 4], [2, 8, 1, 1], [4, 4, 1, 2], [4, 4, 2, 3], [4, 8, 1, 8], [4, 16, 2, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1344, 'exponent': 4, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 0, 2]], 'familial': False, 'frattini_label': '32.46', 'frattini_quotient': '8.5', 'hash': 5716, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [4, 2, 2, 4, 2], 'inner_gens': [[1, 4, 204, 20, 96], [1, 4, 136, 144, 64], [197, 132, 8, 16, 64], [133, 132, 8, 16, 64], [33, 4, 8, 16, 64]], 'inner_hash': 514, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': False, 'inner_tex': 'C_2^4.C_2^3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 12], [4, 4], [8, 2]], 'label': '256.5716', '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': 'C2^4.(C2*D4)', 'ngens': 3, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 34, 'number_divisions': 27, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 171, 'number_subgroup_classes': 357, 'number_subgroups': 1015, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 31], [4, 224]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 58, 0, 32], 'outer_gens': [[1, 4, 136, 16, 64], [57, 132, 76, 52, 224], [3, 4, 136, 16, 96], [181, 36, 236, 244, 64]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [16, 7, 1560, 5887], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [8, 2], [16, 1]], 'representations': {'PC': {'code': 41701280388536636062060357589704273, 'gens': [1, 3, 4, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 16, 6531, 2699, 1107, 804, 1460, 116, 7685, 5382, 5390, 166]}, 'Perm': {'d': 32, 'gens': [152932197174750945594291294277632000, 50974000047308784351309076171336198, 84963054044213327528680006768532993, 76209687101520605238967286053591680, 33988952657421979333956642036350016, 16976205612381906363352243137194303, 1313941673647, 8231691320578226211046411712681647]}}, 'schur_multiplier': [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_2^4.(C_2\\times D_4)', 'transitive_degree': 32, '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: 109465816
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 5716, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 109465827
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 5716, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
  • id: 109465838
    {'aut_label': '2B', 'centralizer': '2.d1', 'counter': 3, 'group_counter': 5716, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 4, 'size': 2}
  • id: 109465844
    {'aut_label': '2B', 'centralizer': '2.d1', 'counter': 4, 'group_counter': 5716, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 36, 'size': 2}
  • id: 109465845
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 5716, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 32, 'size': 2}
  • id: 109465846
    {'aut_label': '2E', 'centralizer': '4.j1', 'counter': 6, 'group_counter': 5716, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 2, 'size': 4}
  • id: 109465847
    {'aut_label': '2E', 'centralizer': '4.j1', 'counter': 7, 'group_counter': 5716, 'group_order': 256, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 38, 'size': 4}
  • id: 109465848
    {'aut_label': '2E', 'centralizer': '4.j1', 'counter': 8, 'group_counter': 5716, 'group_order': 256, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 198, 'size': 4}
  • id: 109465849
    {'aut_label': '2E', 'centralizer': '4.j1', 'counter': 9, 'group_counter': 5716, 'group_order': 256, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 98, 'size': 4}
  • id: 109465817
    {'aut_label': '2I', 'centralizer': '8.bd1', 'counter': 10, 'group_counter': 5716, 'group_order': 256, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 8, 'size': 8}
  • id: 109465818
    {'aut_label': '4A', 'centralizer': '4.e1', 'counter': 11, 'group_counter': 5716, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 64, 'size': 4}
  • id: 109465819
    {'aut_label': '4B', 'centralizer': '4.h1', 'counter': 12, 'group_counter': 5716, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 68, 'size': 4}
  • id: 109465820
    {'aut_label': '4C1', 'centralizer': '4.k1', 'counter': 13, 'group_counter': 5716, 'group_order': 256, 'label': '4C1', 'order': 4, 'powers': [5], 'representative': 16, 'size': 4}
  • id: 109465821
    {'aut_label': '4C1', 'centralizer': '4.k1', 'counter': 14, 'group_counter': 5716, 'group_order': 256, 'label': '4C-1', 'order': 4, 'powers': [5], 'representative': 48, 'size': 4}
  • id: 109465822
    {'aut_label': '4C1', 'centralizer': '4.k1', 'counter': 15, 'group_counter': 5716, 'group_order': 256, 'label': '4D1', 'order': 4, 'powers': [5], 'representative': 80, 'size': 4}
  • id: 109465823
    {'aut_label': '4C1', 'centralizer': '4.k1', 'counter': 16, 'group_counter': 5716, 'group_order': 256, 'label': '4D-1', 'order': 4, 'powers': [5], 'representative': 112, 'size': 4}
  • id: 109465824
    {'aut_label': '4E1', 'centralizer': '4.e1', 'counter': 17, 'group_counter': 5716, 'group_order': 256, 'label': '4E1', 'order': 4, 'powers': [5], 'representative': 24, 'size': 4}
  • id: 109465825
    {'aut_label': '4E1', 'centralizer': '4.e1', 'counter': 18, 'group_counter': 5716, 'group_order': 256, 'label': '4E-1', 'order': 4, 'powers': [5], 'representative': 152, 'size': 4}
  • id: 109465826
    {'aut_label': '4F', 'centralizer': '8.bd1', 'counter': 19, 'group_counter': 5716, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [2], 'representative': 72, 'size': 8}
  • id: 109465828
    {'aut_label': '4G', 'centralizer': '8.ba1', 'counter': 20, 'group_counter': 5716, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [5], 'representative': 18, 'size': 8}
  • id: 109465829
    {'aut_label': '4H', 'centralizer': '8.bm1', 'counter': 21, 'group_counter': 5716, 'group_order': 256, 'label': '4H', 'order': 4, 'powers': [5], 'representative': 10, 'size': 8}
  • id: 109465830
    {'aut_label': '4I', 'centralizer': '8.e1', 'counter': 22, 'group_counter': 5716, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [5], 'representative': 28, 'size': 8}
  • id: 109465831
    {'aut_label': '4G', 'centralizer': '8.ba1', 'counter': 23, 'group_counter': 5716, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [5], 'representative': 82, 'size': 8}
  • id: 109465832
    {'aut_label': '4H', 'centralizer': '8.bm1', 'counter': 24, 'group_counter': 5716, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [5], 'representative': 74, 'size': 8}
  • id: 109465833
    {'aut_label': '4L', 'centralizer': '8.r1', 'counter': 25, 'group_counter': 5716, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [2], 'representative': 26, 'size': 8}
  • id: 109465834
    {'aut_label': '4L', 'centralizer': '8.r1', 'counter': 26, 'group_counter': 5716, 'group_order': 256, 'label': '4M', 'order': 4, 'powers': [2], 'representative': 30, 'size': 8}
  • id: 109465835
    {'aut_label': '4N1', 'centralizer': '16.m1', 'counter': 27, 'group_counter': 5716, 'group_order': 256, 'label': '4N1', 'order': 4, 'powers': [6], 'representative': 1, 'size': 16}
  • id: 109465836
    {'aut_label': '4N1', 'centralizer': '16.m1', 'counter': 28, 'group_counter': 5716, 'group_order': 256, 'label': '4N-1', 'order': 4, 'powers': [6], 'representative': 3, 'size': 16}
  • id: 109465837
    {'aut_label': '4N1', 'centralizer': '16.m1', 'counter': 29, 'group_counter': 5716, 'group_order': 256, 'label': '4O1', 'order': 4, 'powers': [7], 'representative': 17, 'size': 16}
  • id: 109465839
    {'aut_label': '4N1', 'centralizer': '16.m1', 'counter': 30, 'group_counter': 5716, 'group_order': 256, 'label': '4O-1', 'order': 4, 'powers': [7], 'representative': 19, 'size': 16}
  • id: 109465840
    {'aut_label': '4N1', 'centralizer': '16.m1', 'counter': 31, 'group_counter': 5716, 'group_order': 256, 'label': '4P1', 'order': 4, 'powers': [8], 'representative': 9, 'size': 16}
  • id: 109465841
    {'aut_label': '4N1', 'centralizer': '16.m1', 'counter': 32, 'group_counter': 5716, 'group_order': 256, 'label': '4P-1', 'order': 4, 'powers': [8], 'representative': 11, 'size': 16}
  • id: 109465842
    {'aut_label': '4N1', 'centralizer': '16.m1', 'counter': 33, 'group_counter': 5716, 'group_order': 256, 'label': '4Q1', 'order': 4, 'powers': [9], 'representative': 25, 'size': 16}
  • id: 109465843
    {'aut_label': '4N1', 'centralizer': '16.m1', 'counter': 34, 'group_counter': 5716, 'group_order': 256, 'label': '4Q-1', 'order': 4, 'powers': [9], 'representative': 27, 'size': 16}
• 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: 4287809
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1a', '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], 'schur_index': 1}
  • id: 4287820
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1b', '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], 'schur_index': 1}
  • id: 4287829
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1c', '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], 'schur_index': 1}
  • id: 4287830
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1d', '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], 'schur_index': 1}
  • id: 4287831
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1e', '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], 'schur_index': 1}
  • id: 4287832
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1f', '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], 'schur_index': 1}
  • id: 4287833
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1g', '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], 'schur_index': 1}
  • id: 4287834
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1h', '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], 'schur_index': 1}
  • id: 4287835
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1i', '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, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287810
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1j', '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, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287811
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1k', '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, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287812
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.1l', '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, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287813
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287814
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 0, -2, 2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287815
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 2, -2, 0, -2, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287816
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 2, -2, 0, 2, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287817
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, 2, 0, 0, 2, -2, 0, -2, 0, 0, -2, 0, 0, 2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287818
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, 2, 0, 0, 2, -2, 0, 2, 0, 0, 2, 0, 0, -2, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287819
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, 2, -2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287821
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, 2, -2, 2, 0, -2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287822
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2i', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, 2, 2, 0, -2, -2, -2, -2, 0, 2, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287823
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2j', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, 2, 2, 0, 2, -2, -2, 2, 0, -2, -2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287824
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2k', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -2, -2, 0, -2, -2, -2, -2, 0, 2, 2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287825
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.2l', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 2, -2, -2, 2, 0, -2, -2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4287826
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.4a', 'multiplicity': 2, 'nt': [16, 101], 'qdim': 8, 'qvalues': [8, 8, -8, 8, -8, 0, 0, 0, 0, 0, 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: 4287827
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.4b', 'multiplicity': 2, 'nt': [16, 101], 'qdim': 8, 'qvalues': [8, 8, 8, -8, -8, 0, 0, 0, 0, 0, 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: 4287828
    {'cdim': 8, 'counter': 27, 'faithful': True, 'group': '256.5716', 'group_order': 256, 'image': None, 'label': '256.5716.8a', 'multiplicity': 2, 'nt': [32, 6555], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 6373454
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 256, 'label': '256.5716.1a', '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]]]}
  • id: 6373465
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 128, 'label': '256.5716.1b', '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]]]}
  • id: 6373476
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 128, 'label': '256.5716.1c', '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]]]}
  • id: 6373482
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.5716.1d', '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]]]}
  • id: 6373483
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.5716.1e', '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]]]}
  • id: 6373484
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.5716.1f', '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]]]}
  • id: 6373485
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.5716.1g', '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]]]}
  • id: 6373486
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.5716.1h', '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]]]}
  • id: 6373487
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.h1', 'kernel_order': 64, 'label': '256.5716.1i1', '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, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 6373455
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.h1', 'kernel_order': 64, 'label': '256.5716.1i2', '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, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 6373456
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1', 'kernel_order': 64, 'label': '256.5716.1j1', '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, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 6373457
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1', 'kernel_order': 64, 'label': '256.5716.1j2', '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, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 6373458
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1', 'kernel_order': 64, 'label': '256.5716.1k1', '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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 6373459
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1', 'kernel_order': 64, 'label': '256.5716.1k2', '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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 6373460
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1', 'kernel_order': 64, 'label': '256.5716.1l1', '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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 6373461
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1', 'kernel_order': 64, 'label': '256.5716.1l2', '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 6373462
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.l1', 'kernel_order': 32, 'label': '256.5716.2a', '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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373463
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.5716.2b', '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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373464
    {'center': '4.c1', 'center_index': 4, 'center_order': 64, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.k1', 'kernel_order': 32, 'label': '256.5716.2c', '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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373466
    {'center': '4.c1', 'center_index': 4, 'center_order': 64, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.j1', 'kernel_order': 32, 'label': '256.5716.2d', '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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373467
    {'center': '4.c1', 'center_index': 4, 'center_order': 64, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.k1', 'kernel_order': 32, 'label': '256.5716.2e', '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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373468
    {'center': '4.c1', 'center_index': 4, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.j1', 'kernel_order': 32, 'label': '256.5716.2f', '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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373469
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.l1', 'kernel_order': 32, 'label': '256.5716.2g', '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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373470
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.5716.2h', '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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373471
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.5716.2i', '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373472
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.5716.2j', '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]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373473
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.5716.2k', '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373474
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.5716.2l', '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]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373475
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 29, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '64.91', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1', 'kernel_order': 4, 'label': '256.5716.4a1', 'nt': [16, 101], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 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]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373477
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 30, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '64.91', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1', 'kernel_order': 4, 'label': '256.5716.4a2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 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]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373478
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 31, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '64.91', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1', 'kernel_order': 4, 'label': '256.5716.4b1', 'nt': [16, 101], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[0, 0]], [[0, 0]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373479
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 32, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '64.91', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1', 'kernel_order': 4, 'label': '256.5716.4b2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[0, 0]], [[0, 0]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373480
    {'center': '128.a1', 'center_index': 128, 'center_order': 2, 'counter': 33, 'cyclotomic_n': 4, 'dim': 8, 'faithful': True, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '256.5716', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1', 'kernel_order': 1, 'label': '256.5716.8a1', 'nt': [32, 6555], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[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, 1]], [[0, 0]], [[0, 0]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6373481
    {'center': '128.a1', 'center_index': 128, 'center_order': 2, 'counter': 34, 'cyclotomic_n': 4, 'dim': 8, 'faithful': True, 'field': [1, 0, 1], 'group': '256.5716', 'group_counter': 5716, 'group_order': 256, 'image': None, 'image_isoclass': '256.5716', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1', 'kernel_order': 1, 'label': '256.5716.8a2', 'nt': [32, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[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, 1]], [[0, 0]], [[0, 0]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 64589611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.5716.1.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': '256.5716', 'subgroup_hash': 5716, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 2}
  • id: 64589694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.2.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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.2242', 'subgroup_hash': 2242, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64589705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.2.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.859', 'subgroup_hash': 859, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.2.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': '128.560', 'subgroup_hash': 560, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64589727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.857', 'subgroup_hash': 857, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.4.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': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.4.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': ['U1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.199', 'subgroup_hash': 199, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.4.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': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.207', 'subgroup_hash': 207, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.4.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.198', 'subgroup_hash': 198, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.4.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': '4.1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.217', 'subgroup_hash': 217, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.200', 'subgroup_hash': 200, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.214', 'subgroup_hash': 214, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.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': '64.232', 'subgroup_hash': 232, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.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': '64.23', 'subgroup_hash': 23, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.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': '64.210', 'subgroup_hash': 210, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.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': '64.223', 'subgroup_hash': 223, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.240', 'subgroup_hash': 240, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.237', 'subgroup_hash': 237, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.4.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.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': '8.3', '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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.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': '8.5', '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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.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': '8.2', '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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.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': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.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': '8.2', '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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.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': '8.2', '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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.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': '8.2', '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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1', '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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1', '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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1', '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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1', '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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.t2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t2', 'outer_equivalence': True, 'perfect': False, '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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.u2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u2', 'outer_equivalence': True, 'perfect': False, '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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.w2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.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': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.8.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.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': '16.11', '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 64589750
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.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': '16.10', '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.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': '16.3', '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.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': '16.11', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.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': '16.11', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.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': '16.3', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1', '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1', '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1', '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.l1', '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589762
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.m2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64589766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589770
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589614
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589619
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bo2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.16.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.32.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': '32.22', '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'], '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: 64589632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.32.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': '32.27', '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64589633
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589635
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1', '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64589637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589640
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64589641
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589642
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589643
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589644
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589646
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589647
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589649
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589652
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589658
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64589660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589662
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589663
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.32.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64589665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.91', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 91, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.C_2^3', '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: 64589666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5716.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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', 'C6'], '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: 64589668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589670
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 152, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589671
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589672
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589673
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 155, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.64.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589675
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.64.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.64.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589677
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5716.64.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64589679
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589680
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589681
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589682
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589683
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 164, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589684
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.64.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64589685
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 166, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5716.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.514', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 514, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4.C_2^3', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'S', 'U3', 'L3', 'C7'], '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: 64589686
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, '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: 64589687
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.128.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, '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: 64589688
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.128.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 64589690
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5716.128.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 64589691
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5716', 'ambient_counter': 5716, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 171, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.5716.256.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '256.5716', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5716, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4.(C_2\\times D_4)', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U4', 'L4', 'D2', 'C8'], '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: 64589679
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.j1', '32.bc1', '32.bd1'], 'contains': ['128.c1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3200, -1, 3185, -1], 'generators': [16], 'label': '256.5716.64.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1', 'old_label': '64.m1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589680
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1', '32.ba1', '32.bd1'], 'contains': ['128.c1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1812, -1, 1804, -1], 'generators': [24], 'label': '256.5716.64.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '64.n1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589681
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.m1', '32.bc1', '32.be1'], 'contains': ['128.c1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3476, -1, 3461, -1], 'generators': [18], 'label': '256.5716.64.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.q1', 'old_label': '64.o1', 'projective_image': '256.5716', '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': '2.1'}
  • id: 64589682
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.n1', '32.bb1', '32.be1'], 'contains': ['128.c1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4721, -1, 4700, -1], 'generators': [170], 'label': '256.5716.64.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1', 'old_label': '64.p1', 'projective_image': '256.5716', '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': '2.1'}
  • id: 64589683
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1', '32.ba1', '32.be1'], 'contains': ['128.c1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2539, -1, 2527, -1], 'generators': [92], 'label': '256.5716.64.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '64.q1', 'projective_image': '256.5716', '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': '2.1'}
  • id: 64589684
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.q1', '32.y1'], 'contains': ['128.d1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [9224, -1, 9186, -1], 'generators': [1], 'label': '256.5716.64.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.m1', 'old_label': '64.r1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589611
    {'ambient': '256.5716', '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': ['256.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8482, 4443, 8447, 4508], 'generators': [1, 8, 16], 'label': '256.5716.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '128.514', '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': '128.514'}
  • id: 64589612
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.16429', 'aut_weyl_index': 16, 'centralizer': '16.h1', 'complements': ['64.r1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.c1', '8.d1', '8.e1', '8.p1', '8.bd1', '8.be1', '8.bg1', '8.bl1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [1224, 8256, 1219, 8387], 'generators': [8, 16, 68, 192], 'label': '256.5716.4.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.c1', '8.d1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '128.514', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 64589613
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.q1', '8.t1', '8.t2', '8.u1', '8.u2', '8.bf1', '8.bh1'], 'contains': ['32.i1', '32.m1', '32.p1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [4504, -1, 4483, -1], 'generators': [8, 18], 'label': '256.5716.16.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bd1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589614
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '8.y1', '8.bd1', '8.be1', '8.bi1'], 'contains': ['32.c1', '32.j1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [3586, -1, 3570, -1], 'generators': [16, 192], 'label': '256.5716.16.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.be1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589615
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '8.y1', '8.bf1', '8.bj1', '8.bk1'], 'contains': ['32.c1', '32.m1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [4338, -1, 4318, -1], 'generators': [18, 192], 'label': '256.5716.16.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bf1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589616
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '8.x1', '8.bi1', '8.bj1', '8.bk1'], 'contains': ['32.c1', '32.n1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [4851, -1, 4830, -1], 'generators': [170, 192], 'label': '256.5716.16.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bg1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589617
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '8.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '8.ba1', '8.bg1', '8.bl1', '8.bm1'], 'contains': ['32.d1', '32.j1'], 'core': '32.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3726, -1, 3709, -1], 'generators': [16, 68], 'label': '256.5716.16.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bh1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589618
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '8.bb1', '8.bg1', '8.bl1', '8.bn1'], 'contains': ['32.d1', '32.k1', '32.o1'], 'core': '32.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [1708, -1, 1700, -1], 'generators': [24, 68], 'label': '256.5716.16.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bi1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589619
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '8.ba1', '8.bh1', '8.bn1', '8.bo1'], 'contains': ['32.d1', '32.m1'], 'core': '32.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [5908, -1, 5883, -1], 'generators': [18, 68], 'label': '256.5716.16.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bj1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589620
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '16.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1', '8.bb1', '8.bh1', '8.bm1', '8.bo1'], 'contains': ['32.d1', '32.p1', '32.x1'], 'core': '32.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [7992, -1, 7958, -1], 'generators': [186, 68, 160], 'label': '256.5716.16.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bk1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589621
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.p1', '8.v1', '8.v2', '8.bd1', '8.bl1'], 'contains': ['32.j1', '32.k1', '32.l1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1444, -1, 1437, -1], 'generators': [200, 16], 'label': '256.5716.16.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bl1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589622
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.p1', '8.w1', '8.w2', '8.be1', '8.bl1'], 'contains': ['32.j1', '32.l1', '32.o1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2548, -1, 2536, -1], 'generators': [140, 16], 'label': '256.5716.16.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bm1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589623
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.b1', 'complements': ['64.r1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.c1', '8.f1', '8.h1', '8.q1', '8.bf1', '8.bh1', '8.bo1'], 'core': '4.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [6956, 7215, 6928, 7331], 'generators': [8, 18, 68, 192], 'label': '256.5716.4.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.c1', '8.f1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '128.514', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 64589624
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bn1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.r1', '8.t1', '8.u2', '8.v1', '8.w2', '8.bi1', '8.bm1'], 'contains': ['32.j1', '32.n1', '32.p1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3866, -1, 3849, -1], 'generators': [170, 16], 'label': '256.5716.16.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bn1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589625
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.bn2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bn2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.r1', '8.t2', '8.u1', '8.v2', '8.w1', '8.bi1', '8.bm1'], 'contains': ['32.j1', '32.n1', '32.p1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [4006, -1, 3988, -1], 'generators': [110, 16], 'label': '256.5716.16.bn2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bn2', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64589626
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.s1', '8.t1', '8.v2', '8.bj1', '8.bn1'], 'contains': ['32.k1', '32.m1', '32.n1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1848, -1, 1839, -1], 'generators': [170, 18], 'label': '256.5716.16.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bo1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589627
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bo2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.s1', '8.t2', '8.v1', '8.bj1', '8.bn1'], 'contains': ['32.k1', '32.m1', '32.n1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1997, -1, 1986, -1], 'generators': [106, 18], 'label': '256.5716.16.bo2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bo2', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589628
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.q1', '8.v1', '8.v2', '8.w1', '8.w2', '8.bf1', '8.bo1'], 'contains': ['32.l1', '32.m1', '32.p1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5403, -1, 5379, -1], 'generators': [200, 18], 'label': '256.5716.16.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bp1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589629
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.s1', '8.u1', '8.w2', '8.bk1', '8.bn1'], 'contains': ['32.m1', '32.n1', '32.o1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2696, -1, 2684, -1], 'generators': [110, 18], 'label': '256.5716.16.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bq1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589630
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bq2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.s1', '8.u2', '8.w1', '8.bk1', '8.bn1'], 'contains': ['32.m1', '32.n1', '32.o1', '32.be1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2363, -1, 2352, -1], 'generators': [46, 18, 128], 'label': '256.5716.16.bq2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bq2', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589631
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '32.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.q1', '16.r1', '16.s1', '16.t1'], 'contains': ['64.a1', '64.b1', '64.j1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5356, 2624, 5333, 2667], 'generators': [4, 160, 128], 'label': '256.5716.32.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1', '16.d1'], 'normal_contains': ['64.a1', '64.b1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '128.514', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64589632
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '32.b1', 'aut_quo_index': 48, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '16.e1', '16.f1', '16.u1', '16.v1', '16.v2', '16.w1', '16.x1', '16.y1', '16.z1'], 'contains': ['64.b1', '64.c1', '64.k1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5926, 3210, 5900, 3261], 'generators': [2, 160, 128], 'label': '256.5716.32.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.e1', '16.f1'], 'normal_contains': ['64.b1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '128.514', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64589633
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '4.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.e1', '16.h1', '16.i1', '16.j1', '16.ba1', '16.be1', '16.bf1', '16.bg1'], 'contains': ['64.b1', '64.e1'], 'core': '32.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5531, 4148, 5508, 4214], 'generators': [192, 160], 'label': '256.5716.32.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': ['16.b1', '16.e1', '16.h1', '16.i1', '16.j1'], 'normal_contains': ['64.b1'], 'normalizer': '1.a1', 'old_label': '32.c1', 'projective_image': '128.514', 'quotient_action_image': '4.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64589634
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.b1', 'complements': ['64.r1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.d1', '8.g1', '8.h1', '8.r1', '8.bi1', '8.bm1'], 'core': '4.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [5403, 6085, 5381, 6182], 'generators': [170, 16, 68, 192], 'label': '256.5716.4.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.d1', '8.g1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '128.514', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 64589635
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '32.d1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '4.h1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.f1', '16.g1', '16.k1', '16.l1', '16.bh1', '16.bi1', '16.bj1', '16.bk1'], 'contains': ['64.b1', '64.f1'], 'core': '32.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6677, 7863, 6649, 7989], 'generators': [68, 160], 'label': '256.5716.32.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': ['16.b1', '16.f1', '16.g1', '16.k1', '16.l1'], 'normal_contains': ['64.b1'], 'normalizer': '1.a1', 'old_label': '32.d1', 'projective_image': '128.514', 'quotient_action_image': '4.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64589636
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '16.m1', '16.m2', '16.n1'], 'contains': ['64.a1', '64.c1', '64.i1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8452, -1, 8417, -1], 'generators': [2, 4, 128], 'label': '256.5716.32.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.e1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589637
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.o1', '16.q1'], 'contains': ['64.a1', '64.d1', '64.g1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6976, -1, 6947, -1], 'generators': [8, 4], 'label': '256.5716.32.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '32.f1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589638
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '16.n1', '16.o1', '16.p1'], 'contains': ['64.a1', '64.e1', '64.f1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8045, -1, 8011, -1], 'generators': [68, 96], 'label': '256.5716.32.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.g1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589639
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.p1', '16.t1'], 'contains': ['64.a1', '64.h1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7479, -1, 7447, -1], 'generators': [186, 4], 'label': '256.5716.32.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.h1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589640
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '16.q1', '16.u1', '16.ba1', '16.bb1', '16.bc1', '16.bd1'], 'contains': ['64.b1', '64.d1', '64.l1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5005, -1, 4984, -1], 'generators': [8, 160, 128], 'label': '256.5716.32.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.i1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589641
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '16.v1', '16.v2', '16.bb1', '16.bc1', '16.be1', '16.bh1', '16.bl1', '16.bm1', '16.bn1', '16.bn2'], 'contains': ['64.b1', '64.m1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3338, -1, 3323, -1], 'generators': [16, 128], 'label': '256.5716.32.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.j1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589642
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1', '16.r1', '16.w1', '16.bb1', '16.bi1', '16.bl1', '16.bo1', '16.bo2'], 'contains': ['64.b1', '64.n1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1922, -1, 1913, -1], 'generators': [24, 128], 'label': '256.5716.32.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.k1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589643
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1', '16.q1', '16.x1', '16.ba1', '16.bl1', '16.bm1', '16.bp1'], 'contains': ['64.b1', '64.g1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5180, -1, 5158, -1], 'generators': [200, 160], 'label': '256.5716.32.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.l1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589644
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.v1', '16.v2', '16.bd1', '16.bf1', '16.bj1', '16.bo1', '16.bo2', '16.bp1', '16.bq1', '16.bq2'], 'contains': ['64.b1', '64.o1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3557, -1, 3541, -1], 'generators': [18, 128], 'label': '256.5716.32.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.m1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589645
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '4.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.6344809', 'aut_weyl_index': 8, 'centralizer': '32.d1', 'complements': ['64.r1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.e1', '8.f1', '8.g1', '8.s1', '8.bj1', '8.bk1', '8.bn1'], 'core': '4.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [1829, 4959, 1821, 5039], 'generators': [170, 18, 68, 192], 'label': '256.5716.4.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.e1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '128.514', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '32.22'}
  • id: 64589646
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.l1', '16.s1', '16.u1', '16.x1', '16.bg1', '16.bn1', '16.bn2', '16.bo1', '16.bo2', '16.bq1', '16.bq2'], 'contains': ['64.b1', '64.p1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4685, -1, 4665, -1], 'generators': [170, 128], 'label': '256.5716.32.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.n1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589647
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1', '16.r1', '16.y1', '16.bc1', '16.bi1', '16.bm1', '16.bq1', '16.bq2'], 'contains': ['64.b1', '64.q1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2622, -1, 2610, -1], 'generators': [92, 128], 'label': '256.5716.32.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.o1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589648
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.j1', '16.t1', '16.w1', '16.y1', '16.bd1', '16.bk1', '16.bn1', '16.bn2', '16.bp1'], 'contains': ['64.b1', '64.h1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5750, -1, 5726, -1], 'generators': [186, 160], 'label': '256.5716.32.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.p1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589649
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.m1', '16.m2', '16.z1'], 'contains': ['64.c1', '64.r1'], 'core': '128.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [9224, -1, 9186, -1], 'generators': [1, 128], 'label': '256.5716.32.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.o1', 'old_label': '32.q1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589650
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '16.n1'], 'contains': ['64.c1', '64.e1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8212, -1, 8178, -1], 'generators': [2, 96], 'label': '256.5716.32.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.r1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589651
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '16.n1'], 'contains': ['64.c1', '64.f1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8328, -1, 8293, -1], 'generators': [2, 68], 'label': '256.5716.32.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.s1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589652
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.o1', '16.ba1'], 'contains': ['64.d1', '64.e1', '64.g1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7144, -1, 7114, -1], 'generators': [8, 96], 'label': '256.5716.32.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '32.t1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589653
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '16.o1'], 'contains': ['64.d1', '64.f1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7311, -1, 7280, -1], 'generators': [8, 68], 'label': '256.5716.32.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '32.u1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589654
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.j1', '16.p1'], 'contains': ['64.e1', '64.h1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7646, -1, 7614, -1], 'generators': [186, 96], 'label': '256.5716.32.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.v1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589655
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1', '16.o1'], 'contains': ['64.f1', '64.g1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7762, -1, 7729, -1], 'generators': [200, 68], 'label': '256.5716.32.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '32.w1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589656
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 32, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.m1', '8.n1', '8.p1', '8.q1', '8.r1', '8.s1', '8.t1', '8.t2', '8.u1', '8.u2', '8.v1', '8.v2', '8.w1', '8.w2'], 'core': '8.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3256, -1, 3243, -1], 'generators': [8, 16, 2, 4], 'label': '256.5716.4.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.i1', 'projective_image': '128.514', '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': '32.51'}
  • id: 64589657
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.p1', '16.bk1'], 'contains': ['64.f1', '64.h1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7878, -1, 7844, -1], 'generators': [186, 68], 'label': '256.5716.32.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.x1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589658
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.m1'], 'contains': ['64.i1', '64.r1'], 'core': '256.a1', 'coset_action_label': '32T7453', 'count': 64, 'diagramx': [9443, -1, 9404, -1], 'generators': [1, 4], 'label': '256.5716.32.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.m1', 'old_label': '32.y1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589659
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.1', 'aut_weyl_index': 1024, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1'], 'contains': ['64.i1', '64.j1', '64.k1'], 'core': '256.a1', 'coset_action_label': '32T9262', 'count': 16, 'diagramx': [6852, -1, 6823, -1], 'generators': [2, 4, 160], 'label': '256.5716.32.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1', 'old_label': '32.z1', 'projective_image': '256.5716', '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': '2.1'}
  • id: 64589660
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1'], 'contains': ['64.j1', '64.n1', '64.q1'], 'core': '256.a1', 'coset_action_label': '32T7789', 'count': 8, 'diagramx': [1703, -1, 1695, -1], 'generators': [24, 4], 'label': '256.5716.32.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '32.ba1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589661
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.u1'], 'contains': ['64.k1', '64.l1', '64.p1'], 'core': '256.a1', 'coset_action_label': '32T8780', 'count': 32, 'diagramx': [4881, -1, 4860, -1], 'generators': [8, 2], 'label': '256.5716.32.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.t1', 'old_label': '32.bb1', 'projective_image': '256.5716', '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': '4.2'}
  • id: 64589662
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.v1'], 'contains': ['64.k1', '64.m1', '64.o1'], 'core': '256.a1', 'coset_action_label': '32T8577', 'count': 32, 'diagramx': [3119, -1, 3105, -1], 'generators': [16, 2], 'label': '256.5716.32.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.v1', 'old_label': '32.bc1', 'projective_image': '256.5716', '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': '2.1'}
  • id: 64589663
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bb1'], 'contains': ['64.l1', '64.m1', '64.n1'], 'core': '256.a1', 'coset_action_label': '32T6557', 'count': 16, 'diagramx': [1485, -1, 1477, -1], 'generators': [8, 16], 'label': '256.5716.32.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bd1', 'old_label': '32.bd1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589664
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bq2'], 'contains': ['64.o1', '64.p1', '64.q1'], 'core': '256.a1', 'coset_action_label': '32T6555', 'count': 16, 'diagramx': [2455, -1, 2443, -1], 'generators': [46, 18], 'label': '256.5716.32.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bn1', 'old_label': '32.be1', 'projective_image': '256.5716', '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': '4.2'}
  • id: 64589665
    {'ambient': '256.5716', 'aut_centralizer_order': 1024, 'aut_label': '64.a1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '32.e1', '32.f1', '32.g1', '32.h1'], 'contains': ['128.a1', '128.b1'], 'core': '64.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7490, 2704, 7480, 2707], 'generators': [4, 128], 'label': '256.5716.64.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '128.514', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.6', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64589666
    {'ambient': '256.5716', 'aut_centralizer_order': 2048, 'aut_label': '64.b1', 'aut_quo_index': 192, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.b1', '32.c1', '32.d1', '32.i1', '32.j1', '32.k1', '32.l1', '32.m1', '32.n1', '32.o1', '32.p1'], 'contains': ['128.a1', '128.c1'], 'core': '64.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5097, 3210, 5075, 3261], 'generators': [160, 128], 'label': '256.5716.64.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': ['32.a1', '32.b1', '32.c1', '32.d1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.b1', 'projective_image': '128.514', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64589667
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 32, 'centralizer': '64.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1'], 'contains': ['8.a1', '8.o1'], 'core': '8.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8347, -1, 8314, -1], 'generators': [1, 16], 'label': '256.5716.4.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': '128.514', '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': '32.30'}
  • id: 64589668
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.b1', '32.e1', '32.q1', '32.r1', '32.s1'], 'contains': ['128.a1', '128.d1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8212, -1, 8178, -1], 'generators': [2, 128], 'label': '256.5716.64.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '64.c1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589669
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1', '32.i1', '32.t1', '32.u1'], 'contains': ['128.a1', '128.e1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7082, -1, 7053, -1], 'generators': [8, 128], 'label': '256.5716.64.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '64.d1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589670
    {'ambient': '256.5716', 'aut_centralizer_order': 1024, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1', '32.g1', '32.r1', '32.t1', '32.v1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7625, -1, 7610, -1], 'generators': [96], 'label': '256.5716.64.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.e1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589671
    {'ambient': '256.5716', 'aut_centralizer_order': 1024, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1', '32.g1', '32.s1', '32.u1', '32.w1', '32.x1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7762, -1, 7729, -1], 'generators': [68], 'label': '256.5716.64.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.f1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589672
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1', '32.l1', '32.t1', '32.w1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7206, -1, 7176, -1], 'generators': [200], 'label': '256.5716.64.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '64.g1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589673
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.h1', '32.p1', '32.v1', '32.x1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7366, -1, 7357, -1], 'generators': [186], 'label': '256.5716.64.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '64.h1', 'projective_image': '128.514', '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': '2.1'}
  • id: 64589674
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.e1', '32.y1', '32.z1'], 'contains': ['128.b1', '128.d1'], 'core': '256.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [8344, -1, 8309, -1], 'generators': [2, 4], 'label': '256.5716.64.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.o1', 'old_label': '64.i1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589675
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.z1', '32.ba1'], 'contains': ['128.b1', '128.c1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5356, -1, 5333, -1], 'generators': [4, 160], 'label': '256.5716.64.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.j1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589676
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.b1', '32.z1', '32.bb1', '32.bc1'], 'contains': ['128.c1', '128.d1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5707, -1, 5682, -1], 'generators': [2, 160], 'label': '256.5716.64.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '64.k1', 'projective_image': '256.5716', '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': '2.1'}
  • id: 64589677
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.i1', '32.bb1', '32.bd1'], 'contains': ['128.c1', '128.e1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4881, -1, 4860, -1], 'generators': [8, 160], 'label': '256.5716.64.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1', 'old_label': '64.l1', 'projective_image': '256.5716', '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': '2.1'}
  • id: 64589678
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 16, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.j1', '8.t1', '8.t2', '8.v1', '8.v2', '8.x1', '8.y1', '8.bd1', '8.bf1', '8.bi1', '8.bj1'], 'core': '8.j1', 'coset_action_label': None, 'count': 4, 'diagramx': [3582, -1, 3567, -1], 'generators': [8, 16, 2, 192], 'label': '256.5716.4.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': '128.514', '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': '16.14'}
  • id: 64589685
    {'ambient': '256.5716', 'aut_centralizer_order': 4096, 'aut_label': '128.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.c1', '64.d1', '64.e1', '64.f1', '64.g1', '64.h1'], 'contains': ['256.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7369, 2977, 7359, 2944], 'generators': [128], 'label': '256.5716.128.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1', 'normal_contained_in': ['64.a1', '64.b1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.a1', 'projective_image': '128.514', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.514', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64589686
    {'ambient': '256.5716', 'aut_centralizer_order': 1024, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '64.i1', '64.j1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7488, -1, 7477, -1], 'generators': [4], 'label': '256.5716.128.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '128.b1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589687
    {'ambient': '256.5716', 'aut_centralizer_order': 2048, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1', '64.j1', '64.k1', '64.l1', '64.m1', '64.n1', '64.o1', '64.p1', '64.q1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4800, -1, 4780, -1], 'generators': [160], 'label': '256.5716.128.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '128.c1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589688
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '4.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.c1', '64.i1', '64.k1', '64.r1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8212, -1, 8178, -1], 'generators': [2], 'label': '256.5716.128.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '128.d1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589689
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.k1', '8.u1', '8.u2', '8.w1', '8.w2', '8.x1', '8.y1', '8.be1', '8.bf1', '8.bi1', '8.bk1'], 'core': '8.k1', 'coset_action_label': None, 'count': 4, 'diagramx': [4392, -1, 4375, -1], 'generators': [204, 16, 2, 192], 'label': '256.5716.4.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.l1', 'projective_image': '128.514', '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': '32.51'}
  • id: 64589690
    {'ambient': '256.5716', 'aut_centralizer_order': 512, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1', '64.l1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7082, -1, 7053, -1], 'generators': [8], 'label': '256.5716.128.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bd1', 'old_label': '128.e1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589691
    {'ambient': '256.5716', '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': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1', '128.b1', '128.c1', '128.d1', '128.e1'], 'contains': [], 'core': '256.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7369, 2977, 7359, 2944], 'generators': [], 'label': '256.5716.256.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1', 'normal_contained_in': ['128.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '256.a1', 'projective_image': '256.5716', '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': '1.1'}
  • id: 64589692
    {'ambient': '256.5716', 'aut_centralizer_order': 2, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '512.10493082', 'aut_weyl_index': 8, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.i1', '8.t1', '8.t2', '8.u1', '8.u2', '8.ba1', '8.bb1', '8.bg1', '8.bh1', '8.bm1', '8.bn1'], 'core': '8.i1', 'coset_action_label': None, 'count': 4, 'diagramx': [3849, -1, 3833, -1], 'generators': [8, 16, 2, 68], 'label': '256.5716.4.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.m1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64589693
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 16, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['8.i1', '8.bc1'], 'core': '8.i1', 'coset_action_label': None, 'count': 4, 'diagramx': [9019, -1, 8982, -1], 'generators': [1, 8], 'label': '256.5716.4.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.n1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 64589694
    {'ambient': '256.5716', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '64.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.e1', '4.f1', '4.g1', '4.h1', '4.i1', '4.k1', '4.l1', '4.m1', '4.q1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4392, 4959, 4375, 5039], 'generators': [8, 16, 2, 192, 68], 'label': '256.5716.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.e1', '4.f1', '4.g1', '4.h1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '128.514', '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': '64.60'}
  • id: 64589695
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 16, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1'], 'contains': ['8.j1', '8.z1'], 'core': '8.j1', 'coset_action_label': None, 'count': 4, 'diagramx': [8580, -1, 8545, -1], 'generators': [1, 24], 'label': '256.5716.4.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '4.o1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64589696
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 16, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1'], 'contains': ['8.k1', '8.z1'], 'core': '8.k1', 'coset_action_label': None, 'count': 4, 'diagramx': [8811, -1, 8776, -1], 'generators': [69, 92], 'label': '256.5716.4.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '4.p1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64589697
    {'ambient': '256.5716', 'aut_centralizer_order': 2, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '512.10493082', 'aut_weyl_index': 8, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.l1', '8.v1', '8.v2', '8.w1', '8.w2', '8.ba1', '8.bb1', '8.bl1', '8.bm1', '8.bn1', '8.bo1'], 'core': '8.l1', 'coset_action_label': None, 'count': 4, 'diagramx': [4117, -1, 4101, -1], 'generators': [200, 16, 2, 68], 'label': '256.5716.4.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.q1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64589698
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 16, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['8.l1', '8.bc1'], 'core': '8.l1', 'coset_action_label': None, 'count': 4, 'diagramx': [9226, -1, 9189, -1], 'generators': [193, 200], 'label': '256.5716.4.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.r1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 64589699
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '64.202', 'aut_weyl_index': 64, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.i1', '4.j1'], 'contains': ['16.a1', '16.c1', '16.d1', '16.v1', '16.v2'], 'core': '8.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4130, 483, 4113, 491], 'generators': [16, 2, 4], 'label': '256.5716.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.a1', '16.c1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '128.514', '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': '32.27'}
  • id: 64589700
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '256.16984', 'aut_weyl_index': 16, 'centralizer': '32.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'contains': ['16.a1', '16.b1', '16.e1', '16.f1', '16.n1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9260, 4528, 9223, 4600], 'generators': [2, 68, 192, 160], 'label': '256.5716.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'normal_contains': ['16.a1', '16.b1', '16.e1', '16.f1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '128.514', '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': '32.22'}
  • id: 64589701
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.753', 'aut_weyl_index': 32, 'centralizer': '16.h1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.e1', '4.f1'], 'contains': ['16.b1', '16.g1', '16.k1', '16.o1', '16.q1', '16.ba1'], 'core': '8.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8595, 8256, 8561, 8387], 'generators': [8, 68, 192, 160], 'label': '256.5716.8.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': ['4.a1', '4.e1', '4.f1'], 'normal_contains': ['16.b1', '16.g1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '128.514', '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': '16.3'}
  • id: 64589702
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.753', 'aut_weyl_index': 32, 'centralizer': '16.h1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.e1', '4.g1'], 'contains': ['16.b1', '16.c1', '16.be1', '16.bh1'], 'core': '8.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4865, 3574, 4846, 3631], 'generators': [16, 68, 192], 'label': '256.5716.8.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': ['4.b1', '4.e1', '4.g1'], 'normal_contains': ['16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '128.514', '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': '16.3'}
  • id: 64589703
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 64, 'centralizer': '8.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.e1', '4.h1'], 'contains': ['16.b1', '16.h1', '16.i1', '16.r1', '16.bi1'], 'core': '8.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [585, 5426, 583, 5512], 'generators': [24, 68, 192], 'label': '256.5716.8.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': ['4.c1', '4.e1', '4.h1'], 'normal_contains': ['16.b1', '16.h1', '16.i1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '128.514', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 64589704
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 16, 'centralizer': '32.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.f1', '4.h1'], 'contains': ['16.b1', '16.d1', '16.bf1', '16.bj1'], 'core': '8.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [5876, 2568, 5852, 2609], 'generators': [18, 68, 192], 'label': '256.5716.8.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': ['4.b1', '4.f1', '4.h1'], 'normal_contains': ['16.b1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '128.514', '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': '32.22'}
  • id: 64589705
    {'ambient': '256.5716', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1024.dnl', 'aut_weyl_index': 4, 'centralizer': '128.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.n1', '4.r1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9019, 5909, 8982, 6003], 'generators': [1, 8, 192], 'label': '256.5716.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '128.514', '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': '128.514'}
  • id: 64589706
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 16, 'centralizer': '32.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.g1', '4.h1'], 'contains': ['16.b1', '16.l1', '16.s1', '16.bg1'], 'core': '8.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [6663, 7279, 6636, 7394], 'generators': [170, 68, 192], 'label': '256.5716.8.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': ['4.a1', '4.g1', '4.h1'], 'normal_contains': ['16.b1', '16.l1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '128.514', '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': '32.22'}
  • id: 64589707
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '256.16984', 'aut_weyl_index': 16, 'centralizer': '32.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.f1', '4.g1'], 'contains': ['16.b1', '16.j1', '16.p1', '16.t1', '16.bk1'], 'core': '8.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [9005, 6324, 8969, 6424], 'generators': [186, 68, 192, 160], 'label': '256.5716.8.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': ['4.c1', '4.f1', '4.g1'], 'normal_contains': ['16.b1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': '128.514', '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': '32.22'}
  • id: 64589708
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.i1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.m1', '4.n1'], 'contains': ['16.f1', '16.g1', '16.l1', '16.u1'], 'core': '8.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [8386, 8994, 8352, 9137], 'generators': [8, 2, 68], 'label': '256.5716.8.i1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.f1', '16.g1', '16.l1'], 'normalizer': '1.a1', 'old_label': '8.i1', 'projective_image': '128.514', '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': '64.60'}
  • id: 64589709
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.j1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '16.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.k1', '4.o1'], 'contains': ['16.e1', '16.h1', '16.j1', '16.w1'], 'core': '8.j1', 'coset_action_label': None, 'count': 2, 'diagramx': [7794, 1278, 7763, 1299], 'generators': [24, 2, 192], 'label': '256.5716.8.j1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.j1', 'normal_contained_in': ['4.c1'], 'normal_contains': ['16.e1', '16.h1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.j1', 'projective_image': '128.514', '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': '16.3'}
  • id: 64589710
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.k1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '32.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.l1', '4.p1'], 'contains': ['16.e1', '16.i1', '16.j1', '16.y1'], 'core': '8.k1', 'coset_action_label': None, 'count': 2, 'diagramx': [8238, 1801, 8205, 1830], 'generators': [92, 2, 192], 'label': '256.5716.8.k1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': ['4.c1'], 'normal_contains': ['16.e1', '16.i1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.k1', 'projective_image': '128.514', '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': '32.22'}
  • id: 64589711
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.l1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.q1', '4.r1'], 'contains': ['16.f1', '16.k1', '16.l1', '16.x1'], 'core': '8.l1', 'coset_action_label': None, 'count': 2, 'diagramx': [8805, 9517, 8769, 9668], 'generators': [200, 2, 68], 'label': '256.5716.8.l1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.f1', '16.k1', '16.l1'], 'normalizer': '1.a1', 'old_label': '8.l1', 'projective_image': '128.514', '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': '64.60'}
  • id: 64589712
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.60', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.i1'], 'contains': ['16.a1', '16.q1', '16.s1', '16.u1', '16.x1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7248, -1, 7219, -1], 'generators': [8, 2, 4], 'label': '256.5716.8.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.m1', 'projective_image': '128.514', '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': '32.51'}
  • id: 64589713
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.193', 'aut_weyl_index': 64, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.i1'], 'contains': ['16.a1', '16.r1', '16.t1', '16.w1', '16.y1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6958, -1, 6929, -1], 'generators': [24, 2, 4], 'label': '256.5716.8.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.n1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589714
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.j1'], 'contains': ['16.a1', '16.m1', '16.m2', '16.z1'], 'core': '16.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9904, -1, 9864, -1], 'generators': [1, 4, 160], 'label': '256.5716.8.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.o1', 'projective_image': '128.514', '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': '16.13'}
  • id: 64589715
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '4.i1'], 'contains': ['16.c1', '16.q1', '16.r1', '16.bb1', '16.bc1', '16.bl1', '16.bm1'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [96, -1, 95, -1], 'generators': [8, 16, 4], 'label': '256.5716.8.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.p1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589716
    {'ambient': '256.5716', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '128.a1', 'complements': ['128.e1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.d1', '4.j1'], 'core': '2.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8347, 2909, 8314, 2955], 'generators': [1, 16, 192], 'label': '256.5716.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '128.514', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '128.514'}
  • id: 64589717
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.60', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.f1', '4.i1'], 'contains': ['16.d1', '16.q1', '16.t1', '16.bd1', '16.bp1'], 'core': '16.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [6178, -1, 6153, -1], 'generators': [8, 18, 4], 'label': '256.5716.8.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.q1', 'projective_image': '128.514', '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': '32.51'}
  • id: 64589718
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.202', 'aut_weyl_index': 64, 'centralizer': '32.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.g1', '4.i1'], 'contains': ['16.c1', '16.s1', '16.t1', '16.bn1', '16.bn2'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [5150, -1, 5129, -1], 'generators': [170, 16, 4], 'label': '256.5716.8.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.r1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589719
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.h1', '4.i1'], 'contains': ['16.d1', '16.r1', '16.s1', '16.bo1', '16.bo2', '16.bq1', '16.bq2'], 'core': '16.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [1022, -1, 1019, -1], 'generators': [170, 18, 4], 'label': '256.5716.8.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.s1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589720
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.k1', '4.m1'], 'contains': ['16.u1', '16.v1', '16.w1', '16.bb1', '16.bd1', '16.bn1', '16.bo1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [2249, -1, 2240, -1], 'generators': [8, 16, 2], 'label': '256.5716.8.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.t1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589721
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.t2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.k1', '4.m1'], 'contains': ['16.u1', '16.v2', '16.w1', '16.bb1', '16.bd1', '16.bn2', '16.bo2'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [2519, -1, 2509, -1], 'generators': [204, 212, 2], 'label': '256.5716.8.t2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.t2', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t2', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64589722
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.l1', '4.m1'], 'contains': ['16.u1', '16.v1', '16.y1', '16.bc1', '16.bd1', '16.bn2', '16.bq1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3454, -1, 3440, -1], 'generators': [204, 16, 2], 'label': '256.5716.8.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.u1', 'projective_image': '128.514', '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': '32.51'}
  • id: 64589723
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.u2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.l1', '4.m1'], 'contains': ['16.u1', '16.v2', '16.y1', '16.bc1', '16.bd1', '16.bn1', '16.bq2'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3220, -1, 3208, -1], 'generators': [8, 212, 2], 'label': '256.5716.8.u2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.u2', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64589724
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.k1', '4.q1'], 'contains': ['16.v1', '16.w1', '16.x1', '16.bl1', '16.bn1', '16.bo2', '16.bp1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [2821, -1, 2810, -1], 'generators': [200, 16, 2], 'label': '256.5716.8.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.v1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589725
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.v2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.k1', '4.q1'], 'contains': ['16.v2', '16.w1', '16.x1', '16.bl1', '16.bn2', '16.bo1', '16.bp1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3055, -1, 3043, -1], 'generators': [140, 212, 2], 'label': '256.5716.8.v2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.v2', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v2', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64589726
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.l1', '4.q1'], 'contains': ['16.v1', '16.x1', '16.y1', '16.bm1', '16.bn2', '16.bp1', '16.bq2'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3705, -1, 3690, -1], 'generators': [140, 16, 2], 'label': '256.5716.8.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.w1', 'projective_image': '128.514', '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': '32.51'}
  • id: 64589727
    {'ambient': '256.5716', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1024.dnj', 'aut_weyl_index': 4, 'centralizer': '64.a1', 'complements': ['128.e1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '4.o1', '4.p1'], 'core': '2.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [8616, 3920, 8582, 3983], 'generators': [1, 24, 68], 'label': '256.5716.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '128.514', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '64.91'}
  • id: 64589728
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.w2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.l1', '4.q1'], 'contains': ['16.v2', '16.x1', '16.y1', '16.bm1', '16.bn1', '16.bp1', '16.bq1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3887, -1, 3871, -1], 'generators': [200, 212, 2], 'label': '256.5716.8.w2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.w2', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64589729
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.k1', '4.l1'], 'contains': ['16.e1', '16.u1', '16.x1', '16.ba1', '16.bg1'], 'core': '16.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [7481, -1, 7450, -1], 'generators': [8, 2, 192], 'label': '256.5716.8.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.x1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589730
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.k1', '4.l1'], 'contains': ['16.e1', '16.v1', '16.v2', '16.be1', '16.bf1'], 'core': '16.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [4392, -1, 4375, -1], 'generators': [16, 2, 192], 'label': '256.5716.8.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.y1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589731
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.o1', '4.p1'], 'contains': ['16.e1', '16.z1'], 'core': '16.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [9479, -1, 9441, -1], 'generators': [1, 192], 'label': '256.5716.8.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.z1', 'projective_image': '128.514', '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': '32.6'}
  • id: 64589732
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.m1', '4.q1'], 'contains': ['16.f1', '16.v1', '16.v2', '16.bh1', '16.bj1'], 'core': '16.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [4612, -1, 4594, -1], 'generators': [16, 2, 68], 'label': '256.5716.8.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.ba1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589733
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.m1', '4.q1'], 'contains': ['16.f1', '16.w1', '16.y1', '16.bi1', '16.bk1'], 'core': '16.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [7942, -1, 7910, -1], 'generators': [24, 2, 68], 'label': '256.5716.8.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bb1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589734
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.n1', '4.r1'], 'contains': ['16.f1', '16.z1'], 'core': '16.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [9660, -1, 9622, -1], 'generators': [1, 68], 'label': '256.5716.8.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.bc1', 'projective_image': '128.514', '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': '32.6'}
  • id: 64589735
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 64, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '4.k1'], 'contains': ['16.h1', '16.ba1', '16.bb1', '16.be1', '16.bl1'], 'core': '16.h1', 'coset_action_label': None, 'count': 2, 'diagramx': [333, -1, 331, -1], 'generators': [8, 16, 192], 'label': '256.5716.8.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bd1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589736
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '8.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.60', 'aut_weyl_index': 64, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '4.l1'], 'contains': ['16.i1', '16.ba1', '16.bc1', '16.be1', '16.bm1'], 'core': '16.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [1846, -1, 1839, -1], 'generators': [204, 16, 192], 'label': '256.5716.8.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.be1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64589737
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.f1', '4.k1', '4.l1'], 'contains': ['16.j1', '16.ba1', '16.bd1', '16.bf1', '16.bp1'], 'core': '16.j1', 'coset_action_label': None, 'count': 4, 'diagramx': [6430, -1, 6404, -1], 'generators': [8, 18, 192], 'label': '256.5716.8.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bf1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64589738
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.b1', '8.c1', '8.g1', '8.i1', '8.l1', '8.m1', '8.x1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8072, 9295, 8040, 9443], 'generators': [8, 2, 68, 192], 'label': '256.5716.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.b1', '8.c1', '8.g1', '8.i1', '8.l1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '128.514', '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': '64.60'}
  • id: 64589739
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '4.m1'], 'contains': ['16.g1', '16.bb1', '16.bc1', '16.bh1', '16.bi1'], 'core': '16.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [822, -1, 818, -1], 'generators': [8, 16, 68], 'label': '256.5716.8.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bg1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64589740
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '4.m1'], 'contains': ['16.g1', '16.bd1', '16.bj1', '16.bk1'], 'core': '16.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [7646, -1, 7615, -1], 'generators': [8, 18, 68], 'label': '256.5716.8.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bh1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64589741
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.g1', '4.k1', '4.l1'], 'contains': ['16.j1', '16.be1', '16.bg1', '16.bn1', '16.bn2'], 'core': '16.j1', 'coset_action_label': None, 'count': 4, 'diagramx': [5403, -1, 5381, -1], 'generators': [170, 16, 192], 'label': '256.5716.8.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bi1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64589742
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '8.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 64, 'centralizer': '16.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1', '4.k1'], 'contains': ['16.h1', '16.bf1', '16.bg1', '16.bo1', '16.bo2'], 'core': '16.h1', 'coset_action_label': None, 'count': 2, 'diagramx': [1409, -1, 1403, -1], 'generators': [170, 18, 192], 'label': '256.5716.8.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bj1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64589743
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1', '4.l1'], 'contains': ['16.i1', '16.bf1', '16.bg1', '16.bq1', '16.bq2'], 'core': '16.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [2064, -1, 2055, -1], 'generators': [110, 18, 192], 'label': '256.5716.8.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bk1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bk1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64589744
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '4.q1'], 'contains': ['16.k1', '16.bh1', '16.bi1', '16.bl1', '16.bm1'], 'core': '16.k1', 'coset_action_label': None, 'count': 2, 'diagramx': [1224, -1, 1219, -1], 'generators': [200, 16, 68], 'label': '256.5716.8.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bl1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64589745
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.g1', '4.m1', '4.q1'], 'contains': ['16.l1', '16.bh1', '16.bk1', '16.bn1', '16.bn2'], 'core': '16.l1', 'coset_action_label': None, 'count': 4, 'diagramx': [5623, -1, 5601, -1], 'generators': [170, 16, 68], 'label': '256.5716.8.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bm1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64589746
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.h1', '4.m1', '4.q1'], 'contains': ['16.l1', '16.bi1', '16.bj1', '16.bo1', '16.bo2', '16.bq1', '16.bq2'], 'core': '16.l1', 'coset_action_label': None, 'count': 4, 'diagramx': [1594, -1, 1587, -1], 'generators': [170, 18, 68], 'label': '256.5716.8.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bn1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64589747
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '4.q1'], 'contains': ['16.k1', '16.bj1', '16.bk1', '16.bp1'], 'core': '16.k1', 'coset_action_label': None, 'count': 2, 'diagramx': [8089, -1, 8057, -1], 'generators': [200, 18, 68], 'label': '256.5716.8.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bo1', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64589748
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '32.6', 'aut_weyl_index': 128, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.b1', '8.m1', '8.n1', '8.o1'], 'contains': ['32.a1', '32.b1', '32.e1', '32.z1'], 'core': '16.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7815, 2586, 7782, 2626], 'generators': [2, 4, 160, 128], 'label': '256.5716.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['32.a1', '32.b1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '128.514', 'quotient_action_image': '16.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64589749
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.a1', '8.b1', '8.d1', '8.f1', '8.y1', '8.ba1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4766, 1813, 4746, 1841], 'generators': [16, 2, 68, 192], 'label': '256.5716.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.a1', '8.b1', '8.d1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '128.514', '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': '64.60'}
  • id: 64589750
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '16.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '8.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1', '8.h1'], 'contains': ['32.a1', '32.c1', '32.d1', '32.g1'], 'core': '16.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7181, 5767, 7150, 5859], 'generators': [68, 192, 160], 'label': '256.5716.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1', '8.h1'], 'normal_contains': ['32.a1', '32.c1', '32.d1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '128.514', 'quotient_action_image': '8.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 64589751
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '16.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.j1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.d1', '8.p1', '8.r1'], 'contains': ['32.a1', '32.j1'], 'core': '16.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [3428, 2029, 3413, 2061], 'generators': [16, 4], 'label': '256.5716.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.a1', '8.d1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '128.514', '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': '8.3'}
  • id: 64589752
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.f1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.f1', '8.q1', '8.s1'], 'contains': ['32.a1', '32.m1'], 'core': '16.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [4172, 1386, 4153, 1408], 'generators': [18, 4], 'label': '256.5716.16.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': ['8.a1', '8.f1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': '128.514', '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': '16.11'}
  • id: 64589753
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.e1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '16.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.j1', '8.k1', '8.x1', '8.y1', '8.z1'], 'contains': ['32.b1', '32.c1', '32.r1'], 'core': '16.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [8212, 3210, 8178, 3261], 'generators': [2, 192, 160], 'label': '256.5716.16.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': ['8.b1', '8.j1', '8.k1'], 'normal_contains': ['32.b1', '32.c1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': '128.514', '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': '16.3'}
  • id: 64589754
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.f1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.i1', '8.l1', '8.ba1', '8.bb1', '8.bc1'], 'contains': ['32.b1', '32.d1', '32.s1'], 'core': '16.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [8432, 7477, 8397, 7596], 'generators': [2, 68, 160], 'label': '256.5716.16.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': ['8.b1', '8.i1', '8.l1'], 'normal_contains': ['32.b1', '32.d1'], 'normalizer': '1.a1', 'old_label': '16.f1', 'projective_image': '128.514', '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': '16.3'}
  • id: 64589755
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '16.h1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.i1', '8.bg1', '8.bh1'], 'contains': ['32.d1', '32.i1', '32.u1'], 'core': '16.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [6944, 8256, 6915, 8387], 'generators': [8, 68, 160], 'label': '256.5716.16.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': ['8.c1', '8.i1'], 'normal_contains': ['32.d1'], 'normalizer': '1.a1', 'old_label': '16.g1', 'projective_image': '128.514', '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': '16.3'}
  • id: 64589756
    {'ambient': '256.5716', 'aut_centralizer_order': 256, 'aut_label': '16.h1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '4.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '8.j1', '8.bd1', '8.bj1'], 'contains': ['32.c1', '32.k1'], 'core': '16.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [1576, 3835, 1568, 3896], 'generators': [24, 192], 'label': '256.5716.16.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': ['8.e1', '8.j1'], 'normal_contains': ['32.c1'], 'normalizer': '1.a1', 'old_label': '16.h1', 'projective_image': '128.514', 'quotient_action_image': '4.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64589757
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '16.i1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '8.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '8.k1', '8.be1', '8.bk1'], 'contains': ['32.c1', '32.o1'], 'core': '16.i1', 'coset_action_label': None, 'count': 1, 'diagramx': [2836, 5085, 2823, 5166], 'generators': [92, 192], 'label': '256.5716.16.i1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': ['8.e1', '8.k1'], 'normal_contains': ['32.c1'], 'normalizer': '1.a1', 'old_label': '16.i1', 'projective_image': '128.514', 'quotient_action_image': '8.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 64589758
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.j1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '16.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.h1', '8.j1', '8.k1', '8.bf1', '8.bi1'], 'contains': ['32.c1', '32.p1', '32.v1'], 'core': '16.j1', 'coset_action_label': None, 'count': 2, 'diagramx': [7417, 4460, 7386, 4531], 'generators': [186, 192, 160], 'label': '256.5716.16.j1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': ['8.h1', '8.j1', '8.k1'], 'normal_contains': ['32.c1'], 'normalizer': '1.a1', 'old_label': '16.j1', 'projective_image': '128.514', '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': '16.3'}
  • id: 64589759
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.k1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '16.h1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.l1', '8.bl1', '8.bo1'], 'contains': ['32.d1', '32.l1', '32.w1'], 'core': '16.k1', 'coset_action_label': None, 'count': 1, 'diagramx': [7638, 9505, 7606, 9657], 'generators': [200, 68, 160], 'label': '256.5716.16.k1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': ['8.c1', '8.l1'], 'normal_contains': ['32.d1'], 'normalizer': '1.a1', 'old_label': '16.k1', 'projective_image': '128.514', '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': '16.3'}
  • id: 64589760
    {'ambient': '256.5716', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '512.6359056', 'aut_weyl_index': 8, 'centralizer': '32.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.b1', '8.e1', '8.h1', '8.j1', '8.k1', '8.n1', '8.bb1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7777, 3920, 7747, 3983], 'generators': [24, 2, 68, 192], 'label': '256.5716.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.b1', '8.e1', '8.h1', '8.j1', '8.k1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '128.514', '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': '32.22'}
  • id: 64589761
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.l1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.l1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.g1', '8.i1', '8.l1', '8.bm1', '8.bn1'], 'contains': ['32.d1', '32.n1'], 'core': '16.l1', 'coset_action_label': None, 'count': 2, 'diagramx': [6515, 8880, 6487, 9022], 'generators': [170, 68], 'label': '256.5716.16.l1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.l1', 'normal_contained_in': ['8.g1', '8.i1', '8.l1'], 'normal_contains': ['32.d1'], 'normalizer': '1.a1', 'old_label': '16.l1', 'projective_image': '128.514', 'quotient_action_image': '16.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 64589762
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.o1'], 'contains': ['32.e1', '32.q1', '32.y1'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9623, -1, 9583, -1], 'generators': [1, 4, 128], 'label': '256.5716.16.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '16.m1', 'projective_image': '128.514', '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': '4.1'}
  • id: 64589763
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '16.m2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.o1'], 'contains': ['32.e1', '32.q1'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9406, -1, 9367, -1], 'generators': [1, 164], 'label': '256.5716.16.m2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '16.m2', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64589764
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1'], 'contains': ['32.e1', '32.g1', '32.r1', '32.s1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9024, -1, 8985, -1], 'generators': [2, 68, 96], 'label': '256.5716.16.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.n1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589765
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1'], 'contains': ['32.f1', '32.g1', '32.t1', '32.u1', '32.w1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8617, -1, 8582, -1], 'generators': [8, 68, 96], 'label': '256.5716.16.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '16.o1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589766
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.h1'], 'contains': ['32.g1', '32.h1', '32.v1', '32.x1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8803, -1, 8766, -1], 'generators': [186, 68, 96], 'label': '256.5716.16.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '16.p1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589767
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.3', 'aut_weyl_index': 256, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.m1', '8.p1', '8.q1'], 'contains': ['32.a1', '32.f1', '32.i1', '32.l1'], 'core': '32.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6085, -1, 6059, -1], 'generators': [8, 4, 160], 'label': '256.5716.16.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.q1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589768
    {'ambient': '256.5716', 'aut_centralizer_order': 128, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '8.n1', '8.p1', '8.s1'], 'contains': ['32.a1', '32.k1', '32.o1', '32.ba1'], 'core': '32.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1252, -1, 1245, -1], 'generators': [24, 4, 128], 'label': '256.5716.16.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.r1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589769
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '8.m1', '8.r1', '8.s1'], 'contains': ['32.a1', '32.n1'], 'core': '32.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4685, -1, 4665, -1], 'generators': [170, 4], 'label': '256.5716.16.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.s1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589770
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.6', 'aut_weyl_index': 128, 'centralizer': '16.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1', '8.n1', '8.q1', '8.r1'], 'contains': ['32.a1', '32.h1', '32.p1'], 'core': '32.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6708, -1, 6679, -1], 'generators': [186, 4, 160], 'label': '256.5716.16.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.t1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589771
    {'ambient': '256.5716', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 16, 'centralizer': '64.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '2.c1', '2.d1'], 'contains': ['8.b1', '8.o1', '8.z1', '8.bc1'], 'core': '4.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9493, 2909, 9455, 2955], 'generators': [1, 68, 192], 'label': '256.5716.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.c1', '2.d1'], 'normal_contains': ['8.b1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '128.514', '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': '64.91'}
  • id: 64589772
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.i1', '8.m1', '8.t1', '8.t2', '8.u1', '8.u2', '8.x1'], 'contains': ['32.b1', '32.i1', '32.n1', '32.bb1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5218, -1, 5195, -1], 'generators': [8, 2, 128], 'label': '256.5716.16.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.u1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589773
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.t1', '8.u1', '8.v1', '8.w1', '8.y1', '8.ba1'], 'contains': ['32.b1', '32.j1', '32.m1', '32.bc1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3029, -1, 3015, -1], 'generators': [16, 2, 128], 'label': '256.5716.16.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.v1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589774
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.v2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.v2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.t2', '8.u2', '8.v2', '8.w2', '8.y1', '8.ba1'], 'contains': ['32.b1', '32.j1', '32.m1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3246, -1, 3232, -1], 'generators': [212, 2], 'label': '256.5716.16.v2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.v2', 'projective_image': '128.514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64589775
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.j1', '8.n1', '8.t1', '8.t2', '8.v1', '8.v2', '8.bb1'], 'contains': ['32.b1', '32.k1', '32.p1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5016, -1, 4995, -1], 'generators': [24, 2], 'label': '256.5716.16.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.w1', 'projective_image': '128.514', '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': '8.5'}
  • id: 64589776
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.l1', '8.m1', '8.v1', '8.v2', '8.w1', '8.w2', '8.x1'], 'contains': ['32.b1', '32.l1', '32.n1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5568, -1, 5545, -1], 'generators': [200, 2], 'label': '256.5716.16.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.x1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589777
    {'ambient': '256.5716', 'aut_centralizer_order': 32, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.k1', '8.n1', '8.u1', '8.u2', '8.w1', '8.w2', '8.bb1'], 'contains': ['32.b1', '32.o1', '32.p1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5750, -1, 5726, -1], 'generators': [92, 2], 'label': '256.5716.16.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.y1', 'projective_image': '128.514', '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': '16.14'}
  • id: 64589778
    {'ambient': '256.5716', 'aut_centralizer_order': 16, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.o1', '8.z1', '8.bc1'], 'contains': ['32.b1', '32.q1'], 'core': '32.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [9224, -1, 9186, -1], 'generators': [1, 160], 'label': '256.5716.16.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.z1', 'projective_image': '128.514', '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': '8.3'}
  • id: 64589779
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.x1', '8.bd1', '8.be1', '8.bf1'], 'contains': ['32.c1', '32.i1', '32.l1', '32.t1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6321, -1, 6295, -1], 'generators': [8, 192, 160], 'label': '256.5716.16.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.ba1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589780
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.p1', '8.t1', '8.t2', '8.bd1', '8.bg1'], 'contains': ['32.i1', '32.j1', '32.k1', '32.bd1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [999, -1, 993, -1], 'generators': [8, 16, 128], 'label': '256.5716.16.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bb1', 'projective_image': '128.514', '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': '4.2'}
  • id: 64589781
    {'ambient': '256.5716', 'aut_centralizer_order': 64, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.p1', '8.u1', '8.u2', '8.be1', '8.bg1'], 'contains': ['32.i1', '32.j1', '32.o1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2162, -1, 2152, -1], 'generators': [204, 16], 'label': '256.5716.16.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bc1', 'projective_image': '128.514', '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': '8.5'}