Abstract group data - 768.1090187

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 4, 4, 2, 4], 'aut_gens': [[1083180097, 1081547512, 3234148260, 1077385976, 1085736031, 1087431672, 1085758200, 668673292, 1083049080], [1080629953, 1083049080, 3229960413, 1074709624, 1078860511, 1083204600, 1087276152, 963403581, 1081547512], [1080629953, 1079002177, 2153106588, 1080640614, 1076468417, 1083204600, 1081558111, 967974660, 1084840641], [1083180097, 1078860511, 2148922690, 1074698975, 1083049080, 1084842975, 1087298271, 658308085, 1085736031], [1083180097, 1083089793, 3234181443, 1083220920, 1079002177, 1083218598, 1084859295, 658269458, 1087407169], [1087251329, 1081588993, 2152442652, 1080671544, 1078911873, 1076470751, 1078902054, 957069466, 1083089793], [1087251329, 1074840641, 3231402212, 1077396575, 1083089793, 1081596600, 1076479078, 669137676, 1078911873]], 'aut_group': None, 'aut_hash': 8103672493863816722, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 18432, 'aut_permdeg': 52, 'aut_perms': [56107896103203925040113563203387570643472556308666685682405110900353, 55074740819698814438766202097812240381638382115391728060735220744643, 51591250345999768789637557094021936706938633052406135954678678196039, 63354598586234582500454185621666924735154229868808629362054154314621, 4623336147969385926937871961336852817572249800259099515208898995473, 62700773802225051067145944795570526984901090749972714129060444878605], 'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 3, 3, 2], [2, 3, 6, 1], [2, 6, 1, 2], [2, 6, 2, 1], [2, 6, 4, 1], [2, 6, 6, 1], [2, 24, 2, 1], [3, 32, 1, 1], [4, 24, 2, 1], [4, 24, 6, 2], [6, 32, 1, 1], [6, 32, 2, 1], [6, 32, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'A_4^2.C_2^5.C_2^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '576.8654', 'autcentquo_hash': 8654, 'autcentquo_nilpotent': False, 'autcentquo_order': 576, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\POPlus(4,3)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 3, 12], [2, 6, 14], [2, 24, 2], [3, 32, 1], [4, 24, 14], [6, 32, 7]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '192.1538', 'commutator_count': 2, 'commutator_label': '96.229', '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', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1090187, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['384.20100', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 3, 1, 12], [2, 6, 1, 14], [2, 24, 1, 2], [3, 32, 1, 1], [4, 24, 1, 14], [6, 32, 1, 3], [6, 32, 2, 2]], 'element_repr_type': 'GLFq', 'elementary': 1, 'eulerian_function': 5880, 'exponent': 12, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '384.20163', 'hash': 1090187, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 6, 2, 2, 2, 2, 4, 2], 'inner_gens': [[1083180097, 1081547512, 3234148260, 1077385976, 1085736031, 1087431672, 1085758200, 664970539, 1083049080], [1083180097, 1081547512, 3235590045, 1077385976, 1085736031, 1087431672, 1085758200, 660323243, 1083049080], [1083180097, 1078991590, 3234148260, 1087429350, 1083049080, 1085760486, 1074830054, 514442198, 1084818534], [1083180097, 1081547512, 3231428509, 1077385976, 1085736031, 1087431672, 1085758200, 670860011, 1083049080], [1083180097, 1081547512, 3236048826, 1077385976, 1085736031, 1087431672, 1085758200, 670860011, 1083049080], [1083180097, 1081547512, 3227250589, 1077385976, 1085736031, 1087431672, 1085758200, 668673292, 1083049080], [1083180097, 1081547512, 3223023517, 1077385976, 1085736031, 1087431672, 1085758200, 654679147, 1083049080], [1077361921, 1078911873, 2150404828, 1081598886, 1089961217, 1087431672, 1080681375, 668673292, 1085799681], [1083180097, 1081547512, 3235590045, 1077385976, 1085736031, 1087431672, 1085758200, 660323243, 1083049080]], 'inner_hash': 1538, 'inner_nilpotent': False, 'inner_order': 192, 'inner_split': False, 'inner_tex': 'C_2^3:S_4', 'inner_used': [1, 2, 3, 4, 8], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 10], [3, 24], [6, 14]], 'label': '768.1090187', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^3:GL(2,Z/4)', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 56, 'number_divisions': 54, 'number_normal_subgroups': 59, 'number_subgroup_autclasses': 768, 'number_subgroup_classes': 6896, 'number_subgroups': 40588, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 175], [3, 32], [4, 336], [6, 224]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 2, 3], 'outer_gen_pows': [1074791425, 1074791425, 1074791425, 1074791425, 1074791425, 1074791425], 'outer_gens': [[1083180097, 1084840641, 3223023517, 1083202278, 1074840641, 1084842975, 1085758200, 664943564, 1079002177], [1083180097, 1081547512, 3234148260, 1077385976, 1085736031, 1087431672, 1085758200, 658892085, 1083049080], [1083180097, 1087382456, 3233558884, 1083220920, 1085736031, 1081596600, 1074815928, 668673292, 1083049080], [1080629953, 1083049080, 3227191524, 1087276152, 1078860511, 1087431672, 1078871160, 658892085, 1081547512], [1083180097, 1089067713, 2152428923, 1087429350, 1079002177, 1087431672, 1087298271, 663028428, 1074840641], [1083180097, 1078860511, 3231887290, 1087298271, 1084818534, 1084842975, 1074698975, 658833996, 1085736031]], 'outer_group': '96.209', 'outer_hash': 209, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 9, 'outer_perms': [5040, 120, 16, 121, 7, 45360], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times D_6', 'pc_rank': 7, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [3, 24], [4, 2], [6, 14]], 'representations': {'PC': {'code': '233562656894484383470625409380039706775389768915267527303008146297872', 'gens': [1, 2, 4, 6, 7, 8, 9], 'pres': [9, -2, -2, -2, -2, -3, -2, 2, -2, 2, 109, 46, 1443, 732, 102, 1444, 733, 7781, 3902, 1004, 365, 411, 609, 41479, 20752, 3490, 2635, 5867, 1016]}, 'GLFq': {'d': 4, 'q': 4, 'gens': [1083180097, 1081547512, 3234148260, 1077385976, 1085736031, 1087431672, 1085758200, 668673292, 1083049080]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'transitive_degree': 24, '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: 105777444
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 1090187, 'group_order': 768, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 1074791425, 'size': 1}
  • id: 105777455
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 1090187, 'group_order': 768, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1085750593, 'size': 1}
  • id: 105777466
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 1090187, 'group_order': 768, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1089018497, 'size': 1}
  • id: 105777477
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 1090187, 'group_order': 768, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 1078862785, 'size': 1}
  • id: 105777488
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 1090187, 'group_order': 768, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1080629953, 'size': 2}
  • id: 105777496
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 6, 'group_counter': 1090187, 'group_order': 768, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 1083180097, 'size': 2}
  • id: 105777497
    {'aut_label': '2F', 'centralizer': '3.a1', 'counter': 7, 'group_counter': 1090187, 'group_order': 768, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 1074832376, 'size': 3}
  • id: 105777498
    {'aut_label': '2F', 'centralizer': '3.a1', 'counter': 8, 'group_counter': 1090187, 'group_order': 768, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 1083204600, 'size': 3}
  • id: 105777499
    {'aut_label': '2F', 'centralizer': '3.a1', 'counter': 9, 'group_counter': 1090187, 'group_order': 768, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 1087431672, 'size': 3}
  • id: 105777445
    {'aut_label': '2F', 'centralizer': '3.a1', 'counter': 10, 'group_counter': 1090187, 'group_order': 768, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 1074813606, 'size': 3}
  • id: 105777446
    {'aut_label': '2F', 'centralizer': '3.a1', 'counter': 11, 'group_counter': 1090187, 'group_order': 768, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 1077369528, 'size': 3}
  • id: 105777447
    {'aut_label': '2F', 'centralizer': '3.a1', 'counter': 12, 'group_counter': 1090187, 'group_order': 768, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 1079040678, 'size': 3}
  • id: 105777448
    {'aut_label': '2L', 'centralizer': '3.a1', 'counter': 13, 'group_counter': 1090187, 'group_order': 768, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 1087259704, 'size': 3}
  • id: 105777449
    {'aut_label': '2L', 'centralizer': '3.a1', 'counter': 14, 'group_counter': 1090187, 'group_order': 768, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 1078887480, 'size': 3}
  • id: 105777450
    {'aut_label': '2L', 'centralizer': '3.a1', 'counter': 15, 'group_counter': 1090187, 'group_order': 768, 'label': '2N', 'order': 2, 'powers': [1, 15], 'representative': 1083098168, 'size': 3}
  • id: 105777451
    {'aut_label': '2O', 'centralizer': '3.a1', 'counter': 16, 'group_counter': 1090187, 'group_order': 768, 'label': '2O', 'order': 2, 'powers': [1, 16], 'representative': 1074724198, 'size': 3}
  • id: 105777452
    {'aut_label': '2O', 'centralizer': '3.a1', 'counter': 17, 'group_counter': 1090187, 'group_order': 768, 'label': '2P', 'order': 2, 'powers': [1, 17], 'representative': 1074855263, 'size': 3}
  • id: 105777453
    {'aut_label': '2O', 'centralizer': '3.a1', 'counter': 18, 'group_counter': 1090187, 'group_order': 768, 'label': '2Q', 'order': 2, 'powers': [1, 18], 'representative': 1078885734, 'size': 3}
  • id: 105777454
    {'aut_label': '2R', 'centralizer': '6.a1', 'counter': 19, 'group_counter': 1090187, 'group_order': 768, 'label': '2R', 'order': 2, 'powers': [1, 19], 'representative': 1074660408, 'size': 6}
  • id: 105777456
    {'aut_label': '2S', 'centralizer': '6.a1', 'counter': 20, 'group_counter': 1090187, 'group_order': 768, 'label': '2S', 'order': 2, 'powers': [1, 20], 'representative': 1074840641, 'size': 6}
  • id: 105777457
    {'aut_label': '2S', 'centralizer': '6.a1', 'counter': 21, 'group_counter': 1090187, 'group_order': 768, 'label': '2T', 'order': 2, 'powers': [1, 21], 'representative': 1083049080, 'size': 6}
  • id: 105777458
    {'aut_label': '2U', 'centralizer': '6.a1', 'counter': 22, 'group_counter': 1090187, 'group_order': 768, 'label': '2U', 'order': 2, 'powers': [1, 22], 'representative': 1074709624, 'size': 6}
  • id: 105777459
    {'aut_label': '2S', 'centralizer': '6.a1', 'counter': 23, 'group_counter': 1090187, 'group_order': 768, 'label': '2V', 'order': 2, 'powers': [1, 23], 'representative': 1087382456, 'size': 6}
  • id: 105777460
    {'aut_label': '2U', 'centralizer': '6.a1', 'counter': 24, 'group_counter': 1090187, 'group_order': 768, 'label': '2W', 'order': 2, 'powers': [1, 24], 'representative': 1074815928, 'size': 6}
  • id: 105777461
    {'aut_label': '2X', 'centralizer': '6.a1', 'counter': 25, 'group_counter': 1090187, 'group_order': 768, 'label': '2X', 'order': 2, 'powers': [1, 25], 'representative': 1078993912, 'size': 6}
  • id: 105777462
    {'aut_label': '2S', 'centralizer': '6.a1', 'counter': 26, 'group_counter': 1090187, 'group_order': 768, 'label': '2Y', 'order': 2, 'powers': [1, 26], 'representative': 1074684801, 'size': 6}
  • id: 105777463
    {'aut_label': '2U', 'centralizer': '6.a1', 'counter': 27, 'group_counter': 1090187, 'group_order': 768, 'label': '2Z', 'order': 2, 'powers': [1, 27], 'representative': 1078871160, 'size': 6}
  • id: 105777464
    {'aut_label': '2U', 'centralizer': '6.a1', 'counter': 28, 'group_counter': 1090187, 'group_order': 768, 'label': '2AA', 'order': 2, 'powers': [1, 28], 'representative': 1087276152, 'size': 6}
  • id: 105777465
    {'aut_label': '2U', 'centralizer': '6.a1', 'counter': 29, 'group_counter': 1090187, 'group_order': 768, 'label': '2AB', 'order': 2, 'powers': [1, 29], 'representative': 1083220920, 'size': 6}
  • id: 105777467
    {'aut_label': '2U', 'centralizer': '6.a1', 'counter': 30, 'group_counter': 1090187, 'group_order': 768, 'label': '2AC', 'order': 2, 'powers': [1, 30], 'representative': 1079043000, 'size': 6}
  • id: 105777468
    {'aut_label': '2AD', 'centralizer': '6.a1', 'counter': 31, 'group_counter': 1090187, 'group_order': 768, 'label': '2AD', 'order': 2, 'powers': [1, 31], 'representative': 1077411137, 'size': 6}
  • id: 105777469
    {'aut_label': '2X', 'centralizer': '6.a1', 'counter': 32, 'group_counter': 1090187, 'group_order': 768, 'label': '2AE', 'order': 2, 'powers': [1, 32], 'representative': 1076451969, 'size': 6}
  • id: 105777470
    {'aut_label': '2AF', 'centralizer': '24.y1', 'counter': 33, 'group_counter': 1090187, 'group_order': 768, 'label': '2AF', 'order': 2, 'powers': [1, 33], 'representative': 965411076, 'size': 24}
  • id: 105777471
    {'aut_label': '2AF', 'centralizer': '24.y1', 'counter': 34, 'group_counter': 1090187, 'group_order': 768, 'label': '2AG', 'order': 2, 'powers': [1, 34], 'representative': 504398641, 'size': 24}
  • id: 105777472
    {'aut_label': '3A', 'centralizer': '32.a1', 'counter': 35, 'group_counter': 1090187, 'group_order': 768, 'label': '3A', 'order': 3, 'powers': [35, 1], 'representative': 2157300764, 'size': 32}
  • id: 105777473
    {'aut_label': '4A', 'centralizer': '24.z1', 'counter': 36, 'group_counter': 1090187, 'group_order': 768, 'label': '4A', 'order': 4, 'powers': [13, 36], 'representative': 957022532, 'size': 24}
  • id: 105777474
    {'aut_label': '4A', 'centralizer': '24.z1', 'counter': 37, 'group_counter': 1090187, 'group_order': 768, 'label': '4B', 'order': 4, 'powers': [14, 37], 'representative': 508568584, 'size': 24}
  • id: 105777475
    {'aut_label': '4A', 'centralizer': '24.z1', 'counter': 38, 'group_counter': 1090187, 'group_order': 768, 'label': '4C', 'order': 4, 'powers': [15, 38], 'representative': 654639756, 'size': 24}
  • id: 105777476
    {'aut_label': '4D', 'centralizer': '24.bb1', 'counter': 39, 'group_counter': 1090187, 'group_order': 768, 'label': '4D', 'order': 4, 'powers': [2, 39], 'representative': 961233156, 'size': 24}
  • id: 105777478
    {'aut_label': '4E', 'centralizer': '24.bc1', 'counter': 40, 'group_counter': 1090187, 'group_order': 768, 'label': '4E', 'order': 4, 'powers': [16, 40], 'representative': 957039044, 'size': 24}
  • id: 105777479
    {'aut_label': '4E', 'centralizer': '24.bc1', 'counter': 41, 'group_counter': 1090187, 'group_order': 768, 'label': '4F', 'order': 4, 'powers': [17, 41], 'representative': 504423560, 'size': 24}
  • id: 105777480
    {'aut_label': '4E', 'centralizer': '24.bc1', 'counter': 42, 'group_counter': 1090187, 'group_order': 768, 'label': '4G', 'order': 4, 'powers': [18, 42], 'representative': 504284040, 'size': 24}
  • id: 105777481
    {'aut_label': '4D', 'centralizer': '24.bb1', 'counter': 43, 'group_counter': 1090187, 'group_order': 768, 'label': '4H', 'order': 4, 'powers': [2, 43], 'representative': 512770865, 'size': 24}
  • id: 105777482
    {'aut_label': '4E', 'centralizer': '24.bc1', 'counter': 44, 'group_counter': 1090187, 'group_order': 768, 'label': '4I', 'order': 4, 'powers': [17, 44], 'representative': 504382321, 'size': 24}
  • id: 105777483
    {'aut_label': '4A', 'centralizer': '24.z1', 'counter': 45, 'group_counter': 1090187, 'group_order': 768, 'label': '4J', 'order': 4, 'powers': [14, 45], 'representative': 504276017, 'size': 24}
  • id: 105777484
    {'aut_label': '4A', 'centralizer': '24.z1', 'counter': 46, 'group_counter': 1090187, 'group_order': 768, 'label': '4K', 'order': 4, 'powers': [13, 46], 'representative': 512787313, 'size': 24}
  • id: 105777485
    {'aut_label': '4E', 'centralizer': '24.bc1', 'counter': 47, 'group_counter': 1090187, 'group_order': 768, 'label': '4L', 'order': 4, 'powers': [18, 47], 'representative': 508576689, 'size': 24}
  • id: 105777486
    {'aut_label': '4A', 'centralizer': '24.z1', 'counter': 48, 'group_counter': 1090187, 'group_order': 768, 'label': '4M', 'order': 4, 'powers': [15, 48], 'representative': 516981681, 'size': 24}
  • id: 105777487
    {'aut_label': '4E', 'centralizer': '24.bc1', 'counter': 49, 'group_counter': 1090187, 'group_order': 768, 'label': '4N', 'order': 4, 'powers': [16, 49], 'representative': 516965361, 'size': 24}
  • id: 105777489
    {'aut_label': '6A', 'centralizer': '32.a1', 'counter': 50, 'group_counter': 1090187, 'group_order': 768, 'label': '6A', 'order': 6, 'powers': [35, 3], 'representative': 3233558339, 'size': 32}
  • id: 105777490
    {'aut_label': '6A', 'centralizer': '32.a1', 'counter': 51, 'group_counter': 1090187, 'group_order': 768, 'label': '6B', 'order': 6, 'powers': [35, 4], 'representative': 2148258370, 'size': 32}
  • id: 105777491
    {'aut_label': '6C', 'centralizer': '32.a1', 'counter': 52, 'group_counter': 1090187, 'group_order': 768, 'label': '6C', 'order': 6, 'powers': [35, 2], 'representative': 2153114533, 'size': 32}
  • id: 105777492
    {'aut_label': '6D1', 'centralizer': '32.a1', 'counter': 53, 'group_counter': 1090187, 'group_order': 768, 'label': '6D1', 'order': 6, 'powers': [35, 5], 'representative': 3227250589, 'size': 32}
  • id: 105777493
    {'aut_label': '6D1', 'centralizer': '32.a1', 'counter': 54, 'group_counter': 1090187, 'group_order': 768, 'label': '6D-1', 'order': 6, 'powers': [35, 5], 'representative': 2150823260, 'size': 32}
  • id: 105777494
    {'aut_label': '6D1', 'centralizer': '32.a1', 'counter': 55, 'group_counter': 1090187, 'group_order': 768, 'label': '6E1', 'order': 6, 'powers': [35, 6], 'representative': 3235629284, 'size': 32}
  • id: 105777495
    {'aut_label': '6D1', 'centralizer': '32.a1', 'counter': 56, 'group_counter': 1090187, 'group_order': 768, 'label': '6E-1', 'order': 6, 'powers': [35, 6], 'representative': 2152451237, 'size': 32}
• gps_qchar •

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

  
  
  • id: 3596964
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3596975
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3596986
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3596997
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3597008
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3597014
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 3597015
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 3597016
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3597017
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3596965
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 2, 2, -2, 2, 2, -2, 2, -2, -2, 2, -2, -2, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0], 'schur_index': 1}
  • id: 3596966
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 0, 0], 'schur_index': 1}
  • id: 3596967
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, -2, -2, -2, 2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3596968
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, -2, -2, -2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, 2, 2, 2, -2, 2, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 3596969
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, 2, -2, -2, -2, -2, 2, -2, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 3596972
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -1, -1, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, 3, -1, -1, -1, 1, 1, 0, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596973
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3b', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596974
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3c', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, 3, 1, 1, 0, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596976
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3d', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -1, -1, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, 3, -1, -1, -1, -1, -1, 0, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596977
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3e', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596978
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3f', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, 0, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596979
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -3, 3, -3, 1, -3, 1, -1, 1, -1, -1, 1, 3, -1, 3, -1, -1, -1, -1, 1, -1, 1, -1, -3, 1, 1, 1, 1, 3, -1, 1, 0, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596980
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -3, 3, -3, 1, -3, 1, -1, 1, -1, -1, 1, 3, -1, 3, -1, -1, -1, -1, 1, -1, 1, -1, -3, 1, 1, 1, 1, 3, 1, -1, 0, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596981
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3i', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -3, 3, 1, -3, 1, 1, -1, -3, 3, -1, 1, -1, 3, -1, -1, -1, -1, 3, -3, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 0, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596982
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3j', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -3, 3, 1, -3, 1, 1, -1, -3, 3, -1, 1, -1, 3, -1, -1, -1, -1, 3, -3, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 0, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596983
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3k', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -3, 3, 1, 1, 1, -3, 3, 1, -1, 3, -3, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 3, 1, 1, -3, 1, 1, -1, -1, 1, 0, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596984
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3l', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -3, 3, 1, 1, 1, -3, 3, 1, -1, 3, -3, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 3, 1, 1, -3, 1, 1, -1, 1, -1, 0, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596985
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3m', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, -3, -3, 1, -3, 1, -1, 1, -1, -1, 1, 3, -1, 3, -1, 1, -1, 1, -1, 1, 1, 1, 3, -1, -1, 1, -1, -3, -1, 1, 0, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596987
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3n', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, -3, -3, 1, -3, 1, -1, 1, -1, -1, 1, 3, -1, 3, -1, 1, -1, 1, -1, 1, 1, 1, 3, -1, -1, 1, -1, -3, 1, -1, 0, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596988
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3o', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, -3, 1, -3, 1, 1, -1, -3, 3, -1, 1, -1, 3, -1, -1, 1, -1, -3, 3, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 0, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596989
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3p', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, -3, 1, -3, 1, 1, -1, -3, 3, -1, 1, -1, 3, -1, -1, 1, -1, -3, 3, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 0, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596990
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3q', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, -3, 1, 1, 1, -3, 3, 1, -1, 3, -3, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -3, -1, -1, 3, 1, -1, 1, -1, 1, 0, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596991
    {'cdim': 3, 'counter': 34, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3r', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -3, 3, -3, 1, 1, 1, -3, 3, 1, -1, 3, -3, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -3, -1, -1, 3, 1, -1, 1, 1, -1, 0, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596992
    {'cdim': 3, 'counter': 35, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3s', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, -1, -1, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -3, 1, 1, -3, -1, 1, 1, -1, -1, 0, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596993
    {'cdim': 3, 'counter': 36, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3t', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, -1, -1, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -3, 1, 1, -3, -1, 1, 1, 1, 1, 0, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596994
    {'cdim': 3, 'counter': 37, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3u', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, 1, -1, -3, -3, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 0, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596995
    {'cdim': 3, 'counter': 38, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3v', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, 1, -1, -3, -3, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 0, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596996
    {'cdim': 3, 'counter': 39, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3w', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, 3, -1, 3, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, 1, -1, 1, 1, 1, -1, 1, -3, 1, 1, -1, 1, -3, -1, -1, 0, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596998
    {'cdim': 3, 'counter': 40, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.3x', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, -3, 3, -1, 3, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, 1, -1, 1, 1, 1, -1, 1, -3, 1, 1, -1, 1, -3, 1, 1, 0, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3596970
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.2g', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, 4, -4, 4, 4, -4, 4, -4, -4, 4, -4, -4, 4, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0], 'schur_index': 1}
  • id: 3596971
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.2h', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -4, -4, 4, -4, 4, 4, 4, -4, 4, 4, -4, -4, 4, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -2, 0, 0], 'schur_index': 1}
  • id: 3596999
    {'cdim': 6, 'counter': 41, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6a', 'multiplicity': 1, 'nt': [8, 34], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597000
    {'cdim': 6, 'counter': 42, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6b', 'multiplicity': 1, 'nt': [12, 49], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, -2, -2, 2, 6, 6, 2, -2, -6, -6, -2, 2, 2, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597001
    {'cdim': 6, 'counter': 43, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6c', 'multiplicity': 1, 'nt': [12, 49], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, -2, 6, 2, -2, -2, -6, 6, 2, 2, -2, -6, 2, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597002
    {'cdim': 6, 'counter': 44, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6d', 'multiplicity': 1, 'nt': [12, 49], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, 6, -2, -6, -2, -2, 2, -2, 2, 2, 6, 2, -6, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597003
    {'cdim': 6, 'counter': 45, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6e', 'multiplicity': 1, 'nt': [12, 49], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 0, 0, -6, 2, 6, 2, -2, -2, -2, 2, -2, 6, 2, -6, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597004
    {'cdim': 6, 'counter': 46, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6f', 'multiplicity': 1, 'nt': [12, 49], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 0, 0, 2, -6, -2, 2, -2, 6, 6, 2, -2, -2, -6, 2, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597005
    {'cdim': 6, 'counter': 47, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6g', 'multiplicity': 1, 'nt': [12, 49], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 0, 0, 2, 2, -2, -6, 6, -2, -2, -6, 6, -2, 2, 2, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597006
    {'cdim': 6, 'counter': 48, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6h', 'multiplicity': 1, 'nt': [12, 100], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -6, 6, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597007
    {'cdim': 6, 'counter': 49, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6i', 'multiplicity': 1, 'nt': [12, 100], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 6, -6, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597009
    {'cdim': 6, 'counter': 50, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6j', 'multiplicity': 1, 'nt': [12, 100], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597010
    {'cdim': 6, 'counter': 51, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6k', 'multiplicity': 1, 'nt': [12, 135], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 2, 2, 2, -4, -2, 0, 0, 4, -2, 0, 0, -4, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597011
    {'cdim': 6, 'counter': 52, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6l', 'multiplicity': 1, 'nt': [12, 135], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 2, 2, 2, 4, -2, 0, 0, -4, -2, 0, 0, 4, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597012
    {'cdim': 6, 'counter': 53, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6m', 'multiplicity': 1, 'nt': [12, 135], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 0, 0, 2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 2, -4, -2, 0, 0, 4, 2, 0, 0, 4, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3597013
    {'cdim': 6, 'counter': 54, 'faithful': False, 'group': '768.1090187', 'group_order': 768, 'image': None, 'label': '768.1090187.6n', 'multiplicity': 1, 'nt': [12, 135], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 0, 0, 2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 4, -2, 0, 0, -4, 2, 0, 0, -4, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 5181305
    {'center': '1.a1', 'center_index': 1, 'center_order': 768, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 768, 'label': '768.1090187.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5181316
    {'center': '1.a1', 'center_index': 1, 'center_order': 768, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 384, 'label': '768.1090187.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5181327
    {'center': '1.a1', 'center_index': 1, 'center_order': 768, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 384, 'label': '768.1090187.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5181338
    {'center': '1.a1', 'center_index': 1, 'center_order': 768, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 384, 'label': '768.1090187.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5181349
    {'center': '1.a1', 'center_index': 1, 'center_order': 768, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 384, 'label': '768.1090187.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5181357
    {'center': '1.a1', 'center_index': 1, 'center_order': 768, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 384, 'label': '768.1090187.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5181358
    {'center': '1.a1', 'center_index': 1, 'center_order': 768, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 384, 'label': '768.1090187.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5181359
    {'center': '1.a1', 'center_index': 1, 'center_order': 768, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 384, 'label': '768.1090187.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5181360
    {'center': '6.a1', 'center_index': 6, 'center_order': 128, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 128, 'label': '768.1090187.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5181306
    {'center': '4.a1', 'center_index': 4, 'center_order': 192, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 96, 'label': '768.1090187.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181307
    {'center': '4.a1', 'center_index': 4, 'center_order': 192, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 96, 'label': '768.1090187.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181308
    {'center': '6.a1', 'center_index': 6, 'center_order': 128, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 64, 'label': '768.1090187.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-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]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5181309
    {'center': '6.a1', 'center_index': 6, 'center_order': 128, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 64, 'label': '768.1090187.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-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]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5181310
    {'center': '6.a1', 'center_index': 6, 'center_order': 128, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 64, 'label': '768.1090187.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-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]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5181311
    {'center': '12.a1', 'center_index': 12, 'center_order': 64, 'counter': 15, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 32, 'label': '768.1090187.2g1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]]]}
  • id: 5181312
    {'center': '12.a1', 'center_index': 12, 'center_order': 64, 'counter': 16, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 32, 'label': '768.1090187.2g2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]]]}
  • id: 5181313
    {'center': '12.a1', 'center_index': 12, 'center_order': 64, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 32, 'label': '768.1090187.2h1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]]]}
  • id: 5181314
    {'center': '12.a1', 'center_index': 12, 'center_order': 64, 'counter': 18, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 32, 'label': '768.1090187.2h2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]]]}
  • id: 5181315
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 32, 'label': '768.1090187.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181317
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 32, 'label': '768.1090187.3b', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181318
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 21, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 32, 'label': '768.1090187.3c', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181319
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 22, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 32, 'label': '768.1090187.3d', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181320
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 23, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 32, 'label': '768.1090187.3e', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181321
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 24, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 32, 'label': '768.1090187.3f', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181322
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 25, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181323
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 26, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181324
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 27, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3i', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181325
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 28, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3j', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181326
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 29, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3k', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181328
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 30, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3l', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181329
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 31, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3m', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181330
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 32, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3n', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181331
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 33, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3o', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181332
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 34, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3p', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181333
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 35, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3q', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181334
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 36, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 16, 'label': '768.1090187.3r', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181335
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 37, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 16, 'label': '768.1090187.3s', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181336
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 38, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 16, 'label': '768.1090187.3t', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181337
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 39, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 16, 'label': '768.1090187.3u', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181339
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 40, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 16, 'label': '768.1090187.3v', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181340
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 41, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 16, 'label': '768.1090187.3w', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181341
    {'center': '24.a1', 'center_index': 24, 'center_order': 32, 'counter': 42, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 16, 'label': '768.1090187.3x', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181342
    {'center': '96.a1', 'center_index': 96, 'center_order': 8, 'counter': 43, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '96.227', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1', 'kernel_order': 8, 'label': '768.1090187.6a', 'nt': [8, 34], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181343
    {'center': '48.a1', 'center_index': 48, 'center_order': 16, 'counter': 44, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '96.195', 'image_order': 96, 'indicator': 1, 'kernel': '96.c1', 'kernel_order': 8, 'label': '768.1090187.6b', 'nt': [12, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 5181344
    {'center': '48.a1', 'center_index': 48, 'center_order': 16, 'counter': 45, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '96.195', 'image_order': 96, 'indicator': 1, 'kernel': '96.c1', 'kernel_order': 8, 'label': '768.1090187.6c', 'nt': [12, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 5181345
    {'center': '48.a1', 'center_index': 48, 'center_order': 16, 'counter': 46, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '96.195', 'image_order': 96, 'indicator': 1, 'kernel': '96.c1', 'kernel_order': 8, 'label': '768.1090187.6d', 'nt': [12, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[6, 0]], [[2, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 5181346
    {'center': '48.a1', 'center_index': 48, 'center_order': 16, 'counter': 47, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '96.195', 'image_order': 96, 'indicator': 1, 'kernel': '96.c1', 'kernel_order': 8, 'label': '768.1090187.6e', 'nt': [12, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[2, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 5181347
    {'center': '48.a1', 'center_index': 48, 'center_order': 16, 'counter': 48, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '96.195', 'image_order': 96, 'indicator': 1, 'kernel': '96.c1', 'kernel_order': 8, 'label': '768.1090187.6f', 'nt': [12, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 5181348
    {'center': '48.a1', 'center_index': 48, 'center_order': 16, 'counter': 49, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '96.195', 'image_order': 96, 'indicator': 1, 'kernel': '96.c1', 'kernel_order': 8, 'label': '768.1090187.6g', 'nt': [12, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 5181350
    {'center': '96.a1', 'center_index': 96, 'center_order': 8, 'counter': 50, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '192.1538', 'image_order': 192, 'indicator': 1, 'kernel': '192.b1', 'kernel_order': 4, 'label': '768.1090187.6h', 'nt': [12, 100], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181351
    {'center': '96.a1', 'center_index': 96, 'center_order': 8, 'counter': 51, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '192.1538', 'image_order': 192, 'indicator': 1, 'kernel': '192.b1', 'kernel_order': 4, 'label': '768.1090187.6i', 'nt': [12, 100], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181352
    {'center': '96.a1', 'center_index': 96, 'center_order': 8, 'counter': 52, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '192.1538', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1', 'kernel_order': 4, 'label': '768.1090187.6j', 'nt': [12, 100], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181353
    {'center': '192.a1', 'center_index': 192, 'center_order': 4, 'counter': 53, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '384.20100', 'image_order': 384, 'indicator': 1, 'kernel': '384.b1', 'kernel_order': 2, 'label': '768.1090187.6k', 'nt': [12, 135], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181354
    {'center': '192.a1', 'center_index': 192, 'center_order': 4, 'counter': 54, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '384.20100', 'image_order': 384, 'indicator': 1, 'kernel': '384.b1', 'kernel_order': 2, 'label': '768.1090187.6l', 'nt': [12, 135], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181355
    {'center': '192.a1', 'center_index': 192, 'center_order': 4, 'counter': 55, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '384.20100', 'image_order': 384, 'indicator': 1, 'kernel': '384.b1', 'kernel_order': 2, 'label': '768.1090187.6m', 'nt': [12, 135], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5181356
    {'center': '192.a1', 'center_index': 192, 'center_order': 4, 'counter': 56, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090187', 'group_counter': 1090187, 'group_order': 768, 'image': None, 'image_isoclass': '384.20100', 'image_order': 384, 'indicator': 1, 'kernel': '384.b1', 'kernel_order': 2, 'label': '768.1090187.6n', 'nt': [12, 135], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 59633153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 768, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '768.1090187.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090187', 'subgroup_hash': 1090187, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 59633264
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 384, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.20166', 'subgroup_hash': 20166, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 384, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.20163', 'subgroup_hash': 20163, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 59633486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 384, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.20099', 'subgroup_hash': 20099, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 384, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '768.1090187.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.20100', 'subgroup_hash': 20100, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 59633708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '768.1090187.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 59633819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 59633899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 192, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 59633910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1495', 'subgroup_hash': 1495, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.4.e1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 59633176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 59633187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633198
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 128, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 59633209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 59633376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633398
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 64, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633409
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 64, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633431
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59633464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59633531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633553
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59633575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.t2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633664
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633797
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 59633820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.12.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633886
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633905
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633906
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633907
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633912
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633913
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633914
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633915
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633916
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633159
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633160
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633161
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633162
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633163
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.w2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633166
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633167
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633169
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633170
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633171
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633172
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633173
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633174
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633179
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bk2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633181
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633183
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633186
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633191
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633192
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633193
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633197
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633199
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ca2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ca2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633206
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633207
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633212
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633213
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633216
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633222
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633227
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633228
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633229
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633230
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633232
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633233
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633234
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633235
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.de2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.de2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633236
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633237
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633240
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633241
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633243
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633244
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633247
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633248
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633249
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dr2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dr2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633255
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633258
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633259
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633260
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633261
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633262
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633263
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.eb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633266
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633267
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633272
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633273
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 59633274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.24.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633282
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.32.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633294
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 226, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_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: 59633295
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 227, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633296
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 228, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633297
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633299
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633301
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633302
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633303
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633304
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633305
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.j2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633306
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633307
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633308
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633310
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633311
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633312
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633313
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633314
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633315
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633316
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633318
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633319
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633322
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.y2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.y2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633324
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633325
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633326
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633329
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633330
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bi2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633336
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633337
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633338
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633339
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633340
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633343
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633344
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bp3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bp3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bp4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bp4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633349
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633350
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633352
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633354
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633358
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633360
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633362
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633363
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633367
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ct2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ct2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633385
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633386
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633389
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633390
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633391
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633392
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633393
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633394
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633395
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633397
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633399
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633400
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633401
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633402
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633403
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633404
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dk2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633405
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633406
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633407
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633408
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633411
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633412
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dt2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633419
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633421
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633422
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633423
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633424
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633425
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633427
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633428
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633429
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ee2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ee2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ee3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ee3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633432
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ee4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ee4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633436
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633439
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633440
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.el2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.el2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633443
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633444
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633446
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633448
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633449
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.es2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.es2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633450
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633451
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633452
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633456
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633458
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ez2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ez2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633459
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ez3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ez3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633460
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ez4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ez4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633461
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633462
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633463
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633466
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633467
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fe2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fe2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633472
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633476
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633480
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633482
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633485
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633488
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fx3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fx3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fx4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fx4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fy2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fy2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633507
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gf2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633511
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633512
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633513
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633514
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633515
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633516
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633517
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633518
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633521
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633523
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633524
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633526
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633527
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633528
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633529
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633532
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633533
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633536
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633539
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633540
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633541
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633543
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hi2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633548
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633550
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633551
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633555
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.48.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 59633556
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633557
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633559
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59633560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.64.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.64.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.64.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.64.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 59633565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': True, 'core_order': 8, 'counter': 470, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.227', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 227, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59633566
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 471, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.96.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59633567
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 472, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.96.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.195', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 195, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,\\mathbb{Z}/4)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59633568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633572
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633576
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633577
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633578
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633580
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633581
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633582
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633584
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633585
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.s2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633587
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633588
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633589
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633590
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633591
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633592
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633593
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633594
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ba2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ba2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633599
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633602
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633610
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633611
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633613
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633615
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 59633616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633617
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633619
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633622
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.by2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.by2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633633
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633634
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cf2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633635
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633640
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633641
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633643
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633644
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 59633646
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633647
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633649
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633650
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633651
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633652
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633654
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633655
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633656
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633657
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633658
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.cz2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cz2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.da2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.da2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633661
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633662
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633663
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.de2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.de2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633670
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633671
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633673
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633677
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633678
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633679
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633681
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633682
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633683
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ds2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ds2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633684
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633685
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633687
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633688
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dv2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dv2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633691
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633692
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dy2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dy2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ea2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ea2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633698
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633699
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ec2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ec2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ec3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ec3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633701
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ec4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ec4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633702
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633704
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ee2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ee2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633705
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ee3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ee3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633706
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ee4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ee4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633707
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633712
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633713
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ej2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ej2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633716
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ek2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ek2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633717
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633718
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.el2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.el2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633719
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.el3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.el3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633721
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.el4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.el4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633722
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633723
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633727
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633728
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633729
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.es2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.es2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633732
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633734
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633736
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633738
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633739
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fa2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fa2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633740
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633741
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633743
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633744
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633745
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fd3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fd3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633746
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fd4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fd4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633749
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633750
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633751
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633752
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633754
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633762
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633763
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633765
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633766
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633767
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633769
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633770
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633771
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fy2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fy2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633774
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633776
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633777
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633783
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633784
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633785
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633791
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.96.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59633792
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 675, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633793
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 676, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633794
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 677, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.128.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 59633795
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.128.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 59633796
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': True, 'core_order': 4, 'counter': 679, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.192.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1538', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1538, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1'], '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: 59633798
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 4, 'counter': 680, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.192.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1538', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1538, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59633799
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 681, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090187.192.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1488', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1488, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59633800
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633801
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633802
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633803
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633804
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633805
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633806
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633807
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 689, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.192.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633809
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633810
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633811
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633812
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633814
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633818
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633821
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633822
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633823
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633824
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633825
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633826
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633827
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633828
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633829
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633832
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.be2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.be2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633833
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633834
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633835
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633836
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633838
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bi2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633839
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633840
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633841
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633849
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 59633850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633851
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633854
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633860
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.ca2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ca2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633863
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 740, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633866
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633867
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633868
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633873
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633876
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633879
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633880
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090187.192.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 59633881
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 755, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '768.1090187.256.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 59633882
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': True, 'core_order': 2, 'counter': 756, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '768.1090187.384.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '384.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '384.20163', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 20163, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\wr S_3', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], '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: 59633883
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': False, 'core_order': 2, 'counter': 757, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '768.1090187.384.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '384.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '384.20100', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 20100, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\wr S_3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59633884
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 758, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633885
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 759, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633887
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 760, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633888
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 761, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633889
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 762, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633890
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 763, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633891
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 764, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633892
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 765, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633893
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 766, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633894
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 767, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090187.384.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 59633895
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090187', 'ambient_counter': 1090187, 'ambient_order': 768, 'ambient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': True, 'core_order': 1, 'counter': 768, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '768.1090187.768.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '768.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '768.1090187', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1090187, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 59633153
    {'ambient': '768.1090187', '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': '192.a1', 'complements': ['768.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '3.a1', '4.e1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4802, 4601, 5361, 4090], 'generators': [1074660408, 1081574431, 1076429862, 1084867622, 1083180097, 2150763522, 668673292, 1085750593, 3234148260], 'label': '768.1090187.1.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': '192.1538', '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': '192.1538'}
  • id: 59633154
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 16, 'centralizer': '192.a1', 'complements': ['192.bg1', '192.s1', '192.l1', '192.x1', '192.t1', '192.bc1', '192.cl1', '192.bd1', '192.p1', '192.cn1', '192.cp1', '192.q1', '192.be2', '192.be1'], 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '2.d1'], 'contains': ['8.a1', '12.bh1', '16.h1'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [4829, 5209, 5457, 716], 'generators': [1074660408, 1081574431, 1076429862, 1084867622, 506952305, 2150763522, 1085750593], 'label': '768.1090187.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.c1', '2.d1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '384.20163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 59633155
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.f1', '12.i1', '12.k1'], 'contains': ['48.j2', '48.k1', '48.m1', '48.u1', '48.bn1', '48.cj1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9943, -1, 9745, -1], 'generators': [660749132, 1085750593, 1074830054, 1089045606, 1089946655], 'label': '768.1090187.24.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.p1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633156
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.e1', '12.i1', '12.l1'], 'contains': ['48.j1', '48.k1', '48.n1', '48.ck1', '48.dw1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9148, -1, 7175, -1], 'generators': [660749132, 1085750593, 1087276152, 1077385976, 1089946655], 'label': '768.1090187.24.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.q1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633157
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.e1', '12.i1', '12.m1'], 'contains': ['48.j1', '48.l1', '48.m1', '48.cl1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9716, -1, 8637, -1], 'generators': [1085750593, 1087276152, 1077385976, 668673292, 1089946655], 'label': '768.1090187.24.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.r1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633158
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.g1', '12.i1', '12.k1'], 'contains': ['48.j2', '48.l1', '48.n1', '48.cm1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9337, -1, 7622, -1], 'generators': [1085750593, 1074830054, 1089045606, 668673292, 1089946655], 'label': '768.1090187.24.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.s1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633159
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.j1', '12.o1'], 'contains': ['48.h1', '48.j1', '48.j2', '48.o1', '48.q1', '48.s1', '48.bi1', '48.bi2', '48.bx1', '48.cq1', '48.dx1', '48.dx2', '48.dz1', '48.eb1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6022, -1, 3825, -1], 'generators': [1076429862, 1085750593, 1081574431, 1076479078, 1089067713], 'label': '768.1090187.24.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.t1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633160
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.d1', '12.o1'], 'contains': ['48.h1', '48.i1', '48.o1', '48.q1', '48.r1', '48.bj1', '48.by1', '48.cr1', '48.dy1', '48.ea1', '48.ec1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4227, -1, 2410, -1], 'generators': [1076429862, 1078860511, 1085750593, 1081574431, 1083049080], 'label': '768.1090187.24.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.u1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633161
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.d1', '12.j1'], 'contains': ['48.g1', '48.o1', '48.t1', '48.bk1', '48.bo1', '48.ca1', '48.cs1', '48.ed1', '48.ej1', '48.ek1', '48.ep1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2015, -1, 1701, -1], 'generators': [1076429862, 1074660408, 1085750593, 1081574431, 1087249055], 'label': '768.1090187.24.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.v1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633162
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.h1', '12.k1', '12.o1'], 'contains': ['48.a1', '48.h1', '48.i1', '48.j2', '48.bp1', '48.bp2', '48.ct1', '48.ee1', '48.ee2', '48.el1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7756, -1, 4694, -1], 'generators': [1074840641, 1083098168, 1085750593, 1081547512, 1081574431], 'label': '768.1090187.24.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.w1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633163
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.w2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.h1', '12.l1', '12.m1', '12.n1', '12.o1'], 'contains': ['48.h1', '48.i1', '48.j1', '48.p1', '48.bp3', '48.bp4', '48.ct2', '48.ee3', '48.ee4', '48.el2'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7937, -1, 4792, -1], 'generators': [1083098168, 1089963103, 1085750593, 1081547512, 1080656934], 'label': '768.1090187.24.w2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.w2', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633164
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.e1', '12.e1', '12.k1', '12.p1'], 'contains': ['48.a1', '48.k1', '48.l1', '48.bq1', '48.cu1', '48.ef1', '48.em1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8981, -1, 9059, -1], 'generators': [1083098168, 1085750593, 1081574431, 1081596600, 658250892], 'label': '768.1090187.24.x1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.x1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633165
    {'ambient': '768.1090187', 'aut_centralizer_order': 2, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '768.1088763', 'aut_weyl_index': 24, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['8.c1', '8.e1', '8.f1', '8.g1', '12.e1', '16.b1'], 'core': '24.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4795, -1, 5344, -1], 'generators': [1083180097, 1083098168, 1085750593, 1081574431, 670833676, 3234148260, 2154597435], 'label': '768.1090187.4.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '4.e1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 59633166
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 96, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.l1', '12.p1'], 'contains': ['48.k1', '48.p1', '48.br1', '48.cv1', '48.eg1', '48.en1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8999, -1, 9630, -1], 'generators': [1083218598, 660749132, 1083098168, 1085750593, 1080656934], 'label': '768.1090187.24.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.y1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633167
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.226', 'aut_weyl_index': 288, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.g1', '12.m1', '12.n1', '12.p1', '12.q1'], 'contains': ['48.l1', '48.p1', '48.bs1', '48.cw1', '48.eh1', '48.eo1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8799, -1, 8422, -1], 'generators': [1083218598, 1083098168, 1085750593, 1080656934, 668673292], 'label': '768.1090187.24.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.z1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633168
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.f1', '12.e1', '12.k1', '12.r1'], 'contains': ['48.a1', '48.m1', '48.n1', '48.bt1', '48.cx1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9392, -1, 7246, -1], 'generators': [1083098168, 1085750593, 506952305, 508566806, 1081574431], 'label': '768.1090187.24.ba1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.ba1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633169
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 96, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.m1', '12.r1'], 'contains': ['48.m1', '48.p1', '48.bu1', '48.cy1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9846, -1, 9516, -1], 'generators': [1085750593, 506952305, 506930390, 1078887480, 1085785119], 'label': '768.1090187.24.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bb1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633170
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.226', 'aut_weyl_index': 288, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.g1', '12.l1', '12.n1', '12.r1', '12.s1'], 'contains': ['48.n1', '48.p1', '48.bv1', '48.cz1', '48.ei1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9041, -1, 6441, -1], 'generators': [1085750593, 508566806, 1078887480, 1085785119, 508576689], 'label': '768.1090187.24.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bc1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633171
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.a1', '12.h1', '12.o1', '12.p1', '12.q1', '12.r1', '12.s1'], 'contains': ['48.a1', '48.g1', '48.o1', '48.p1', '48.bw1', '48.bw2', '48.bz1', '48.cb1', '48.da1', '48.eq1', '48.er1', '48.es1', '48.es2', '48.et1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7646, -1, 4909, -1], 'generators': [1074660408, 1085750593, 1081574431, 1083229185, 1089936056], 'label': '768.1090187.24.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bd1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633172
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 384, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.j1'], 'contains': ['48.q1', '48.s1', '48.t1', '48.db1', '48.dc1', '48.eu1', '48.ev1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1978, -1, 1126, -1], 'generators': [1085750593, 1081547512, 1087390721, 1087276152, 1083229185], 'label': '768.1090187.24.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.be1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633173
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.d1', '12.w1'], 'contains': ['48.v1', '48.w1', '48.bb1', '48.be1', '48.bg1', '48.bj1', '48.bk1', '48.bl1', '48.cg1', '48.cr1', '48.db1', '48.ew1', '48.ex1', '48.ey1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [3737, -1, 2368, -1], 'generators': [1083180097, 1076429862, 1078860511, 1085750593, 1081574431], 'label': '768.1090187.24.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bf1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633174
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.d1', '12.w1', '12.x1'], 'contains': ['48.v1', '48.w1', '48.z1', '48.ba1', '48.bg1', '48.bj1', '48.bl2', '48.bo1', '48.by1', '48.cc1', '48.db1', '48.fa1', '48.fb1', '48.fd1', '48.fd2'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2810, -1, 1920, -1], 'generators': [1083180097, 1085750593, 1081547512, 1081574431, 1077347359], 'label': '768.1090187.24.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bg1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633175
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '32.51', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.e1', '12.t2', '12.v1'], 'contains': ['48.y1', '48.bc1', '48.bd1', '48.bq1', '48.bt1', '48.ck1', '48.cl1'], 'core': '192.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9419, -1, 8210, -1], 'generators': [1083180097, 1085750593, 1077385976, 668673292, 1089946655], 'label': '768.1090187.24.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bh1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633176
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 16, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.h1', '12.bk1', '16.i1', '16.j1'], 'core': '8.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [181, -1, 3719, -1], 'generators': [1074660408, 1081574431, 1076429862, 1084867622, 1083180097, 2150763522, 3234148260], 'label': '768.1090187.4.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.f1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 59633177
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.f1', '12.t1', '12.v1'], 'contains': ['48.x1', '48.y2', '48.bc1', '48.bn1', '48.br1', '48.bu1', '48.cj1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9897, -1, 9810, -1], 'generators': [660749132, 1085750593, 1080629953, 1089045606, 1089946655], 'label': '768.1090187.24.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bi1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633178
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.t1', '12.v1'], 'contains': ['48.y2', '48.bd1', '48.bs1', '48.bv1', '48.cm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9309, -1, 7920, -1], 'generators': [1083180097, 1085750593, 1074830054, 668673292, 1089946655], 'label': '768.1090187.24.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bj1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633179
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.t1', '12.w1'], 'contains': ['48.b1', '48.v1', '48.y2', '48.bb1', '48.bi1', '48.bp3', '48.bw1', '48.cn1', '48.ct1', '48.ez1', '48.ez2', '48.fc1'], 'core': '48.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7670, -1, 4826, -1], 'generators': [1083180097, 1078860511, 1083098168, 1085750593, 1081574431], 'label': '768.1090187.24.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bk1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633180
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.bk2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.t2', '12.u1', '12.w1'], 'contains': ['48.v1', '48.y1', '48.bb1', '48.bf1', '48.bi2', '48.bp1', '48.bw2', '48.cn1', '48.ct2', '48.ez3', '48.ez4', '48.fc2'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7720, -1, 4860, -1], 'generators': [1083180097, 1078860511, 1083098168, 1085750593, 1080656934], 'label': '768.1090187.24.bk2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bk2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633181
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.h1', '12.w1', '12.x1'], 'contains': ['48.v1', '48.w1', '48.y1', '48.y2', '48.z1', '48.be1', '48.bi1', '48.bi2', '48.bm1', '48.bp2', '48.bp4', '48.bx1', '48.bz1', '48.cq1', '48.fe1', '48.fe2', '48.ff1', '48.fg1'], 'core': '192.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [6009, -1, 4005, -1], 'generators': [1083180097, 1076429862, 1085750593, 1081574431, 1089985272], 'label': '768.1090187.24.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bl1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633182
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 768, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.x1'], 'contains': ['48.w1', '48.z1', '48.bh1', '48.bl1', '48.by1', '48.ca1', '48.dc1', '48.fh1', '48.fi1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1991, -1, 1160, -1], 'generators': [1083180097, 1078860511, 1085750593, 1087390721, 1083229185], 'label': '768.1090187.24.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bm1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633183
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.v1', '12.x1'], 'contains': ['48.y1', '48.y2', '48.z1', '48.ba1', '48.bp1', '48.bp3', '48.bx1', '48.cb1', '48.cd1', '48.fj1', '48.fk1', '48.fl1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7540, -1, 4490, -1], 'generators': [1083180097, 1085750593, 1081574431, 1089985272, 1077347359], 'label': '768.1090187.24.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bn1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633184
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.c1', '12.v1', '12.y1'], 'contains': ['48.ba1', '48.bc1', '48.bd1', '48.ce1', '48.cf1', '48.ch1', '48.ci1'], 'core': '192.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9525, -1, 8067, -1], 'generators': [1076429862, 1083180097, 1085750593, 506952305, 1087390721], 'label': '768.1090187.24.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bo1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633185
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '32.51', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.c1', '12.t1', '12.t2'], 'contains': ['48.bb1', '48.bc1', '48.bd1', '48.ch1', '48.ci1', '48.co1', '48.cp1'], 'core': '192.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9609, -1, 8282, -1], 'generators': [1083180097, 1078860511, 1085750593, 668673292, 1089946655], 'label': '768.1090187.24.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bp1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633186
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.d1', '12.x1'], 'contains': ['48.ba1', '48.be1', '48.bh1', '48.cc1', '48.cr1', '48.cs1', '48.dc1', '48.fm1', '48.fo1', '48.fr1', '48.ft1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2180, -1, 1397, -1], 'generators': [1076429862, 1074660408, 1078860511, 1085750593, 1081574431], 'label': '768.1090187.24.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bq1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633187
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 16, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['8.b1', '8.i1', '12.bo1', '16.k1'], 'core': '8.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1878, -1, 5167, -1], 'generators': [1076429862, 2150763522, 1074660408, 1084867622, 3229953892, 1081574431, 668673292], 'label': '768.1090187.4.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.g1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 59633188
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.g1', '12.e1', '12.t1', '12.y1'], 'contains': ['48.b1', '48.bc1', '48.bd1', '48.ck1', '48.cl1', '48.cu1', '48.cx1'], 'core': '48.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9364, -1, 7995, -1], 'generators': [1083180097, 1083098168, 1085750593, 506952305, 1081574431], 'label': '768.1090187.24.br1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.br1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633189
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.226', 'aut_weyl_index': 192, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.f1', '12.t2', '12.y1'], 'contains': ['48.bc1', '48.bf1', '48.cj1', '48.cv1', '48.cy1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [9445, -1, 9581, -1], 'generators': [1083180097, 1085750593, 506952305, 1078887480, 1085785119], 'label': '768.1090187.24.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bs1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633190
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.g1', '12.t2', '12.u1', '12.y1', '12.z1'], 'contains': ['48.bd1', '48.bf1', '48.cm1', '48.cw1', '48.cz1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9121, -1, 6960, -1], 'generators': [1083180097, 1085750593, 1078887480, 1085785119, 508576689], 'label': '768.1090187.24.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bt1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633191
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.b1', '12.h1', '12.w1', '12.y1', '12.z1'], 'contains': ['48.b1', '48.ba1', '48.be1', '48.bf1', '48.cd1', '48.cq1', '48.ct1', '48.ct2', '48.da1', '48.fn1', '48.fp1', '48.fq1', '48.fq2', '48.fs1'], 'core': '48.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7452, -1, 4659, -1], 'generators': [1074660408, 1085750593, 1081547512, 1081574431, 1083229185], 'label': '768.1090187.24.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bu1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633192
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '12.w1'], 'contains': ['48.bi1', '48.bi2', '48.bk1', '48.bl2', '48.bm1', '48.cg1', '48.cn1', '48.cq1', '48.db1', '48.fu1', '48.fv1', '48.fw1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4181, -1, 3146, -1], 'generators': [1076429862, 1085750593, 1081574431, 1089985272, 1076479078], 'label': '768.1090187.24.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bv1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633193
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '12.w1', '12.x1'], 'contains': ['48.bi1', '48.bi2', '48.bl1', '48.bm1', '48.bo1', '48.bx1', '48.cc1', '48.cd1', '48.db1', '48.ga1', '48.gb1', '48.gf1', '48.gf2'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3079, -1, 2296, -1], 'generators': [1085750593, 1081574431, 1089985272, 1077347359, 1084818534], 'label': '768.1090187.24.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bw1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633194
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '64.267', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.k1', '12.t2', '12.v1'], 'contains': ['48.bp1', '48.bq1', '48.bt1', '48.ch1', '48.ci1', '48.cj1', '48.cm1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9636, -1, 8562, -1], 'generators': [1078860511, 1085750593, 1089045606, 668673292, 1089946655], 'label': '768.1090187.24.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bx1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633195
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.l1', '12.t1', '12.v1'], 'contains': ['48.bp3', '48.br1', '48.bv1', '48.ch1', '48.ck1', '48.gg1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9200, -1, 7693, -1], 'generators': [1078860511, 660749132, 1085750593, 1087276152, 1089946655], 'label': '768.1090187.24.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.by1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633196
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.m1', '12.t1', '12.v1'], 'contains': ['48.bp3', '48.bs1', '48.bu1', '48.ci1', '48.cl1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9745, -1, 8792, -1], 'generators': [1085750593, 1077385976, 1085736031, 668673292, 1089946655], 'label': '768.1090187.24.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bz1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633197
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.o1', '12.w1'], 'contains': ['48.bi2', '48.bj1', '48.bp4', '48.bw1', '48.cg1', '48.ct1', '48.fx1', '48.fx2', '48.gc1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [6112, -1, 4523, -1], 'generators': [1074840641, 1078860511, 1083098168, 1085750593, 1081574431], 'label': '768.1090187.24.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ca1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633198
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.958', 'aut_weyl_index': 64, 'centralizer': '6.a1', 'complements': ['128.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.d1', '12.h1', '12.j1', '12.o1', '12.w1', '12.x1', '12.bi1', '12.bj1', '12.bk1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4019, 6594, 3780, 8387], 'generators': [1083180097, 1076429862, 1074660408, 1084867622, 1078860511, 1085750593, 1081574431], 'label': '768.1090187.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '12.b1', '24.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '192.1538', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633199
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.ca2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.o1', '12.w1', '12.ba1', '12.bb1'], 'contains': ['48.bi1', '48.bj1', '48.bp2', '48.bw2', '48.cg1', '48.ct2', '48.fx3', '48.fx4', '48.gc2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6221, -1, 4625, -1], 'generators': [1078860511, 1083098168, 1089963103, 1085750593, 1080656934], 'label': '768.1090187.24.ca2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ca2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633200
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.p1', '12.t1'], 'contains': ['48.br1', '48.bs1', '48.bw1', '48.co1', '48.cu1', '48.fy1', '48.gd1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8955, -1, 9385, -1], 'generators': [1083098168, 1085750593, 1081574431, 658250892, 1089936056], 'label': '768.1090187.24.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cb1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633201
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.cb2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.p1', '12.t2', '12.ba1', '12.bc1'], 'contains': ['48.bq1', '48.bw2', '48.co1', '48.cv1', '48.cw1', '48.fy2', '48.gd2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8775, -1, 8929, -1], 'generators': [1083098168, 1085750593, 1080656934, 668673292, 1087249055], 'label': '768.1090187.24.cb2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cb2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb2', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633202
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.q1', '12.u1', '12.bb1', '12.bc1'], 'contains': ['48.bw2', '48.cw1', '48.ge1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8668, -1, 6370, -1], 'generators': [1083098168, 1085750593, 1084856961, 1080656934, 668673292], 'label': '768.1090187.24.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cc1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633203
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.r1', '12.t1'], 'contains': ['48.bu1', '48.bv1', '48.bw1', '48.cp1', '48.cx1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [9582, -1, 7765, -1], 'generators': [1083098168, 1085750593, 506952305, 1081574431, 510198550], 'label': '768.1090187.24.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cd1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633204
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.cd2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.r1', '12.t2', '12.bb1', '12.bd1'], 'contains': ['48.bt1', '48.bw2', '48.cp1', '48.cy1', '48.cz1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9174, -1, 6882, -1], 'generators': [1085750593, 506952305, 508566806, 1078887480, 1085785119], 'label': '768.1090187.24.cd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cd2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd2', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633205
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.s1', '12.u1', '12.ba1', '12.bd1'], 'contains': ['48.bw2', '48.cz1', '48.fz1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8720, -1, 5851, -1], 'generators': [1085750593, 508566806, 1078887480, 1085785119, 518610417], 'label': '768.1090187.24.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ce1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633206
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.o1', '12.w1', '12.x1'], 'contains': ['48.bi1', '48.bi2', '48.bj1', '48.bl1', '48.bl2', '48.bp1', '48.bp2', '48.bp3', '48.bp4', '48.bx1', '48.by1', '48.bz1', '48.cq1', '48.cr1', '48.gh1', '48.gh2', '48.gi1', '48.gj1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5700, -1, 3758, -1], 'generators': [1076429862, 1085750593, 1081574431, 1089985272, 1083049080], 'label': '768.1090187.24.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cf1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633207
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.8', 'aut_weyl_index': 768, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '12.x1'], 'contains': ['48.bl2', '48.bm1', '48.bx1', '48.ca1', '48.dc1', '48.gk1', '48.gl1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2003, -1, 1431, -1], 'generators': [1078860511, 1085750593, 1087390721, 1087276152, 1083229185], 'label': '768.1090187.24.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cg1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633208
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.o1', '12.x1'], 'contains': ['48.bp2', '48.bp4', '48.bx1', '48.by1', '48.cb1', '48.cc1', '48.gn1', '48.gp1', '48.gu1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4842, -1, 3069, -1], 'generators': [1085750593, 1087298271, 1081574431, 1077347359, 1084818534], 'label': '768.1090187.24.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ch1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633209
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '512.7536911', 'aut_weyl_index': 36, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.a1'], 'contains': ['12.c1', '12.e1', '12.f1', '12.g1', '12.h1', '12.i1', '12.k1', '12.l1', '12.m1', '12.p1', '12.r1', '12.t1', '12.t2', '12.v1', '12.y1'], 'core': '24.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9317, -1, 7858, -1], 'generators': [1083180097, 1074660408, 1081547512, 1085750593, 1081574431, 670833676, 1083229185], 'label': '768.1090187.6.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633210
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.p1', '12.v1'], 'contains': ['48.bq1', '48.br1', '48.bs1', '48.cb1', '48.ce1', '48.go1', '48.gq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8931, -1, 9190, -1], 'generators': [1076429862, 1085750593, 1081596600, 658250892, 1080656934], 'label': '768.1090187.24.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.ci1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633211
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.r1', '12.v1'], 'contains': ['48.bt1', '48.bu1', '48.bv1', '48.cb1', '48.cf1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9471, -1, 7544, -1], 'generators': [1076429862, 1085750593, 506952305, 508566806, 1087390721], 'label': '768.1090187.24.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cj1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633212
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.a1', '12.w1', '12.bc1', '12.bd1'], 'contains': ['48.bk1', '48.bo1', '48.bw1', '48.bw2', '48.bz1', '48.da1', '48.gm1', '48.gr1', '48.gs1', '48.gs2', '48.gt1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5730, -1, 4591, -1], 'generators': [1074660408, 1085750593, 1081574431, 1083229185, 1087249055], 'label': '768.1090187.24.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ck1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633213
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.x1'], 'contains': ['48.bo1', '48.bz1', '48.ca1', '48.cb1', '48.cs1', '48.gv1', '48.gw1', '48.gx1', '48.gy1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2512, -1, 2123, -1], 'generators': [1076429862, 1074660408, 1085750593, 1081574431, 1081596600], 'label': '768.1090187.24.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cl1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633214
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '32.51', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.i1', '12.v1', '12.y1'], 'contains': ['48.cd1', '48.ce1', '48.cf1', '48.cj1', '48.ck1', '48.cl1', '48.cm1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9498, -1, 8138, -1], 'generators': [1076429862, 1089963103, 1085750593, 506952305, 1087390721], 'label': '768.1090187.24.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cm1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633215
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '64.267', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.i1', '12.t1', '12.t2'], 'contains': ['48.cj1', '48.ck1', '48.cl1', '48.cm1', '48.cn1', '48.co1', '48.cp1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9662, -1, 8491, -1], 'generators': [1085750593, 1089045606, 1077385976, 668673292, 1089946655], 'label': '768.1090187.24.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cn1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633216
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.j1', '12.x1'], 'contains': ['48.cc1', '48.cd1', '48.cq1', '48.cs1', '48.dc1', '48.gz1', '48.hf1', '48.hm1', '48.hr1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2285, -1, 1735, -1], 'generators': [1076429862, 1074660408, 1085750593, 1081574431, 1089985272], 'label': '768.1090187.24.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.co1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633217
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '32.51', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.k1', '12.t1', '12.y1'], 'contains': ['48.ch1', '48.ci1', '48.cj1', '48.cm1', '48.ct1', '48.cu1', '48.cx1'], 'core': '96.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9688, -1, 8354, -1], 'generators': [1083098168, 1085750593, 506952305, 1081574431, 1084818534], 'label': '768.1090187.24.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cp1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633218
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.l1', '12.t2', '12.y1', '12.ba1', '12.be1'], 'contains': ['48.ch1', '48.ck1', '48.ct2', '48.cv1', '48.cz1', '48.ha1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9017, -1, 6662, -1], 'generators': [1089963103, 1085750593, 1078887480, 1085785119, 508576689], 'label': '768.1090187.24.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cq1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633219
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.m1', '12.t2', '12.y1', '12.bb1', '12.bf1'], 'contains': ['48.ci1', '48.cl1', '48.ct2', '48.cw1', '48.cy1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9227, -1, 7842, -1], 'generators': [1089963103, 1085750593, 506952305, 1078887480, 1085785119], 'label': '768.1090187.24.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cr1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633220
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '512.7536911', 'aut_weyl_index': 36, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.a1'], 'contains': ['12.g1', '12.h1', '12.n1', '12.q1', '12.s1', '12.u1', '12.z1'], 'core': '24.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8635, -1, 6103, -1], 'generators': [1083180097, 1074660408, 1081547512, 1085750593, 1081574431, 1083229185, 668673292], 'label': '768.1090187.6.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633221
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '32.51', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.n1', '12.u1', '12.z1', '12.ba1', '12.bb1', '12.be1', '12.bf1'], 'contains': ['48.ct2', '48.cw1', '48.cz1', '48.hb1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8749, -1, 6143, -1], 'generators': [1089963103, 1085750593, 512648241, 1078887480, 1085785119], 'label': '768.1090187.24.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cs1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633222
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.b1', '12.o1', '12.w1', '12.be1', '12.bf1'], 'contains': ['48.cc1', '48.cq1', '48.cr1', '48.ct1', '48.ct2', '48.da1', '48.hc1', '48.hg1', '48.hh1', '48.hh2', '48.ho1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [5778, -1, 4039, -1], 'generators': [1074660408, 1078860511, 1085750593, 1081574431, 1083229185], 'label': '768.1090187.24.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ct1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633223
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.p1', '12.y1', '12.bc1', '12.be1', '12.bg1'], 'contains': ['48.ce1', '48.cu1', '48.cv1', '48.cw1', '48.da1', '48.hd1', '48.hi1', '48.hi2', '48.hp1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8694, -1, 8864, -1], 'generators': [1076429862, 1085750593, 1081574431, 504396399, 1085785119], 'label': '768.1090187.24.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cu1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633224
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.q1', '12.z1', '12.bc1', '12.bf1', '12.bg1'], 'contains': ['48.cw1', '48.da1', '48.hj1', '48.hq1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8598, -1, 6292, -1], 'generators': [1076429862, 1085750593, 1081574431, 1085785119, 514417711], 'label': '768.1090187.24.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cv1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633225
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.r1', '12.y1', '12.bd1', '12.bf1', '12.bh1'], 'contains': ['48.cf1', '48.cx1', '48.cy1', '48.cz1', '48.da1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [9093, -1, 6590, -1], 'generators': [1076429862, 1085750593, 506952305, 1081574431, 1085785119], 'label': '768.1090187.24.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cw1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cw1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633226
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.s1', '12.z1', '12.bd1', '12.be1', '12.bh1'], 'contains': ['48.cz1', '48.da1', '48.he1', '48.hk1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8639, -1, 5629, -1], 'generators': [1076429862, 1085750593, 1081574431, 512648241, 1085785119], 'label': '768.1090187.24.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cx1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633227
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.d1', '12.bi1', '12.bj1'], 'contains': ['48.dd1', '48.df1', '48.dg1', '48.di1', '48.dl1', '48.dn1', '48.dt1', '48.dy1', '48.ec1', '48.ed1', '48.eu1', '48.ew1', '48.ey1', '48.fa1', '48.fd1', '48.fh1', '48.fm1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2618, -1, 1464, -1], 'generators': [1083180097, 1078860511, 1083063654, 1081574431, 1077347359], 'label': '768.1090187.24.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cy1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633228
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.d1', '12.bj1'], 'contains': ['48.de1', '48.df1', '48.dg1', '48.dh1', '48.dl1', '48.dq1', '48.dt2', '48.dy1', '48.ea1', '48.ej1', '48.eu1', '48.ew1', '48.ex1', '48.fb1', '48.fd2', '48.fh1', '48.fo1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2564, -1, 1769, -1], 'generators': [1076429862, 1084833144, 1083180097, 1078860511, 1081574431], 'label': '768.1090187.24.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cz1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633229
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.bi1', '12.bk1'], 'contains': ['48.dd1', '48.dh1', '48.dm1', '48.dn1', '48.ea1', '48.ek1', '48.ev1', '48.ex1', '48.fa1', '48.fi1', '48.fr1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1875, -1, 1363, -1], 'generators': [1076429862, 1083180097, 1074660408, 1078860511, 1081574431], 'label': '768.1090187.24.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.da1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633230
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.bi1'], 'contains': ['48.df1', '48.di1', '48.dm1', '48.dt2', '48.ec1', '48.ep1', '48.ev1', '48.ey1', '48.fd2', '48.fi1', '48.ft1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1887, -1, 923, -1], 'generators': [1083180097, 1081547512, 1087390721, 1089060216, 1083229185], 'label': '768.1090187.24.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.db1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633231
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '512.7536911', 'aut_weyl_index': 36, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.a1'], 'contains': ['12.l1', '12.n1', '12.o1', '12.p1', '12.s1', '12.ba1', '12.be1', '12.bl1', '12.bm1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8574, -1, 5967, -1], 'generators': [1074660408, 1078860511, 1085750593, 1081574431, 670833676, 1083229185, 1084818534], 'label': '768.1090187.6.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633232
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.bi1'], 'contains': ['48.dd1', '48.di1', '48.dj1', '48.dj2', '48.do1', '48.eb1', '48.ee1', '48.ee3', '48.eq1', '48.ez1', '48.ez3', '48.fg1', '48.fj1', '48.fn1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6099, -1, 4287, -1], 'generators': [1074724198, 1083180097, 1078860511, 1081574431, 1077347359], 'label': '768.1090187.24.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dc1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633233
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dd1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.h1', '12.bi1', '12.bj1'], 'contains': ['48.df1', '48.dg1', '48.dh1', '48.di1', '48.dj1', '48.dj2', '48.du1', '48.dx1', '48.dx2', '48.dz1', '48.eb1', '48.ee2', '48.ee4', '48.er1', '48.ez2', '48.ez4', '48.fe1', '48.fe2', '48.ff1', '48.fg1', '48.fl1', '48.fp1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [4213, -1, 3357, -1], 'generators': [1076429862, 1074724198, 1083180097, 1081574431, 1078991590], 'label': '768.1090187.24.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dd1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633234
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.bj1'], 'contains': ['48.de1', '48.dg1', '48.dj1', '48.dk2', '48.dr1', '48.dx1', '48.ee1', '48.el2', '48.es1', '48.ez1', '48.fc2', '48.fe1', '48.fk1', '48.fq1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6982, -1, 4456, -1], 'generators': [1083180097, 1083098168, 1074830054, 1087421791, 1080656934], 'label': '768.1090187.24.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.de1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633235
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.de2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.bj1'], 'contains': ['48.de1', '48.dg1', '48.dj2', '48.dk1', '48.dr1', '48.dx2', '48.ee3', '48.el1', '48.es2', '48.ez3', '48.fc1', '48.fe2', '48.fk1', '48.fq2'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [7280, -1, 4557, -1], 'generators': [1083180097, 1083098168, 1081574431, 1089985272, 1077411137], 'label': '768.1090187.24.de2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.de2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633236
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.df1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.bj1', '12.bk1'], 'contains': ['48.dd1', '48.dh1', '48.dk1', '48.dk2', '48.do1', '48.dz1', '48.el1', '48.el2', '48.et1', '48.fc1', '48.fc2', '48.ff1', '48.fj1', '48.fs1'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [4618, -1, 4320, -1], 'generators': [1083180097, 1074660408, 1081547512, 1081574431, 1083229185], 'label': '768.1090187.24.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.df1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.df1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633237
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.j1', '12.bi1', '12.bj1'], 'contains': ['48.dn1', '48.do1', '48.dt2', '48.du1', '48.dx1', '48.dx2', '48.eb1', '48.ed1', '48.eu1', '48.fu1', '48.fw1', '48.ga1', '48.gf1', '48.gk1', '48.gz1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2686, -1, 1988, -1], 'generators': [1083063654, 1081574431, 1089985272, 1076479078, 1077347359], 'label': '768.1090187.24.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dg1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633238
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '24.dh1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '32.51', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.l1', '12.bl1', '12.bm1'], 'contains': ['48.dv1', '48.dw1', '48.ee4', '48.eg1', '48.ei1', '48.gg1', '48.ha1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [8554, -1, 6071, -1], 'generators': [1087290726, 660749132, 1087407169, 1076468417, 1089946655], 'label': '768.1090187.24.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.dh1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633239
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '24.di1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '32.51', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.n1', '12.bl1', '12.bm1'], 'contains': ['48.ee4', '48.eh1', '48.ei1', '48.hb1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [8378, -1, 5928, -1], 'generators': [1087290726, 1074698975, 668673292, 1083049080, 1089946655], 'label': '768.1090187.24.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.di1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.di1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633240
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dj1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.j1', '12.bj1'], 'contains': ['48.dq1', '48.dr1', '48.dt1', '48.du1', '48.dx1', '48.dx2', '48.dz1', '48.ej1', '48.eu1', '48.fu1', '48.fv1', '48.gb1', '48.gf2', '48.gk1', '48.hf1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2852, -1, 2225, -1], 'generators': [1076429862, 1084833144, 1081574431, 1089985272, 1076479078], 'label': '768.1090187.24.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dj1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633241
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.j1', '12.bi1', '12.bk1'], 'contains': ['48.dn1', '48.do1', '48.dz1', '48.ek1', '48.ev1', '48.fv1', '48.ga1', '48.gl1', '48.hm1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2047, -1, 1651, -1], 'generators': [1076429862, 1074660408, 1081574431, 1089985272, 1076479078], 'label': '768.1090187.24.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dk1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633242
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '512.7536911', 'aut_weyl_index': 36, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.a1'], 'contains': ['12.m1', '12.n1', '12.o1', '12.q1', '12.r1', '12.bb1', '12.bf1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8742, -1, 6326, -1], 'generators': [1074660408, 1078860511, 1085750593, 1081574431, 1083229185, 668673292, 1084818534], 'label': '768.1090187.6.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633243
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.j1', '12.bi1'], 'contains': ['48.dt1', '48.du1', '48.eb1', '48.ep1', '48.ev1', '48.fw1', '48.gf2', '48.gl1', '48.hr1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2028, -1, 1194, -1], 'generators': [1078860511, 1087390721, 1089060216, 1083229185, 1084818534], 'label': '768.1090187.24.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dl1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633244
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dm1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.o1', '12.bi1', '12.bl1'], 'contains': ['48.dn1', '48.eb1', '48.ec1', '48.ee2', '48.ee4', '48.eq1', '48.fx1', '48.fx3', '48.gj1', '48.gn1', '48.hc1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5584, -1, 3289, -1], 'generators': [1074724198, 1081547512, 1081574431, 1077347359, 1084818534], 'label': '768.1090187.24.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dm1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633245
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.dn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.p1', '12.bl1'], 'contains': ['48.dp1', '48.ef1', '48.eg1', '48.eh1', '48.eq1', '48.fy1', '48.fy2', '48.go1', '48.hd1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8506, -1, 9320, -1], 'generators': [1076429862, 1080655224, 1081596600, 658250892, 1080656934], 'label': '768.1090187.24.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.dn1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633246
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.do1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.s1', '12.bl1'], 'contains': ['48.ei1', '48.eq1', '48.fz1', '48.he1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8224, -1, 5474, -1], 'generators': [1076429862, 1087390721, 1087421791, 512648241, 518587222], 'label': '768.1090187.24.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.do1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.do1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633247
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dp1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.o1', '12.bi1', '12.bj1'], 'contains': ['48.dt1', '48.dt2', '48.dx1', '48.dx2', '48.dy1', '48.dz1', '48.ea1', '48.eb1', '48.ec1', '48.ee1', '48.ee2', '48.ee3', '48.ee4', '48.er1', '48.fx2', '48.fx4', '48.gh1', '48.gh2', '48.gi1', '48.gj1', '48.gu1', '48.hg1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [3959, -1, 3019, -1], 'generators': [1076429862, 1074724198, 1078860511, 1081574431, 1083049080], 'label': '768.1090187.24.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dp1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633248
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.o1', '12.bj1'], 'contains': ['48.dq1', '48.dx2', '48.dy1', '48.ee2', '48.el2', '48.es1', '48.fx1', '48.gc2', '48.gh1', '48.gp1', '48.hh1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5625, -1, 3792, -1], 'generators': [1078860511, 1083098168, 1087421791, 1087276152, 1080656934], 'label': '768.1090187.24.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dq1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633249
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dq2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.o1', '12.bj1', '12.bm1'], 'contains': ['48.dq1', '48.dx1', '48.dy1', '48.ee4', '48.el1', '48.es2', '48.fx3', '48.gc1', '48.gh2', '48.gp1', '48.hh2'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [5718, -1, 3859, -1], 'generators': [1078860511, 1083098168, 1081574431, 1076479078, 1077411137], 'label': '768.1090187.24.dq2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dq2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dq2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633250
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.dr1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.p1', '12.bm1'], 'contains': ['48.ds1', '48.eg1', '48.eh1', '48.em1', '48.es2', '48.fy2', '48.gd1', '48.gq1', '48.hi1'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [8530, -1, 9255, -1], 'generators': [1083098168, 1081574431, 658250892, 1089936056, 1077411137], 'label': '768.1090187.24.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.dr1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633251
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.dr2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.p1', '12.bn1'], 'contains': ['48.ds1', '48.ef1', '48.en1', '48.eo1', '48.es1', '48.fy1', '48.gd2', '48.gq1', '48.hi2'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8404, -1, 9451, -1], 'generators': [1083218598, 660749132, 1083098168, 1087421791, 1080656934], 'label': '768.1090187.24.dr2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.dr2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dr2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633252
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.ds1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.q1', '12.bn1'], 'contains': ['48.eo1', '48.es1', '48.ge1', '48.hj1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8146, -1, 6805, -1], 'generators': [1083218598, 1083098168, 1087421791, 1080656934, 668673292], 'label': '768.1090187.24.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ds1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ds1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633253
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 48, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.p1', '12.q1', '12.bc1', '12.bg1', '12.bn1', '12.bo1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8126, -1, 6460, -1], 'generators': [1076429862, 1074660408, 1084867622, 1085750593, 1081574431, 1087249055, 668673292], 'label': '768.1090187.6.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633254
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.dt1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.s1', '12.bm1'], 'contains': ['48.ei1', '48.es2', '48.fz1', '48.hk1'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [8323, -1, 5552, -1], 'generators': [1083098168, 1083063654, 1081574431, 512648241, 518587222], 'label': '768.1090187.24.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.dt1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633255
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.du1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.o1', '12.bj1', '12.bk1'], 'contains': ['48.dn1', '48.dz1', '48.ea1', '48.el1', '48.el2', '48.et1', '48.gc1', '48.gc2', '48.gi1', '48.gn1', '48.ho1'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [4301, -1, 3724, -1], 'generators': [1074660408, 1078860511, 1081574431, 1083229185, 1084818534], 'label': '768.1090187.24.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.du1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.du1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633256
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.dv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.p1', '12.bn1', '12.bo1'], 'contains': ['48.dp1', '48.em1', '48.en1', '48.eo1', '48.et1', '48.gd1', '48.gd2', '48.go1', '48.hp1'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [8250, -1, 8994, -1], 'generators': [1074660408, 1081574431, 670833676, 1083229185, 1089936056], 'label': '768.1090187.24.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.dv1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633257
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.dw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.q1', '12.bn1', '12.bo1'], 'contains': ['48.eo1', '48.et1', '48.ge1', '48.hq1'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [7917, -1, 6512, -1], 'generators': [1074660408, 1081574431, 1083229185, 668673292, 1089936056], 'label': '768.1090187.24.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.dw1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633258
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '24.dx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.bi1'], 'contains': ['48.ed1', '48.ek1', '48.ep1', '48.eq1', '48.er1', '48.gm1', '48.gr1', '48.gv1', '48.gx1', '48.gy1', '48.hl1'], 'core': '384.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2673, -1, 2330, -1], 'generators': [1076429862, 1074724198, 1074660408, 1081574431, 1087249055], 'label': '768.1090187.24.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dx1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633259
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '24.dy1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.a1', '12.bj1', '12.bn1'], 'contains': ['48.ed1', '48.ej1', '48.er1', '48.es1', '48.es2', '48.et1', '48.gr1', '48.gs1', '48.gs2', '48.gt1', '48.gv1', '48.gw1', '48.hn1'], 'core': '96.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [5278, -1, 4388, -1], 'generators': [1074660408, 1083063654, 1081574431, 1083229185, 1087249055], 'label': '768.1090187.24.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dy1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dy1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633260
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.dz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.w1', '12.bi1'], 'contains': ['48.ey1', '48.ez2', '48.ez4', '48.fa1', '48.fg1', '48.fn1', '48.fw1', '48.fx2', '48.fx4', '48.ga1', '48.gj1', '48.gm1', '48.hc1'], 'core': '768.a1', 'coset_action_label': '24T2472', 'count': 72, 'diagramx': [4133, -1, 2985, -1], 'generators': [1074724198, 1083180097, 1081547512, 1081574431, 1077347359], 'label': '768.1090187.24.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dz1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633261
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.ea1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['12.w1', '12.bi1', '12.bj1'], 'contains': ['48.ew1', '48.ex1', '48.ey1', '48.ez1', '48.ez2', '48.ez3', '48.ez4', '48.fd1', '48.fd2', '48.fe1', '48.fe2', '48.ff1', '48.fg1', '48.fp1', '48.fu1', '48.fv1', '48.fw1', '48.fx1', '48.fx2', '48.fx3', '48.fx4', '48.gf1', '48.gf2', '48.gh1', '48.gh2', '48.gi1', '48.gj1', '48.gr1', '48.hg1'], 'core': '768.a1', 'coset_action_label': '24T2470', 'count': 288, 'diagramx': [3813, -1, 2951, -1], 'generators': [1076429862, 1074724198, 1083180097, 1078860511, 1081574431], 'label': '768.1090187.24.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ea1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ea1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633262
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.eb1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.w1', '12.bj1'], 'contains': ['48.ew1', '48.ez2', '48.fb1', '48.fc2', '48.fe2', '48.fq1', '48.fu1', '48.fx2', '48.gb1', '48.gc2', '48.gh2', '48.gs1', '48.hh1'], 'core': '768.a1', 'coset_action_label': '24T1974', 'count': 72, 'diagramx': [5429, -1, 3589, -1], 'generators': [1083180097, 1078860511, 1083098168, 1087421791, 1080656934], 'label': '768.1090187.24.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.eb1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633263
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.eb2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.w1', '12.bj1'], 'contains': ['48.ew1', '48.ez4', '48.fb1', '48.fc1', '48.fe1', '48.fq2', '48.fu1', '48.fx4', '48.gb1', '48.gc1', '48.gh1', '48.gs2', '48.hh2'], 'core': '192.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [5416, -1, 3690, -1], 'generators': [1083180097, 1078860511, 1083098168, 1081574431, 1077411137], 'label': '768.1090187.24.eb2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.eb2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eb2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633264
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4608.dp', 'aut_weyl_index': 4, 'centralizer': '96.a1', 'complements': ['384.l1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.f1', '6.a1', '8.c1', '8.d1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1848, 7659, 3853, 8292], 'generators': [1074660408, 1081574431, 1076429862, 1084867622, 1083180097, 2150763522, 1085750593, 3234148260], 'label': '768.1090187.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '192.1538', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 59633265
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 48, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '12.r1', '12.s1', '12.bd1', '12.bh1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8552, -1, 5579, -1], 'generators': [1074660408, 1081574431, 1076429862, 1084867622, 506952305, 1085750593, 508566806], 'label': '768.1090187.6.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.g1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633266
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.ec1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.w1', '12.bj1', '12.bk1'], 'contains': ['48.ex1', '48.fa1', '48.fc1', '48.fc2', '48.ff1', '48.fs1', '48.fv1', '48.ga1', '48.gc1', '48.gc2', '48.gi1', '48.gt1', '48.ho1'], 'core': '192.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [4201, -1, 3656, -1], 'generators': [1083180097, 1074660408, 1078860511, 1081574431, 1083229185], 'label': '768.1090187.24.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ec1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ec1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633267
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.ed1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.x1', '12.bi1', '12.bj1'], 'contains': ['48.fa1', '48.fd2', '48.fe1', '48.fe2', '48.fg1', '48.fh1', '48.fj1', '48.fl1', '48.fm1', '48.ga1', '48.gf2', '48.gh1', '48.gh2', '48.gj1', '48.gk1', '48.gn1', '48.gu1', '48.gv1', '48.gz1'], 'core': '768.a1', 'coset_action_label': '24T2469', 'count': 144, 'diagramx': [2865, -1, 2089, -1], 'generators': [1083180097, 1083063654, 1081574431, 1089985272, 1077347359], 'label': '768.1090187.24.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ed1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ed1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633268
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.ee1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.x1', '12.bj1'], 'contains': ['48.fb1', '48.fd1', '48.fe1', '48.fe2', '48.ff1', '48.fh1', '48.fk1', '48.fl1', '48.fo1', '48.gb1', '48.gf1', '48.gh1', '48.gh2', '48.gi1', '48.gk1', '48.gp1', '48.gu1', '48.gw1', '48.hf1'], 'core': '768.a1', 'coset_action_label': '24T2204', 'count': 144, 'diagramx': [3027, -1, 2262, -1], 'generators': [1081574431, 1076429862, 1089985272, 1084833144, 1083180097], 'label': '768.1090187.24.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ee1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ee1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633269
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.ef1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.x1', '12.bi1', '12.bk1'], 'contains': ['48.fa1', '48.ff1', '48.fi1', '48.fj1', '48.fr1', '48.ga1', '48.gi1', '48.gl1', '48.gn1', '48.gx1', '48.hm1'], 'core': '768.a1', 'coset_action_label': '24T2476', 'count': 48, 'diagramx': [2206, -1, 1852, -1], 'generators': [1076429862, 1083180097, 1074660408, 1081574431, 1089985272], 'label': '768.1090187.24.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ef1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ef1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633270
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.eg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.x1', '12.bi1'], 'contains': ['48.fd1', '48.fg1', '48.fi1', '48.fl1', '48.ft1', '48.gf1', '48.gj1', '48.gl1', '48.gu1', '48.gy1', '48.hr1'], 'core': '768.a1', 'coset_action_label': '24T2471', 'count': 48, 'diagramx': [2193, -1, 1228, -1], 'generators': [1083180097, 1078860511, 1087390721, 1089060216, 1083229185], 'label': '768.1090187.24.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.eg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633271
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.eh1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.bi1'], 'contains': ['48.fm1', '48.fn1', '48.fp1', '48.fr1', '48.ft1', '48.gz1', '48.hc1', '48.hg1', '48.hl1', '48.hm1', '48.hr1'], 'core': '768.a1', 'coset_action_label': '24T2475', 'count': 24, 'diagramx': [2303, -1, 1886, -1], 'generators': [1074724198, 1076429862, 1074660408, 1078860511, 1081574431], 'label': '768.1090187.24.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.eh1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633272
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.ei1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.b1', '12.bj1'], 'contains': ['48.fm1', '48.fo1', '48.fp1', '48.fq1', '48.fq2', '48.fs1', '48.gz1', '48.hf1', '48.hg1', '48.hh1', '48.hh2', '48.hn1', '48.ho1'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [4162, -1, 3622, -1], 'generators': [1074660408, 1078860511, 1083063654, 1081574431, 1083229185], 'label': '768.1090187.24.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ei1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ei1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633273
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.ej1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 512, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.h1', '12.b1', '12.bk1'], 'contains': ['48.c1', '48.fr1', '48.fs1', '48.hm1', '48.ho1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1569, -1, 3555, -1], 'generators': [1076429862, 1074660408, 1084867622, 1078860511, 1081574431], 'label': '768.1090187.24.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.ej1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ej1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633274
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '24.ek1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['12.ba1', '12.bl1', '12.bm1'], 'contains': ['48.fx3', '48.fy2', '48.fz1', '48.ha1', '48.hb1'], 'core': '768.a1', 'coset_action_label': '24T2498', 'count': 288, 'diagramx': [8430, -1, 5776, -1], 'generators': [1087290726, 1076468417, 668673292, 1083049080, 1089946655], 'label': '768.1090187.24.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.ek1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ek1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633275
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.el1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.bc1', '12.bn1'], 'contains': ['48.gd2', '48.ge1', '48.gs1', '48.hi2', '48.hj1'], 'core': '768.a1', 'coset_action_label': '24T1932', 'count': 72, 'diagramx': [8103, -1, 7106, -1], 'generators': [1083098168, 1087421791, 1080656934, 668673292, 1087249055], 'label': '768.1090187.24.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.el1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.el1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633276
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['3.a1'], 'contains': ['12.t2', '12.u1', '12.w1', '12.y1', '12.z1', '12.ba1', '12.bb1', '12.bc1', '12.bd1', '12.be1', '12.bf1'], 'core': '48.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8695, -1, 6149, -1], 'generators': [1083180097, 1074660408, 1078860511, 1085750593, 1081574431, 1083229185, 668673292], 'label': '768.1090187.6.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633277
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.em1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.bc1', '12.bn1', '12.bo1'], 'contains': ['48.gd2', '48.ge1', '48.gt1', '48.hp1', '48.hq1'], 'core': '192.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [8077, -1, 6730, -1], 'generators': [1074660408, 1081574431, 1083229185, 668673292, 1087249055], 'label': '768.1090187.24.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.em1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.em1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633278
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.en1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.be1', '12.bl1'], 'contains': ['48.ha1', '48.hb1', '48.hc1', '48.hd1', '48.he1'], 'core': '768.a1', 'coset_action_label': '24T2525', 'count': 144, 'diagramx': [8351, -1, 5704, -1], 'generators': [1076429862, 1087390721, 1076479078, 1087421791, 512648241], 'label': '768.1090187.24.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.en1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.en1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633279
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.eo1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.be1', '12.bm1'], 'contains': ['48.ha1', '48.hb1', '48.hh2', '48.hi1', '48.hk1'], 'core': '192.c1', 'coset_action_label': None, 'count': 144, 'diagramx': [8473, -1, 6003, -1], 'generators': [1083098168, 1083063654, 1081574431, 1076479078, 512648241], 'label': '768.1090187.24.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.eo1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eo1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633280
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.ep1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bg1', '12.bn1'], 'contains': ['48.hi2', '48.hj1', '48.hn1', '48.hp1', '48.hq1'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [7889, -1, 7035, -1], 'generators': [1076429862, 1074724198, 1081574431, 504396399, 1085785119], 'label': '768.1090187.24.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ep1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ep1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633281
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.eq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.i1', '12.bg1', '12.bo1'], 'contains': ['48.c1', '48.hp1', '48.hq1'], 'core': '48.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [4643, -1, 6217, -1], 'generators': [1076429862, 1074660408, 1084867622, 1081574431, 504396399], 'label': '768.1090187.24.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.eq1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633282
    {'ambient': '768.1090187', 'aut_centralizer_order': 72, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.d1', '16.b1'], 'contains': ['64.a1', '64.b1', '64.e1', '96.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [172, -1, 5487, -1], 'generators': [2148207653, 1083180097, 1085750593, 3234148260], 'label': '768.1090187.32.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '32.a1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633283
    {'ambient': '768.1090187', 'aut_centralizer_order': 24, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.38', 'aut_weyl_index': 384, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '16.b1'], 'contains': ['64.a1', '64.c1', '64.f1', '96.h1'], 'core': '192.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4652, -1, 6455, -1], 'generators': [2148207653, 660749132, 3229953892, 1085750593], 'label': '768.1090187.32.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '32.b1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 59633284
    {'ambient': '768.1090187', 'aut_centralizer_order': 24, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.38', 'aut_weyl_index': 384, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '16.b1'], 'contains': ['64.a1', '64.d1', '96.i1'], 'core': '192.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5176, -1, 6576, -1], 'generators': [2159201282, 654646443, 1085750593, 506952305], 'label': '768.1090187.32.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '32.c1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 59633285
    {'ambient': '768.1090187', 'aut_centralizer_order': 12, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.14', 'aut_weyl_index': 768, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '16.b1'], 'contains': ['64.b1', '64.c1', '64.d1', '96.n1'], 'core': '192.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [4688, -1, 6522, -1], 'generators': [1083180097, 1085750593, 506952305, 2148863004], 'label': '768.1090187.32.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '32.d1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 59633286
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '16.c1', '16.e1', '16.g1', '16.h1'], 'contains': ['64.g1', '96.b1', '128.a1'], 'core': '96.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1619, -1, 6350, -1], 'generators': [2150763522, 1083098168, 1085750593, 1081574431], 'label': '768.1090187.32.e1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '32.e1', 'projective_image': '384.20163', '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': '24.12'}
  • id: 59633287
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 96, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.b1', '12.y1', '12.z1', '12.be1', '12.bf1', '12.bg1', '12.bh1'], 'core': '12.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8535, -1, 6056, -1], 'generators': [1074660408, 1081574431, 1076429862, 1084867622, 506952305, 1083180097, 1085750593], 'label': '768.1090187.6.i1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.i1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633288
    {'ambient': '768.1090187', 'aut_centralizer_order': 96, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '16.d1', '16.f1'], 'contains': ['64.h1', '96.bm1', '128.a1'], 'core': '384.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [64, -1, 152, -1], 'generators': [2150763522, 1085750593, 1087390721, 1083229185], 'label': '768.1090187.32.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '32.f1', 'projective_image': '384.20163', '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': '12.3'}
  • id: 59633289
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '16.c1', '16.i1', '16.k1'], 'contains': ['64.g1', '96.c1', '128.b1'], 'core': '96.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [143, -1, 6244, -1], 'generators': [1083098168, 3229953892, 1081574431, 2154597435], 'label': '768.1090187.32.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '32.g1', 'projective_image': '384.20100', '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': '24.12'}
  • id: 59633290
    {'ambient': '768.1090187', 'aut_centralizer_order': 48, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '16.d1', '16.j1'], 'contains': ['64.h1', '96.cr1', '128.b1'], 'core': '384.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [9, -1, 80, -1], 'generators': [3229953892, 2160806949, 1087390721, 1083229185], 'label': '768.1090187.32.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '32.h1', 'projective_image': '384.20100', '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': '12.3'}
  • id: 59633291
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.h1', '16.e1', '16.i1'], 'contains': ['64.g1', '96.dj1', '128.c1'], 'core': '192.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [109, -1, 5716, -1], 'generators': [1083098168, 1081574431, 3234148260, 2154597435], 'label': '768.1090187.32.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '32.i1', 'projective_image': '768.1090187', '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': '12.3'}
  • id: 59633292
    {'ambient': '768.1090187', 'aut_centralizer_order': 24, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.h1', '16.f1', '16.j1'], 'contains': ['64.h1', '96.dp1', '128.c1'], 'core': '768.a1', 'coset_action_label': '32T34970', 'count': 32, 'diagramx': [38, -1, 24, -1], 'generators': [2160806949, 1087390721, 3234148260, 1083229185], 'label': '768.1090187.32.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '32.j1', 'projective_image': '768.1090187', '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': '12.3'}
  • id: 59633293
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.i1', '16.g1', '16.k1'], 'contains': ['64.g1', '96.fz1', '128.d1'], 'core': '192.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [1597, -1, 6408, -1], 'generators': [1083098168, 1081574431, 504396399, 2154990594], 'label': '768.1090187.32.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '32.k1', 'projective_image': '768.1090187', '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': '24.12'}
  • id: 59633294
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['16.c1', '24.a1', '24.w1', '24.x1', '24.ba1', '24.bd1'], 'contains': ['96.b1', '96.c1', '96.d1', '96.v1', '96.cl1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8212, 6206, 6289, 8144], 'generators': [1083098168, 1085750593, 1081574431, 1081596600], 'label': '768.1090187.48.a1', 'mobius_quo': -2, 'mobius_sub': 24, 'normal_closure': '48.a1', 'normal_contained_in': ['12.a1', '24.a1'], 'normal_contains': ['96.b1', '96.c1', '192.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '192.1538', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633295
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': ['16.k1'], 'conjugacy_class_count': 6, 'contained_in': ['16.e1', '24.a1', '24.bk1', '24.br1', '24.bu1'], 'contains': ['96.b1', '96.k1', '96.ba1', '96.de1', '96.dj1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8032, 5389, 6165, 7273], 'generators': [1083098168, 1085750593, 1081574431, 1089985272], 'label': '768.1090187.48.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.b1', 'normal_contained_in': ['12.b1', '24.a1'], 'normal_contains': ['96.b1', '192.b1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '384.20163', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633296
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '48.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 512, 'centralizer': '6.a1', 'complements': ['16.b1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.b1', '24.c1', '24.ej1', '24.eq1'], 'contains': ['96.fx1', '96.gc1'], 'core': '48.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1632, 3427, 4354, 5682], 'generators': [1076429862, 1074660408, 1084867622, 1081574431], 'label': '768.1090187.48.c1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': ['16.a1', '24.b1', '24.c1'], 'normal_contains': ['192.c1'], 'normalizer': '1.a1', 'old_label': '48.c1', 'projective_image': '768.1090187', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633297
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '24.d1', '24.e1', '24.f1', '24.g1', '24.h1'], 'contains': ['96.a1', '96.d1', '96.g1', '96.j1', '96.k1', '96.br1', '96.bs1'], 'core': '96.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8289, -1, 5962, -1], 'generators': [1083180097, 1085750593, 1080629953, 1078887480], 'label': '768.1090187.48.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.d1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633298
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '8.a1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 32, 'centralizer': '96.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'contains': ['16.a1', '24.b1', '32.e1', '32.f1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1921, 4373, 3924, 3974], 'generators': [1076429862, 1074660408, 2150763522, 1084867622, 1085750593, 1081574431], 'label': '768.1090187.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'normal_contains': ['16.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '384.20163', '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': '96.227'}
  • id: 59633299
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.g1', '24.i1'], 'contains': ['96.a1', '96.e1', '96.f1', '96.l1', '96.m1', '96.bt1', '96.bu1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5814, -1, 1886, -1], 'generators': [1076429862, 1083180097, 1085750593, 1078991590], 'label': '768.1090187.48.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.e1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633300
    {'ambient': '768.1090187', 'aut_centralizer_order': 48, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.e1'], 'contains': ['96.a1', '96.h1', '96.i1', '96.n1'], 'core': '96.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9468, -1, 9560, -1], 'generators': [1083180097, 1085750593, 1080629953, 658250892], 'label': '768.1090187.48.f1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.f1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633301
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.d1', '24.j1', '24.k1', '24.l1', '24.m1', '24.v1', '24.bd1'], 'contains': ['96.d1', '96.e1', '96.p1', '96.x1', '96.bb1', '96.bv1', '96.bz1', '96.cc1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7475, -1, 4117, -1], 'generators': [1085750593, 1081574431, 1077347359, 1087249055], 'label': '768.1090187.48.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.g1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633302
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.g1', '24.j1', '24.t1', '24.u1', '24.w1', '24.w2'], 'contains': ['96.d1', '96.f1', '96.g1', '96.q1', '96.y1', '96.bw1', '96.cd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6991, -1, 4625, -1], 'generators': [1085750593, 1078991590, 1078887480, 1084818534], 'label': '768.1090187.48.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.h1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633303
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.d1', '24.n1', '24.o1', '24.u1', '24.w1', '24.w2'], 'contains': ['96.d1', '96.f1', '96.r1', '96.z1', '96.bx1', '96.ce1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7894, -1, 5268, -1], 'generators': [1085750593, 1081547512, 1078887480, 1083049080], 'label': '768.1090187.48.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.i1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633304
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '24.k1', '24.q1', '24.r1', '24.t1', '24.w2'], 'contains': ['96.d1', '96.g1', '96.s1', '96.ba1', '96.by1', '96.cf1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8135, -1, 5879, -1], 'generators': [1085750593, 1076479078, 1087429350, 1078887480], 'label': '768.1090187.48.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.j1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633305
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.j2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.h1', '24.k1', '24.p1', '24.s1', '24.t1', '24.w1'], 'contains': ['96.d1', '96.g1', '96.s2', '96.ba2', '96.by2', '96.cf2'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8237, -1, 6030, -1], 'generators': [1077396575, 1085750593, 1087298271, 1078887480], 'label': '768.1090187.48.j2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.j2', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633306
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.e1', '24.l1', '24.n1', '24.p1', '24.q1', '24.x1', '24.y1'], 'contains': ['96.d1', '96.h1', '96.t1', '96.bc1', '96.ca1', '96.cg1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9340, -1, 9783, -1], 'generators': [1089018497, 660749132, 1085750593, 1089946655], 'label': '768.1090187.48.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.k1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633307
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.f1', '24.l1', '24.o1', '24.r1', '24.s1', '24.x1', '24.z1'], 'contains': ['96.d1', '96.bd1', '96.cb1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9320, -1, 8176, -1], 'generators': [1089018497, 1085750593, 668673292, 1089946655], 'label': '768.1090187.48.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.l1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633308
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.e1', '24.m1', '24.o1', '24.p1', '24.r1', '24.ba1', '24.bb1'], 'contains': ['96.d1', '96.i1', '96.u1', '96.be1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9905, -1, 9621, -1], 'generators': [516831830, 1085750593, 506952305, 1078887480], 'label': '768.1090187.48.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.m1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633309
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 32, 'centralizer': '96.a1', 'complements': ['96.gg1', '96.n1', '96.bp1', '96.gh1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.f1', '4.g1'], 'contains': ['16.a1', '24.c1', '32.g1', '32.h1'], 'core': '8.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [168, 2121, 3846, 6838], 'generators': [1076429862, 1074660408, 2150763522, 1084867622, 3229953892, 1081574431], 'label': '768.1090187.8.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.a1', '24.c1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '384.20100', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 59633310
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.f1', '24.m1', '24.n1', '24.q1', '24.s1', '24.ba1', '24.bc1'], 'contains': ['96.d1', '96.bf1', '96.ch1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9358, -1, 7318, -1], 'generators': [1085750593, 511124502, 512648241, 1078887480], 'label': '768.1090187.48.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.n1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633311
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.g1', '24.t1', '24.u1', '24.v1', '24.bd1'], 'contains': ['96.d1', '96.e1', '96.o1', '96.w1', '96.bg1', '96.ci1', '96.cj1', '96.ck1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6002, -1, 3222, -1], 'generators': [1076429862, 1087380134, 1085750593, 1081574431], 'label': '768.1090187.48.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.o1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633312
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '24.w2', '24.y1', '24.z1', '24.bb1', '24.bc1', '24.bd1'], 'contains': ['96.d1', '96.v2', '96.bh1', '96.cl2', '96.cm1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8774, -1, 6783, -1], 'generators': [1083218598, 1083098168, 1085750593, 1080656934], 'label': '768.1090187.48.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.p1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633313
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.d1', '24.j1', '24.t1', '24.u1', '24.be1'], 'contains': ['96.e1', '96.f1', '96.g1', '96.bi1', '96.bn1', '96.cn1', '96.cs1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4705, -1, 2089, -1], 'generators': [1076429862, 1085750593, 1089045606, 1076468417], 'label': '768.1090187.48.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.q1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633314
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '24.j1', '24.u1'], 'contains': ['96.e1', '96.f1', '96.bj1', '96.bo1', '96.co1', '96.ct1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1595, -1, 720, -1], 'generators': [1076429862, 1078860511, 1085750593, 1083049080], 'label': '768.1090187.48.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.r1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633315
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.g1', '24.j1', '24.k1', '24.t1', '24.be1'], 'contains': ['96.e1', '96.g1', '96.bk1', '96.bq1', '96.cp1', '96.cu1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5858, -1, 2342, -1], 'generators': [1076429862, 1089963103, 1085750593, 1077385976], 'label': '768.1090187.48.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.s1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633316
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '24.i1', '24.v1', '24.be1'], 'contains': ['96.e1', '96.bl1', '96.bm1', '96.cq1', '96.cr1'], 'core': '192.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [250, -1, 280, -1], 'generators': [1085750593, 1084856961, 1087390721, 1083229185], 'label': '768.1090187.48.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '48.t1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633317
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.27', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.e1', '24.p1'], 'contains': ['96.g1', '96.h1', '96.i1', '96.bp1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9951, -1, 9862, -1], 'generators': [1085750593, 1089985272, 1074709624, 658250892], 'label': '768.1090187.48.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.u1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633318
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.g1', '24.bf1', '24.bg1', '24.bk1', '24.bk2', '24.bl1'], 'contains': ['96.j1', '96.k1', '96.m1', '96.o1', '96.q1', '96.y1', '96.bq1', '96.cv1', '96.cw1'], 'core': '192.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [6531, -1, 4591, -1], 'generators': [1083180097, 1078860511, 1085750593, 1078887480], 'label': '768.1090187.48.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.v1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633319
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.d1', '24.bf1', '24.bg1', '24.bl1', '24.bm1'], 'contains': ['96.j1', '96.l1', '96.m1', '96.p1', '96.r1', '96.bi1', '96.bn1', '96.cx1', '96.cy1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [4267, -1, 2157, -1], 'generators': [1076429862, 1083180097, 1085750593, 1076468417], 'label': '768.1090187.48.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.w1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633320
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 96, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '4.e1'], 'contains': ['16.c1', '16.e1', '16.i1', '24.a1', '32.a1'], 'core': '24.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1597, -1, 4943, -1], 'generators': [1083180097, 1083098168, 1085750593, 1081574431, 3234148260, 2154597435], 'label': '768.1090187.8.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '8.c1', 'projective_image': '192.1538', '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': '24.12'}
  • id: 59633321
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.e1', '24.bi1'], 'contains': ['96.j1', '96.n1', '96.t1', '96.u1', '96.bp1'], 'core': '192.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9972, -1, 9919, -1], 'generators': [1083180097, 1085750593, 1074830054, 658250892], 'label': '768.1090187.48.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.x1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633322
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.a1', '24.bh1', '24.bk2', '24.bl1', '24.bn1'], 'contains': ['96.j1', '96.k1', '96.s1', '96.v1', '96.ba1', '96.cz1', '96.da1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8019, -1, 5913, -1], 'generators': [1083180097, 1085750593, 1087429350, 1078887480], 'label': '768.1090187.48.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.y1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633323
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.y2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '24.bi1', '24.bj1', '24.bk1', '24.bl1', '24.bn1'], 'contains': ['96.j1', '96.k1', '96.s2', '96.v2', '96.ba2', '96.cz2', '96.da2'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8225, -1, 6063, -1], 'generators': [1083180097, 1085750593, 1087298271, 1078887480], 'label': '768.1090187.48.y2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.y2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633324
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.g1', '24.bg1', '24.bl1', '24.bm1', '24.bn1'], 'contains': ['96.j1', '96.l1', '96.q1', '96.w1', '96.bk1', '96.db1', '96.dc1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5916, -1, 2191, -1], 'generators': [1076429862, 1083180097, 1085750593, 1077385976], 'label': '768.1090187.48.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.z1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633325
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.d1', '24.bg1', '24.bn1', '24.bo1', '24.bq1', '24.bu1'], 'contains': ['96.k1', '96.l1', '96.x1', '96.z1', '96.bi1', '96.df1', '96.dh1', '96.dk1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7488, -1, 3188, -1], 'generators': [1078860511, 1085750593, 1081574431, 1077347359], 'label': '768.1090187.48.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ba1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633326
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.d1', '24.bf1', '24.bk1', '24.bk2', '24.bp1'], 'contains': ['96.k1', '96.m1', '96.z1', '96.bb1', '96.bn1', '96.dg1', '96.dl1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7808, -1, 5234, -1], 'generators': [1083180097, 1085750593, 1081547512, 1078887480], 'label': '768.1090187.48.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bb1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633327
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.e1', '24.bh1', '24.bi1', '24.bo1', '24.bp1', '24.br1', '24.bs1'], 'contains': ['96.k1', '96.n1', '96.bc1', '96.be1', '96.bp1'], 'core': '192.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9769, -1, 9681, -1], 'generators': [1083180097, 1085750593, 506952305, 1078887480], 'label': '768.1090187.48.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bc1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633328
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.f1', '24.bh1', '24.bj1', '24.bo1', '24.bp1', '24.br1', '24.bt1'], 'contains': ['96.k1', '96.bd1', '96.bf1'], 'core': '192.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9530, -1, 7803, -1], 'generators': [1083180097, 1085750593, 512648241, 1078887480], 'label': '768.1090187.48.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bd1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633329
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.g1', '24.bf1', '24.bl1', '24.bq1', '24.bu1'], 'contains': ['96.k1', '96.l1', '96.y1', '96.bg1', '96.bk1', '96.dd1', '96.di1', '96.dm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5953, -1, 2849, -1], 'generators': [1076429862, 1085750593, 1081574431, 1078991590], 'label': '768.1090187.48.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.be1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633330
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.bk2', '24.bs1', '24.bt1', '24.bu1'], 'contains': ['96.k1', '96.ba2', '96.bh1', '96.de2', '96.dj2'], 'core': '192.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8610, -1, 6199, -1], 'generators': [1083098168, 1085750593, 1074830054, 1080656934], 'label': '768.1090187.48.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bf1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633331
    {'ambient': '768.1090187', 'aut_centralizer_order': 12, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 96, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['16.d1', '16.f1', '16.j1', '24.i1', '32.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [108, -1, 375, -1], 'generators': [1083180097, 2160806949, 1085750593, 1087390721, 3234148260, 1083229185], 'label': '768.1090187.8.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '8.d1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 59633332
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.i1', '24.bf1', '24.bg1'], 'contains': ['96.l1', '96.m1', '96.bj1', '96.bl1', '96.bo1', '96.dn1', '96.dq1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1583, -1, 618, -1], 'generators': [1076429862, 1083180097, 1078860511, 1085750593], 'label': '768.1090187.48.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bg1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633333
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '24.i1', '24.bm1', '24.bq1'], 'contains': ['96.l1', '96.bj1', '96.bm1', '96.do1', '96.dp1'], 'core': '192.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [263, -1, 246, -1], 'generators': [1085750593, 1087390721, 1076468417, 1083229185], 'label': '768.1090187.48.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '48.bh1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633334
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.t1', '24.bk1', '24.bl1', '24.bv1', '24.bw1', '24.ca2', '24.cf1'], 'contains': ['96.o1', '96.q1', '96.s2', '96.y1', '96.ba1', '96.bn1', '96.bq1', '96.ds1', '96.dv1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6400, -1, 4692, -1], 'generators': [1085750593, 1087429350, 1078887480, 1084818534], 'label': '768.1090187.48.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bi1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633335
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bi2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.t1', '24.bk2', '24.bl1', '24.bv1', '24.bw1', '24.ca1', '24.cf1'], 'contains': ['96.o1', '96.q1', '96.s1', '96.y1', '96.ba2', '96.bn1', '96.bq1', '96.ds2', '96.dv2'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6245, -1, 4659, -1], 'generators': [1085750593, 1087298271, 1078887480, 1084818534], 'label': '768.1090187.48.bi2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bi2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633336
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.u1', '24.bf1', '24.bg1', '24.ca1', '24.ca2', '24.cf1'], 'contains': ['96.o1', '96.q1', '96.r1', '96.y1', '96.z1', '96.bn1', '96.bo1', '96.dt1', '96.dw1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5928, -1, 4151, -1], 'generators': [1085750593, 1081547512, 1078887480, 1084818534], 'label': '768.1090187.48.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bj1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633337
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.v1', '24.bf1', '24.bv1', '24.ck1'], 'contains': ['96.o1', '96.p1', '96.bb1', '96.bg1', '96.bl1', '96.dr1', '96.du1', '96.dx1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3077, -1, 2748, -1], 'generators': [1076429862, 1085750593, 1081574431, 1087249055], 'label': '768.1090187.48.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bk1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633338
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.j1', '24.bf1', '24.bm1', '24.bw1', '24.cf1'], 'contains': ['96.p1', '96.q1', '96.bj1', '96.bk1', '96.bn1', '96.dy1', '96.ea1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2702, -1, 1566, -1], 'generators': [1076429862, 1078860511, 1089963103, 1085750593], 'label': '768.1090187.48.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bl1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633339
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bl2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.j1', '24.bg1', '24.bv1', '24.cf1', '24.cg1'], 'contains': ['96.p1', '96.q1', '96.bi1', '96.bo1', '96.bq1', '96.dy2', '96.ea2'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1608, -1, 1954, -1], 'generators': [1076429862, 1085750593, 1089045606, 1083202278], 'label': '768.1090187.48.bl2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bl2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633340
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.k1', '24.bl1', '24.bv1', '24.bw1', '24.cg1'], 'contains': ['96.p1', '96.s1', '96.s2', '96.bk1', '96.bq1', '96.dz1', '96.eb1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4779, -1, 3154, -1], 'generators': [1076429862, 1089963103, 1085750593, 1089985272], 'label': '768.1090187.48.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bm1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633341
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '32.27', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.p1', '24.bi1'], 'contains': ['96.s2', '96.t1', '96.u1', '96.bp1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9993, -1, 9976, -1], 'generators': [1085750593, 1074709624, 1083071199, 658250892], 'label': '768.1090187.48.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.bn1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633342
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 96, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.b1', '4.e1'], 'contains': ['16.c1', '16.g1', '16.k1', '24.x1', '32.b1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4689, -1, 5244, -1], 'generators': [1083098168, 3229953892, 1085750593, 1081574431, 670833676, 2154597435], 'label': '768.1090187.8.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '8.e1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 59633343
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.v1', '24.bg1', '24.bw1', '24.ck1', '24.cl1'], 'contains': ['96.o1', '96.p1', '96.w1', '96.x1', '96.bl1', '96.ed1', '96.ef1', '96.ek1', '96.ek2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2341, -1, 1701, -1], 'generators': [1085750593, 1081574431, 1077347359, 1089936056], 'label': '768.1090187.48.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bo1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633344
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w1', '24.bk2', '24.bn1', '24.bx1', '24.cf1'], 'contains': ['96.q1', '96.v1', '96.z1', '96.ba2', '96.ee1', '96.el1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7906, -1, 5604, -1], 'generators': [1085750593, 1087298271, 1078887480, 1083049080], 'label': '768.1090187.48.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bp1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633345
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bp2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w1', '24.bl1', '24.ca2', '24.cf1', '24.ch1'], 'contains': ['96.q1', '96.r1', '96.s2', '96.v1', '96.y1', '96.ee2', '96.el2'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6947, -1, 4997, -1], 'generators': [1085750593, 1089067713, 1078887480, 1084818534], 'label': '768.1090187.48.bp2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bp2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633346
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bp3', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w2', '24.bk1', '24.bn1', '24.by1', '24.bz1', '24.cf1'], 'contains': ['96.q1', '96.v2', '96.z1', '96.ba1', '96.ee3', '96.el3'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7933, -1, 5811, -1], 'generators': [1085750593, 1087429350, 1078887480, 1083049080], 'label': '768.1090187.48.bp3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bp3', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633347
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bp4', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w2', '24.bl1', '24.ca1', '24.cf1', '24.ch1'], 'contains': ['96.q1', '96.r1', '96.s1', '96.v2', '96.y1', '96.ee4', '96.el4'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7050, -1, 5031, -1], 'generators': [1085750593, 1089985272, 1078887480, 1084818534], 'label': '768.1090187.48.bp4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bp4', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633348
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.x1', '24.bh1', '24.bx1', '24.cb2', '24.ci1'], 'contains': ['96.v1', '96.bc1', '96.bd1', '96.eg1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9240, -1, 8706, -1], 'generators': [1085774520, 1085750593, 668673292, 1089946655], 'label': '768.1090187.48.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bq1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633349
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.27', 'aut_weyl_index': 576, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.y1', '24.bi1', '24.by1', '24.cb1', '24.ci1'], 'contains': ['96.t1', '96.v2', '96.bc1', '96.eh1', '96.em1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9302, -1, 9817, -1], 'generators': [1083218598, 660749132, 1085750593, 1089946655], 'label': '768.1090187.48.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.br1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633350
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.27', 'aut_weyl_index': 576, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.z1', '24.bj1', '24.bz1', '24.cb1', '24.ci1'], 'contains': ['96.v2', '96.bd1', '96.ei1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9263, -1, 8306, -1], 'generators': [1083218598, 1085750593, 668673292, 1089946655], 'label': '768.1090187.48.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bs1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633351
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ba1', '24.bh1', '24.bx1', '24.cd2', '24.cj1'], 'contains': ['96.v1', '96.be1', '96.bf1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9552, -1, 7710, -1], 'generators': [1085750593, 506952305, 511124502, 1078887480], 'label': '768.1090187.48.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bt1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633352
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.27', 'aut_weyl_index': 576, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bb1', '24.bi1', '24.bz1', '24.cd1', '24.cj1'], 'contains': ['96.u1', '96.v2', '96.be1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9929, -1, 9431, -1], 'generators': [1085750593, 506952305, 1078887480, 510198550], 'label': '768.1090187.48.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bu1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633353
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 96, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.c1', '4.e1'], 'contains': ['16.c1', '16.h1', '24.ba1', '32.c1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4857, -1, 5416, -1], 'generators': [2150370363, 1083098168, 654646443, 1085750593, 506952305, 1081574431], 'label': '768.1090187.8.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '8.f1', 'projective_image': '192.1538', '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': '48.48'}
  • id: 59633354
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.27', 'aut_weyl_index': 576, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bc1', '24.bj1', '24.by1', '24.cd1', '24.cj1'], 'contains': ['96.v2', '96.bf1', '96.en1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9437, -1, 7440, -1], 'generators': [516955478, 1085750593, 512648241, 1078887480], 'label': '768.1090187.48.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bv1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633355
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bd1', '24.bk1', '24.ca1', '24.cb1', '24.cd1', '24.ck1'], 'contains': ['96.b1', '96.o1', '96.v2', '96.bb1', '96.ec1', '96.ec2', '96.ej1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7869, -1, 6097, -1], 'generators': [1083098168, 1085750593, 1081574431, 1087249055], 'label': '768.1090187.48.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bw1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633356
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.bw2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bd1', '24.bk2', '24.ca2', '24.cb2', '24.cc1', '24.cd2', '24.ce1', '24.ck1'], 'contains': ['96.o1', '96.v1', '96.bb1', '96.bh1', '96.ec3', '96.ec4', '96.ej2'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7921, -1, 6131, -1], 'generators': [1083098168, 1085750593, 1080656934, 1087249055], 'label': '768.1090187.48.bw2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bw2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633357
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.t1', '24.bl1', '24.bn1', '24.bw1', '24.cf1', '24.cg1', '24.ch1'], 'contains': ['96.q1', '96.s1', '96.s2', '96.w1', '96.bi1', '96.bk1', '96.eo1', '96.eq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6015, -1, 3120, -1], 'generators': [1076429862, 1089963103, 1085750593, 1083202278], 'label': '768.1090187.48.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bx1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633358
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.u1', '24.bg1', '24.bm1', '24.cf1', '24.ch1'], 'contains': ['96.q1', '96.r1', '96.w1', '96.bi1', '96.bj1', '96.ep1', '96.er1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4157, -1, 1667, -1], 'generators': [1076429862, 1085750593, 1076468417, 1083049080], 'label': '768.1090187.48.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.by1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633359
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bd1', '24.bl1', '24.cf1', '24.ck1', '24.cl1'], 'contains': ['96.o1', '96.p1', '96.v1', '96.v2', '96.w1', '96.bg1', '96.es1', '96.es2', '96.et1', '96.eu1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6060, -1, 4253, -1], 'generators': [1076429862, 1085750593, 1081574431, 1081596600], 'label': '768.1090187.48.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bz1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633360
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1', '24.bm1', '24.cg1', '24.cl1'], 'contains': ['96.p1', '96.w1', '96.bm1', '96.ev1', '96.ew1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1508, -1, 551, -1], 'generators': [1085750593, 1087390721, 1083229185, 1087249055], 'label': '768.1090187.48.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ca1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633361
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bd1', '24.bn1', '24.ch1', '24.ci1', '24.cj1', '24.cl1'], 'contains': ['96.v1', '96.v2', '96.w1', '96.x1', '96.ex1', '96.ey1', '96.ez1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7796, -1, 5335, -1], 'generators': [1085750593, 1081574431, 1081596600, 1077347359], 'label': '768.1090187.48.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cb1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633362
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.j1', '24.bg1', '24.bq1', '24.bw1', '24.ch1', '24.co1', '24.ct1'], 'contains': ['96.x1', '96.y1', '96.bi1', '96.bj1', '96.bk1', '96.fj1', '96.fn1', '96.gd1', '96.gd2'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2406, -1, 1058, -1], 'generators': [1085750593, 1081547512, 1081574431, 1077347359], 'label': '768.1090187.48.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cc1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633363
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.k1', '24.bn1', '24.bu1', '24.bw1', '24.cm1', '24.co1'], 'contains': ['96.x1', '96.ba1', '96.ba2', '96.bk1', '96.fk1', '96.fp1', '96.ge1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7530, -1, 4557, -1], 'generators': [1085750593, 1081574431, 1089985272, 1077347359], 'label': '768.1090187.48.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cd1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633364
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '96.226', 'aut_weyl_index': 192, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['2.d1', '4.e1'], 'contains': ['16.e1', '16.g1', '16.h1', '24.br1', '32.d1'], 'core': '48.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [4813, -1, 5361, -1], 'generators': [1083180097, 1083098168, 1085750593, 506952305, 1081574431, 2154990594], 'label': '768.1090187.8.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '8.g1', 'projective_image': '384.20163', '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': '48.48'}
  • id: 59633365
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.l1', '24.bo1', '24.ci1', '24.cm1', '24.cu1'], 'contains': ['96.x1', '96.bc1', '96.bd1', '96.fl1', '96.fr1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9220, -1, 8593, -1], 'generators': [1076429862, 1085750593, 1087390721, 504396399], 'label': '768.1090187.48.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ce1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633366
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.m1', '24.bo1', '24.cj1', '24.cm1', '24.cw1'], 'contains': ['96.x1', '96.be1', '96.bf1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9649, -1, 7542, -1], 'generators': [1076429862, 1085750593, 506952305, 1087390721], 'label': '768.1090187.48.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cf1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633367
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.j1', '24.bf1', '24.bv1', '24.ca1', '24.ca2'], 'contains': ['96.y1', '96.bb1', '96.bn1', '96.bo1', '96.bq1', '96.fm1', '96.gf1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4799, -1, 3729, -1], 'generators': [1078860511, 1085750593, 1078887480, 1084818534], 'label': '768.1090187.48.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cg1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633368
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.n1', '24.bo1', '24.bp1', '24.bx1', '24.by1', '24.cp1', '24.cq1'], 'contains': ['96.z1', '96.bc1', '96.bf1', '96.gg1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9674, -1, 7855, -1], 'generators': [1085750593, 512648241, 1078887480, 1083049080], 'label': '768.1090187.48.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ch1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633369
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.o1', '24.bo1', '24.bp1', '24.bx1', '24.bz1', '24.cp1', '24.cr1'], 'contains': ['96.z1', '96.bd1', '96.be1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9789, -1, 8056, -1], 'generators': [1085750593, 506952305, 1078887480, 1083049080], 'label': '768.1090187.48.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ci1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633370
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.p1', '24.bi1', '24.bs1', '24.bx1', '24.cm1', '24.cn1', '24.cp1'], 'contains': ['96.ba2', '96.bc1', '96.be1', '96.bp1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9857, -1, 9738, -1], 'generators': [1077396575, 1085750593, 506952305, 1078887480], 'label': '768.1090187.48.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cj1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633371
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.q1', '24.bh1', '24.br1', '24.by1', '24.cm1', '24.cn1', '24.cq1'], 'contains': ['96.ba1', '96.bc1', '96.bf1', '96.gh1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9405, -1, 7658, -1], 'generators': [1085750593, 1076479078, 512648241, 1078887480], 'label': '768.1090187.48.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ck1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633372
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.r1', '24.bh1', '24.br1', '24.bz1', '24.cm1', '24.cn1', '24.cr1'], 'contains': ['96.ba1', '96.bd1', '96.be1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9748, -1, 8009, -1], 'generators': [1085750593, 506952305, 1076479078, 1078887480], 'label': '768.1090187.48.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cl1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633373
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.s1', '24.bj1', '24.bt1', '24.bx1', '24.cm1', '24.cn1', '24.cp1'], 'contains': ['96.ba2', '96.bd1', '96.bf1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9693, -1, 7906, -1], 'generators': [1077396575, 1085750593, 512648241, 1078887480], 'label': '768.1090187.48.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cm1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633374
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.k1', '24.bk1', '24.bk2', '24.bv1', '24.cn1'], 'contains': ['96.ba1', '96.ba2', '96.bb1', '96.bq1', '96.fo1', '96.gi1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7856, -1, 5403, -1], 'generators': [1085750593, 1087298271, 1076479078, 1078887480], 'label': '768.1090187.48.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cn1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633375
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4608.dp', 'aut_weyl_index': 4, 'centralizer': '192.a1', 'complements': ['384.c1', '384.h1', '384.i1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.g1', '6.f1', '8.e1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4697, 1215, 5236, 5395], 'generators': [1076429862, 2150763522, 1074660408, 1084867622, 3229953892, 1085750593, 1081574431, 668673292], 'label': '768.1090187.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '192.1538', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 59633376
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 32, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.f1'], 'contains': ['16.a1', '24.ej1', '32.i1', '32.j1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [203, -1, 3719, -1], 'generators': [1076429862, 1074660408, 2150763522, 1084867622, 1081574431, 3234148260], 'label': '768.1090187.8.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.h1', 'projective_image': '768.1090187', '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': '48.50'}
  • id: 59633377
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.l1', '24.bp1', '24.cb1', '24.cb2', '24.cn1'], 'contains': ['96.bb1', '96.bc1', '96.bd1', '96.fq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9285, -1, 8940, -1], 'generators': [1085750593, 668673292, 1087249055, 1089946655], 'label': '768.1090187.48.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.co1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633378
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.m1', '24.bp1', '24.cd1', '24.cd2', '24.cn1'], 'contains': ['96.bb1', '96.be1', '96.bf1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9731, -1, 7756, -1], 'generators': [1085750593, 512648241, 1078887480, 510198550], 'label': '768.1090187.48.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cp1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633379
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.t1', '24.bl1', '24.bu1', '24.bv1', '24.cf1', '24.co1', '24.ct1'], 'contains': ['96.y1', '96.ba1', '96.ba2', '96.bg1', '96.bi1', '96.bk1', '96.fa1', '96.fa2', '96.fu1', '96.gj1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6039, -1, 3594, -1], 'generators': [1076429862, 1085750593, 1081574431, 1089985272], 'label': '768.1090187.48.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cq1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633380
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.u1', '24.bf1', '24.bq1', '24.cf1', '24.ct1'], 'contains': ['96.y1', '96.z1', '96.bg1', '96.bi1', '96.bj1', '96.fb1', '96.fv1', '96.gk1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4189, -1, 2410, -1], 'generators': [1076429862, 1078860511, 1085750593, 1081574431], 'label': '768.1090187.48.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cr1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633381
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '48.cs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.v1', '24.bq1', '24.cl1', '24.co1'], 'contains': ['96.x1', '96.bg1', '96.bm1', '96.fc1', '96.fs1', '96.fx1', '96.gl1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1674, -1, 1397, -1], 'generators': [1076429862, 1074660408, 1085750593, 1081574431], 'label': '768.1090187.48.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cs1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633382
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.ct1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w1', '24.bk1', '24.bu1', '24.ca1', '24.cp1', '24.ct1'], 'contains': ['96.b1', '96.y1', '96.z1', '96.ba2', '96.fd1', '96.fd2', '96.fy1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7881, -1, 5777, -1], 'generators': [1078860511, 1083098168, 1085750593, 1081574431], 'label': '768.1090187.48.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ct1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ct1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633383
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.ct2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w2', '24.bk2', '24.bu1', '24.ca2', '24.cq1', '24.cr1', '24.cs1', '24.ct1'], 'contains': ['96.y1', '96.z1', '96.ba1', '96.bh1', '96.fd3', '96.fd4', '96.fy2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7945, -1, 5845, -1], 'generators': [1078860511, 1083098168, 1085750593, 1080656934], 'label': '768.1090187.48.ct2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ct2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ct2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633384
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.cu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.g1', '24.x1', '24.br1', '24.cb1', '24.cp1', '24.cu1'], 'contains': ['96.b1', '96.bc1', '96.bd1', '96.fe1', '96.fz1'], 'core': '96.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9142, -1, 8536, -1], 'generators': [1083098168, 1085750593, 1081574431, 504396399], 'label': '768.1090187.48.cu1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cu1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633385
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.cv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.y1', '24.bs1', '24.cb2', '24.cq1', '24.cu1'], 'contains': ['96.bc1', '96.bh1', '96.ff1', '96.ga1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9158, -1, 9481, -1], 'generators': [1085750593, 504396399, 1078887480, 1085785119], 'label': '768.1090187.48.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cv1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cv1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633386
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.cw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.z1', '24.bt1', '24.cb2', '24.cc1', '24.cr1', '24.cs1', '24.cu1', '24.cv1'], 'contains': ['96.bd1', '96.bh1', '96.fg1', '96.gb1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9037, -1, 7598, -1], 'generators': [1085750593, 511132591, 1078887480, 1085785119], 'label': '768.1090187.48.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cw1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633387
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 32, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.g1'], 'contains': ['16.a1', '24.eq1', '32.k1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1878, -1, 5188, -1], 'generators': [1076429862, 1074660408, 2150763522, 1084867622, 1081574431, 504396399], 'label': '768.1090187.8.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.i1', 'projective_image': '768.1090187', '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': '96.227'}
  • id: 59633388
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.cx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.h1', '24.ba1', '24.br1', '24.cd1', '24.cp1', '24.cw1'], 'contains': ['96.b1', '96.be1', '96.bf1'], 'core': '96.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9487, -1, 7495, -1], 'generators': [1083098168, 1085750593, 506952305, 1081574431], 'label': '768.1090187.48.cx1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cx1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633389
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.cy1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bb1', '24.bs1', '24.cd2', '24.cr1', '24.cw1'], 'contains': ['96.be1', '96.bh1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9507, -1, 8880, -1], 'generators': [1085750593, 506952305, 1078887480, 1085785119], 'label': '768.1090187.48.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cy1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cy1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633390
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.cz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bc1', '24.bt1', '24.cd2', '24.ce1', '24.cq1', '24.cs1', '24.cw1', '24.cx1'], 'contains': ['96.bf1', '96.bh1', '96.fh1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9176, -1, 7000, -1], 'generators': [1085750593, 1078887480, 1085785119, 508576689], 'label': '768.1090187.48.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cz1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633391
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '48.da1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.b1', '24.bd1', '24.bu1', '24.ck1', '24.ct1', '24.cu1', '24.cv1', '24.cw1', '24.cx1'], 'contains': ['96.b1', '96.x1', '96.bg1', '96.bh1', '96.fi1', '96.ft1', '96.fw1', '96.fw2', '96.gc1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7844, -1, 5996, -1], 'generators': [1074660408, 1085750593, 1081574431, 1083229185], 'label': '768.1090187.48.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.da1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.da1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633392
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.db1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.be1', '24.bf1', '24.bg1', '24.bv1', '24.bw1'], 'contains': ['96.bi1', '96.bk1', '96.bl1', '96.bn1', '96.bq1', '96.gm1', '96.gp1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2418, -1, 1194, -1], 'generators': [1076429862, 1089963103, 1085750593, 1076468417], 'label': '768.1090187.48.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.db1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.db1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633393
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.dc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.be1', '24.bm1', '24.bq1', '24.cg1', '24.co1'], 'contains': ['96.bi1', '96.bk1', '96.bm1', '96.gn1', '96.go1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1496, -1, 382, -1], 'generators': [1078860511, 1085750593, 1087390721, 1083229185], 'label': '768.1090187.48.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dc1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633394
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.dd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.d1', '24.cy1', '24.da1', '24.dc1', '24.df1'], 'contains': ['96.br1', '96.bt1', '96.bv1', '96.bx1', '96.cn1', '96.cx1', '96.df1', '96.dg1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [4606, -1, 2613, -1], 'generators': [1083180097, 1078860511, 1081574431, 1077347359], 'label': '768.1090187.48.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dd1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633395
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.de1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.d1', '24.cz1', '24.de1', '24.de2'], 'contains': ['96.br1', '96.bu1', '96.bx1', '96.bz1', '96.cs1', '96.cy1', '96.dg1', '96.dh1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6506, -1, 3628, -1], 'generators': [1084833144, 1083180097, 1081547512, 1078887480], 'label': '768.1090187.48.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.de1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.de1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633396
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.df1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.d1', '24.cy1', '24.cz1', '24.db1', '24.dd1'], 'contains': ['96.bs1', '96.bt1', '96.bu1', '96.cc1', '96.ce1', '96.cn1', '96.cs1', '96.cx1', '96.cy1', '96.dk1', '96.dl1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2628, -1, 1329, -1], 'generators': [1076429862, 1087290726, 1083180097, 1076468417], 'label': '768.1090187.48.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.df1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.df1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633397
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dg1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.g1', '24.cy1', '24.cz1', '24.dd1', '24.de1', '24.de2'], 'contains': ['96.br1', '96.bs1', '96.bu1', '96.bw1', '96.cd1', '96.ci1', '96.cu1', '96.cv1', '96.cw1', '96.dc1', '96.dd1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [5369, -1, 3255, -1], 'generators': [1083180097, 1083063654, 1078991590, 1078887480], 'label': '768.1090187.48.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dg1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633398
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 256, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1', '6.f1', '6.g1'], 'contains': ['24.b1', '24.c1', '24.v1', '24.bd1', '24.ck1', '24.cl1', '24.dx1', '24.dy1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4748, 3775, 3980, 8270], 'generators': [1076429862, 1074660408, 1084867622, 1085750593, 1081574431, 1087249055], 'label': '768.1090187.12.a1', 'mobius_quo': 4, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.b1', '24.c1', '48.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '192.1538', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633399
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dh1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.g1', '24.cz1', '24.da1', '24.dd1', '24.df1'], 'contains': ['96.br1', '96.bt1', '96.bw1', '96.cj1', '96.cp1', '96.cv1', '96.db1', '96.di1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3654, -1, 2511, -1], 'generators': [1076429862, 1083180097, 1081574431, 1078991590], 'label': '768.1090187.48.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dh1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633400
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.di1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.g1', '24.cy1', '24.db1', '24.dc1', '24.dd1'], 'contains': ['96.bs1', '96.bt1', '96.cd1', '96.ck1', '96.cp1', '96.cw1', '96.db1', '96.dm1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3641, -1, 1920, -1], 'generators': [1076429862, 1083180097, 1078991590, 1087421791], 'label': '768.1090187.48.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.di1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.di1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633401
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.dj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.a1', '24.dc1', '24.dd1', '24.de1'], 'contains': ['96.br1', '96.bs1', '96.by1', '96.cf1', '96.cl1', '96.cz1', '96.da1', '96.de1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [7438, -1, 5133, -1], 'generators': [1074724198, 1083180097, 1080629953, 1078887480], 'label': '768.1090187.48.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dj1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633402
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.dj2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '24.dc1', '24.dd1', '24.de2'], 'contains': ['96.br1', '96.bs1', '96.by2', '96.cf2', '96.cl2', '96.cz2', '96.da2', '96.de2'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [7450, -1, 5302, -1], 'generators': [1083180097, 1080629953, 1074855263, 1078887480], 'label': '768.1090187.48.dj2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dj2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dj2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633403
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.dk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.i1', '24.a1', '24.de2', '24.df1'], 'contains': ['96.c1', '96.br1', '96.by1', '96.cz1', '96.dj1'], 'core': '96.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [7463, -1, 5437, -1], 'generators': [1083180097, 1083098168, 1081574431, 1089985272], 'label': '768.1090187.48.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '48.dk1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dk1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633404
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.dk2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.de1', '24.df1'], 'contains': ['96.br1', '96.by2', '96.cm1', '96.cz2', '96.dj2'], 'core': '384.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [7759, -1, 5570, -1], 'generators': [1083180097, 1083098168, 1074830054, 1080656934], 'label': '768.1090187.48.dk2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dk2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dk2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633405
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '48.dl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.i1', '24.cy1', '24.cz1'], 'contains': ['96.bt1', '96.bu1', '96.co1', '96.cq1', '96.ct1', '96.dn1', '96.do1', '96.dq1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1686, -1, 415, -1], 'generators': [1076429862, 1084833144, 1083180097, 1078860511], 'label': '768.1090187.48.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dl1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633406
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '48.dm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.j1', '24.i1', '24.da1', '24.db1'], 'contains': ['96.bt1', '96.co1', '96.cr1', '96.dn1', '96.dp1'], 'core': '384.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [222, -1, 212, -1], 'generators': [1083180097, 1087390721, 1076468417, 1083229185], 'label': '768.1090187.48.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '48.dm1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dm1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633407
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.j1', '24.cy1', '24.da1', '24.dg1', '24.dk1', '24.dm1', '24.du1'], 'contains': ['96.bv1', '96.bw1', '96.cn1', '96.co1', '96.cp1', '96.dy1', '96.dy2', '96.fj1', '96.fm1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2153, -1, 1025, -1], 'generators': [1081547512, 1081574431, 1077347359, 1084818534], 'label': '768.1090187.48.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dn1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633408
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.do1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.k1', '24.dc1', '24.df1', '24.dg1', '24.dk1'], 'contains': ['96.bv1', '96.by1', '96.by2', '96.cp1', '96.dz1', '96.fk1', '96.fo1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5051, -1, 4034, -1], 'generators': [1081574431, 1089985272, 1076479078, 1077347359], 'label': '768.1090187.48.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.do1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.do1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633409
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 256, 'centralizer': '6.a1', 'complements': ['64.f1'], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.a1', '6.i1'], 'contains': ['24.b1', '24.bq1', '24.bu1', '24.co1', '24.ct1', '24.eh1', '24.ei1', '24.ej1'], 'core': '12.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4019, 5996, 3775, 5406], 'generators': [1076429862, 1074660408, 1084867622, 1078860511, 1085750593, 1081574431], 'label': '768.1090187.12.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': ['4.b1', '6.a1'], 'normal_contains': ['24.b1', '48.b1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '384.20163', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633410
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.dp1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.l1', '24.dn1', '24.dv1'], 'contains': ['96.bv1', '96.ca1', '96.cb1', '96.fl1', '96.fq1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [8846, -1, 8997, -1], 'generators': [1076429862, 1084856961, 658250892, 1080656934], 'label': '768.1090187.48.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '48.dp1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633411
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.j1', '24.cz1', '24.dj1', '24.dq1', '24.dq2'], 'contains': ['96.bw1', '96.bz1', '96.cs1', '96.ct1', '96.cu1', '96.ea1', '96.ea2', '96.fm1', '96.fn1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2791, -1, 1988, -1], 'generators': [1084833144, 1078860511, 1078887480, 1084818534], 'label': '768.1090187.48.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dq1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633412
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dr1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.k1', '24.de1', '24.de2', '24.dj1'], 'contains': ['96.by1', '96.by2', '96.bz1', '96.cu1', '96.eb1', '96.fo1', '96.fp1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [7340, -1, 4388, -1], 'generators': [1084833144, 1087298271, 1076479078, 1078887480], 'label': '768.1090187.48.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dr1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633413
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.ds1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.l1', '24.dr1', '24.dr2'], 'contains': ['96.bz1', '96.ca1', '96.cb1', '96.fq1', '96.fr1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [8971, -1, 9167, -1], 'generators': [668673292, 1087249055, 1089946655, 1083194719], 'label': '768.1090187.48.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '48.ds1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ds1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633414
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dt1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.j1', '24.cy1', '24.dj1', '24.dl1', '24.dp1'], 'contains': ['96.cc1', '96.cd1', '96.cn1', '96.ct1', '96.cu1', '96.dy2', '96.ea1', '96.gd1', '96.gf1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [1762, -1, 889, -1], 'generators': [1076429862, 1087290726, 1076479078, 1083202278], 'label': '768.1090187.48.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dt1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dt1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633415
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dt2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.j1', '24.cz1', '24.db1', '24.dg1', '24.dp1'], 'contains': ['96.cc1', '96.cd1', '96.co1', '96.cp1', '96.cs1', '96.dy1', '96.ea2', '96.gd2', '96.gf1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [1750, -1, 923, -1], 'generators': [1076429862, 1087290726, 1078860511, 1089963103], 'label': '768.1090187.48.dt2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dt2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dt2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633416
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.du1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.k1', '24.dd1', '24.dg1', '24.dj1', '24.dl1'], 'contains': ['96.cc1', '96.cf1', '96.cf2', '96.cp1', '96.cu1', '96.dz1', '96.eb1', '96.ge1', '96.gi1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3090, -1, 2225, -1], 'generators': [1076429862, 1087290726, 1089985272, 1078871160], 'label': '768.1090187.48.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.du1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.du1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633417
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '48.dv1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.n1', '24.dh1'], 'contains': ['96.ce1', '96.cg1', '96.ch1', '96.gg1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [9121, -1, 7257, -1], 'generators': [1081547512, 1076493688, 658250892, 1083049080], 'label': '768.1090187.48.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '48.dv1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633418
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '48.dw1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.q1', '24.dh1'], 'contains': ['96.cf1', '96.cg1', '96.ch1', '96.gh1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [9071, -1, 7154, -1], 'generators': [1079016799, 1076479078, 1077385976, 658250892], 'label': '768.1090187.48.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '48.dw1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633419
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dx1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.t1', '24.dd1', '24.de1', '24.dg1', '24.dj1', '24.dp1', '24.dq2'], 'contains': ['96.bw1', '96.by2', '96.cd1', '96.cf1', '96.ci1', '96.cs1', '96.cu1', '96.ds2', '96.dv1', '96.eq1', '96.fa1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [4301, -1, 3526, -1], 'generators': [1077396575, 1083063654, 1089985272, 1078887480], 'label': '768.1090187.48.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dx1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633420
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1'], 'contains': ['24.d1', '24.e1', '24.f1', '24.l1', '24.m1', '24.n1', '24.o1', '24.bo1', '24.bp1'], 'core': '96.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9415, -1, 7909, -1], 'generators': [1076429862, 1080656934, 1083180097, 658250892, 1085750593, 1076468417], 'label': '768.1090187.12.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.c1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633421
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dx2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.t1', '24.dd1', '24.de2', '24.dg1', '24.dj1', '24.dp1', '24.dq1'], 'contains': ['96.bw1', '96.by1', '96.cd1', '96.cf2', '96.ci1', '96.cs1', '96.cu1', '96.ds1', '96.dv2', '96.eq1', '96.fa2'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [4349, -1, 3425, -1], 'generators': [1083063654, 1076479078, 1089067713, 1078887480], 'label': '768.1090187.48.dx2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dx2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dx2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633422
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dy1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.u1', '24.cy1', '24.cz1', '24.dp1', '24.dq1', '24.dq2'], 'contains': ['96.bw1', '96.bx1', '96.cd1', '96.ce1', '96.ci1', '96.cs1', '96.ct1', '96.dt1', '96.dw1', '96.er1', '96.fb1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [3801, -1, 2545, -1], 'generators': [1078860511, 1083063654, 1078887480, 1083049080], 'label': '768.1090187.48.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dy1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633423
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.dz1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.t1', '24.dd1', '24.df1', '24.dj1', '24.dk1', '24.dp1', '24.du1'], 'contains': ['96.bw1', '96.by1', '96.by2', '96.cj1', '96.cn1', '96.cp1', '96.ds1', '96.ds2', '96.eo1', '96.fu1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [4033, -1, 3019, -1], 'generators': [1076429862, 1081574431, 1076479078, 1089067713], 'label': '768.1090187.48.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dz1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633424
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ea1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.u1', '24.cz1', '24.da1', '24.dp1', '24.du1'], 'contains': ['96.bw1', '96.bx1', '96.cj1', '96.cn1', '96.co1', '96.dt1', '96.ep1', '96.fv1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2715, -1, 1852, -1], 'generators': [1076429862, 1078860511, 1081574431, 1083049080], 'label': '768.1090187.48.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ea1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ea1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633425
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.eb1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.t1', '24.dc1', '24.dd1', '24.dg1', '24.dl1', '24.dm1', '24.dp1'], 'contains': ['96.cd1', '96.cf1', '96.cf2', '96.ck1', '96.cn1', '96.cp1', '96.dv1', '96.dv2', '96.eo1', '96.gj1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [3949, -1, 2680, -1], 'generators': [1076429862, 1076479078, 1089067713, 1087421791], 'label': '768.1090187.48.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.eb1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633426
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ec1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.u1', '24.cy1', '24.db1', '24.dm1', '24.dp1'], 'contains': ['96.cd1', '96.ce1', '96.ck1', '96.cn1', '96.co1', '96.dw1', '96.ep1', '96.gk1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2640, -1, 1261, -1], 'generators': [1076429862, 1078860511, 1087421791, 1083049080], 'label': '768.1090187.48.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ec1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ec1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633427
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.ed1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.v1', '24.cy1', '24.dg1', '24.dx1', '24.dy1'], 'contains': ['96.bv1', '96.cc1', '96.ci1', '96.ck1', '96.cq1', '96.dr1', '96.dx1', '96.ed1', '96.ek1', '96.ev1', '96.fc1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [1927, -1, 1498, -1], 'generators': [1083063654, 1081574431, 1077347359, 1087249055], 'label': '768.1090187.48.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ed1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ed1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633428
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ee1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w1', '24.dc1', '24.de1', '24.dp1'], 'contains': ['96.bx1', '96.by2', '96.cd1', '96.cl1', '96.ee1', '96.el2', '96.fd1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [7281, -1, 4760, -1], 'generators': [1074724198, 1081547512, 1078887480, 1083049080], 'label': '768.1090187.48.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ee1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ee1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633429
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ee2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.w1', '24.dd1', '24.dm1', '24.dp1', '24.dq1'], 'contains': ['96.bw1', '96.cd1', '96.ce1', '96.cf2', '96.cl1', '96.ee2', '96.el1', '96.el2', '96.fd2'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [6143, -1, 3865, -1], 'generators': [1074724198, 1078991590, 1078887480, 1084818534], 'label': '768.1090187.48.ee2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ee2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ee2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633430
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ee3', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w2', '24.dc1', '24.de2', '24.dp1'], 'contains': ['96.bx1', '96.by1', '96.cd1', '96.cl2', '96.ee3', '96.el4', '96.fd3'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [7297, -1, 4794, -1], 'generators': [1081547512, 1074855263, 1078887480, 1083049080], 'label': '768.1090187.48.ee3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ee3', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ee3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633431
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 384, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1'], 'contains': ['24.d1', '24.g1', '24.i1', '24.j1', '24.u1', '24.v1', '24.be1', '24.bf1', '24.bg1', '24.bm1', '24.bq1', '24.cy1', '24.cz1', '24.da1', '24.db1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2581, -1, 1735, -1], 'generators': [1083180097, 1076429862, 1074660408, 1078860511, 1085750593, 1081574431], 'label': '768.1090187.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.d1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633496
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.fy1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cb1', '24.dn1', '24.dr2'], 'contains': ['96.ec1', '96.eh1', '96.ei1', '96.fe1', '96.fq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8805, -1, 9336, -1], 'generators': [660749132, 1089060216, 1087249055, 1089946655], 'label': '768.1090187.48.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '48.fy1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fy1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633432
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ee4', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.w2', '24.dd1', '24.dh1', '24.di1', '24.dm1', '24.dp1', '24.dq2'], 'contains': ['96.bw1', '96.cd1', '96.ce1', '96.cf1', '96.cl2', '96.ee4', '96.el3', '96.el4', '96.fd4'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [6543, -1, 4320, -1], 'generators': [1078991590, 1074855263, 1078887480, 1084818534], 'label': '768.1090187.48.ee4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ee4', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ee4', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633433
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.ef1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.x1', '24.dn1', '24.dr2'], 'contains': ['96.ca1', '96.cb1', '96.cl1', '96.eg1', '96.fe1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [8887, -1, 9223, -1], 'generators': [1085774520, 660749132, 1089060216, 1089946655], 'label': '768.1090187.48.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '48.ef1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ef1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633434
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.eg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.y1', '24.dh1', '24.dn1', '24.dr1'], 'contains': ['96.ca1', '96.cg1', '96.cl2', '96.eh1', '96.em1', '96.ff1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9012, -1, 9382, -1], 'generators': [1089018497, 1087290726, 660749132, 1089946655], 'label': '768.1090187.48.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.eg1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633435
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.eh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.z1', '24.di1', '24.dn1', '24.dr1'], 'contains': ['96.cb1', '96.cl2', '96.ei1', '96.fg1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8717, -1, 8241, -1], 'generators': [1083218598, 1087290726, 668673292, 1089946655], 'label': '768.1090187.48.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.eh1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633436
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.ei1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bc1', '24.dh1', '24.di1', '24.do1', '24.dt1'], 'contains': ['96.ch1', '96.cl2', '96.en1', '96.fh1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [8573, -1, 6832, -1], 'generators': [508566806, 1074855263, 1078887480, 504259697], 'label': '768.1090187.48.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.ei1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ei1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633437
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.ej1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.v1', '24.cz1', '24.dj1', '24.dy1'], 'contains': ['96.bz1', '96.cc1', '96.ci1', '96.cj1', '96.cq1', '96.dr1', '96.du1', '96.ef1', '96.ek2', '96.ev1', '96.fs1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [1774, -1, 1819, -1], 'generators': [1076429862, 1084833144, 1081574431, 1087249055], 'label': '768.1090187.48.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ej1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ej1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633438
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.ek1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.v1', '24.da1', '24.dk1', '24.dx1'], 'contains': ['96.bv1', '96.cj1', '96.cr1', '96.du1', '96.ed1', '96.ew1', '96.fx1'], 'core': '384.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1558, -1, 1363, -1], 'generators': [1076429862, 1074660408, 1081574431, 1087249055], 'label': '768.1090187.48.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ek1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ek1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633439
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.el1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w1', '24.de2', '24.df1', '24.dq2', '24.du1'], 'contains': ['96.c1', '96.bw1', '96.bx1', '96.by2', '96.ee1', '96.ee2', '96.fy1'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [7365, -1, 5099, -1], 'generators': [1074840641, 1083098168, 1081547512, 1081574431], 'label': '768.1090187.48.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.el1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.el1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633440
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.el2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.w2', '24.de1', '24.df1', '24.dq1', '24.du1'], 'contains': ['96.bw1', '96.bx1', '96.by1', '96.cm1', '96.ee3', '96.ee4', '96.fy2'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6934, -1, 4456, -1], 'generators': [1083098168, 1089963103, 1081547512, 1080656934], 'label': '768.1090187.48.el2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.el2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.el2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633441
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.em1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.k1', '24.x1', '24.dr1', '24.dv1'], 'contains': ['96.c1', '96.ca1', '96.cb1', '96.eg1', '96.fz1'], 'core': '96.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [8538, -1, 8763, -1], 'generators': [1083098168, 1081574431, 1081596600, 658250892], 'label': '768.1090187.48.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '48.em1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.em1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633442
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.e1', '6.b1'], 'contains': ['24.a1', '24.e1', '24.f1', '24.q1', '24.r1', '24.x1', '24.ba1', '24.bh1', '24.br1'], 'core': '24.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9288, -1, 7807, -1], 'generators': [1083180097, 1083098168, 1085750593, 1081574431, 1089985272, 658250892], 'label': '768.1090187.12.e1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.e1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633443
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.en1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.y1', '24.dr2', '24.dv1'], 'contains': ['96.ca1', '96.cm1', '96.eh1', '96.ga1'], 'core': '384.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8555, -1, 9514, -1], 'generators': [1083218598, 660749132, 1083098168, 1080656934], 'label': '768.1090187.48.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.en1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.en1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633444
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.eo1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.z1', '24.dr2', '24.ds1', '24.dv1', '24.dw1'], 'contains': ['96.cb1', '96.cm1', '96.ei1', '96.gb1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8487, -1, 8112, -1], 'generators': [1083218598, 1083098168, 1080656934, 668673292], 'label': '768.1090187.48.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.eo1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633445
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.ep1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '24.db1', '24.dl1', '24.dx1'], 'contains': ['96.cc1', '96.ck1', '96.cr1', '96.dx1', '96.ek2', '96.ew1', '96.gl1'], 'core': '384.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [813, -1, 483, -1], 'generators': [1087390721, 1089060216, 1083229185, 1089936056], 'label': '768.1090187.48.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ep1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ep1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633446
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.eq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bd1', '24.dc1', '24.dm1', '24.dn1', '24.do1', '24.dx1'], 'contains': ['96.bv1', '96.ck1', '96.cl1', '96.cl2', '96.ec1', '96.ec3', '96.eu1', '96.ex1', '96.fi1'], 'core': '384.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7517, -1, 5369, -1], 'generators': [1074724198, 1081574431, 1077347359, 1087249055], 'label': '768.1090187.48.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.eq1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633447
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.er1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bd1', '24.dd1', '24.dp1', '24.dx1', '24.dy1'], 'contains': ['96.cc1', '96.ci1', '96.cj1', '96.ck1', '96.cl1', '96.cl2', '96.ec2', '96.ec4', '96.es1', '96.es2', '96.et1', '96.eu1', '96.ez1', '96.ft1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [4242, -1, 3898, -1], 'generators': [1076429862, 1074724198, 1087380134, 1081574431], 'label': '768.1090187.48.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.er1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.er1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633448
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.es1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bd1', '24.de1', '24.dq1', '24.dr2', '24.ds1', '24.dy1'], 'contains': ['96.bz1', '96.ci1', '96.cl1', '96.cm1', '96.ec1', '96.ej2', '96.es1', '96.ey1', '96.fw1'], 'core': '384.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7771, -1, 5638, -1], 'generators': [1083218598, 1083098168, 1087421791, 1080656934], 'label': '768.1090187.48.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.es1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.es1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633795
    {'ambient': '768.1090187', 'aut_centralizer_order': 48, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.k1', '64.c1', '64.f1'], 'contains': ['256.a1', '384.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [1776, -1, 6455, -1], 'generators': [2148863004, 504396399], 'label': '768.1090187.128.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1', 'old_label': '128.d1', 'projective_image': '768.1090187', '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': '6.1'}
  • id: 59633449
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.es2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bd1', '24.de2', '24.dq2', '24.dr1', '24.dt1', '24.dy1'], 'contains': ['96.c1', '96.bz1', '96.ci1', '96.cl2', '96.ec3', '96.ej1', '96.es2', '96.ey1', '96.fw2'], 'core': '96.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [7783, -1, 5672, -1], 'generators': [1083098168, 1081574431, 1081596600, 1077411137], 'label': '768.1090187.48.es2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.es2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.es2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633450
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.et1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.c1', '24.bd1', '24.df1', '24.du1', '24.dv1', '24.dw1', '24.dy1'], 'contains': ['96.c1', '96.bv1', '96.cj1', '96.cm1', '96.ej1', '96.ej2', '96.et1', '96.ex1', '96.gc1'], 'core': '96.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [6518, -1, 5536, -1], 'generators': [1074660408, 1081574431, 1083229185, 1089936056], 'label': '768.1090187.48.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.et1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.et1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633451
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.eu1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.be1', '24.cy1', '24.cz1', '24.dg1', '24.dj1'], 'contains': ['96.cn1', '96.cp1', '96.cq1', '96.cs1', '96.cu1', '96.gm1', '96.gn1', '96.gp1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [1737, -1, 652, -1], 'generators': [1076429862, 1084833144, 1089963103, 1076468417], 'label': '768.1090187.48.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.eu1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633452
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ev1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.be1', '24.da1', '24.db1', '24.dk1', '24.dl1'], 'contains': ['96.cn1', '96.cp1', '96.cr1', '96.gm1', '96.go1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [788, -1, 314, -1], 'generators': [1081547512, 1087390721, 1087276152, 1083229185], 'label': '768.1090187.48.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ev1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ev1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633453
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1088763', 'aut_weyl_index': 24, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['24.e1', '24.h1', '24.p1', '24.y1', '24.bb1', '24.bi1', '24.bs1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9595, -1, 9606, -1], 'generators': [1083180097, 660749132, 1083098168, 1085750593, 1074830054, 1080656934], 'label': '768.1090187.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.f1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633454
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ew1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.bf1', '24.cy1', '24.cz1', '24.ea1', '24.eb1', '24.eb2'], 'contains': ['96.cv1', '96.cw1', '96.cy1', '96.dd1', '96.dg1', '96.dl1', '96.dq1', '96.dr1', '96.dt1', '96.dw1', '96.ea1', '96.fb1', '96.fm1', '96.gf1', '96.gp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [2830, -1, 2258, -1], 'generators': [1083180097, 1078860511, 1083063654, 1078887480], 'label': '768.1090187.48.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ew1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ew1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633455
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ex1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bf1', '24.cz1', '24.da1', '24.ea1', '24.ec1'], 'contains': ['96.cv1', '96.cx1', '96.dg1', '96.di1', '96.dn1', '96.dt1', '96.du1', '96.dy1', '96.fm1', '96.fv1', '96.gm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2449, -1, 1600, -1], 'generators': [1076429862, 1083180097, 1078860511, 1081574431], 'label': '768.1090187.48.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ex1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ex1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633456
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ey1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bf1', '24.cy1', '24.db1', '24.dz1', '24.ea1'], 'contains': ['96.cw1', '96.cx1', '96.dl1', '96.dm1', '96.dn1', '96.dw1', '96.dx1', '96.dy1', '96.gf1', '96.gk1', '96.gm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2437, -1, 1228, -1], 'generators': [1076429862, 1083180097, 1078860511, 1087421791], 'label': '768.1090187.48.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ey1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ey1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633457
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ez1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bk1', '24.dc1', '24.de1', '24.ea1'], 'contains': ['96.cw1', '96.cz2', '96.de1', '96.dg1', '96.dv1', '96.ec1', '96.ee3', '96.fd1', '96.fo1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6922, -1, 4828, -1], 'generators': [1074724198, 1083180097, 1081547512, 1078887480], 'label': '768.1090187.48.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ez1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ez1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633458
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ez2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bk1', '24.dd1', '24.dz1', '24.ea1', '24.eb1'], 'contains': ['96.cv1', '96.cw1', '96.da2', '96.de1', '96.dl1', '96.ds1', '96.dv1', '96.ec2', '96.el3', '96.fd2', '96.gi1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4820, -1, 3797, -1], 'generators': [1074724198, 1083180097, 1078860511, 1078887480], 'label': '768.1090187.48.ez2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ez2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ez2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633459
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ez3', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bk2', '24.dc1', '24.de2', '24.ea1'], 'contains': ['96.cw1', '96.cz1', '96.de2', '96.dg1', '96.dv2', '96.ec3', '96.ee1', '96.fd3', '96.fo1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7264, -1, 4896, -1], 'generators': [1083180097, 1081547512, 1074855263, 1078887480], 'label': '768.1090187.48.ez3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ez3', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ez3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633460
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ez4', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bk2', '24.dd1', '24.dz1', '24.ea1', '24.eb2'], 'contains': ['96.cv1', '96.cw1', '96.da1', '96.de2', '96.dl1', '96.ds2', '96.dv2', '96.ec4', '96.el1', '96.fd4', '96.gi1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4910, -1, 3831, -1], 'generators': [1083180097, 1078860511, 1074855263, 1078887480], 'label': '768.1090187.48.ez4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ez4', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ez4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633461
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fa1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bg1', '24.cy1', '24.da1', '24.dz1', '24.ec1', '24.ed1', '24.ef1'], 'contains': ['96.cv1', '96.cx1', '96.db1', '96.df1', '96.dn1', '96.dt1', '96.dy2', '96.ed1', '96.ep1', '96.fj1', '96.gm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1889, -1, 991, -1], 'generators': [1083180097, 1081547512, 1081574431, 1077347359], 'label': '768.1090187.48.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fa1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fa1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633462
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fb1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bg1', '24.cz1', '24.eb1', '24.eb2', '24.ee1'], 'contains': ['96.cv1', '96.cy1', '96.dc1', '96.dh1', '96.dq1', '96.dt1', '96.ea2', '96.ef1', '96.er1', '96.fn1', '96.gp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2554, -1, 1751, -1], 'generators': [1084833144, 1083180097, 1078860511, 1078887480], 'label': '768.1090187.48.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fb1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633463
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fc1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bk1', '24.de2', '24.df1', '24.eb2', '24.ec1'], 'contains': ['96.cv1', '96.cz2', '96.dg1', '96.dj1', '96.ds1', '96.ee3', '96.ej1', '96.fo1', '96.fy1'], 'core': '192.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [6809, -1, 5065, -1], 'generators': [1083180097, 1078860511, 1083098168, 1081574431], 'label': '768.1090187.48.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fc1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633464
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '256.29080', 'aut_weyl_index': 72, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '6.c1'], 'contains': ['24.f1', '24.h1', '24.s1', '24.z1', '24.bc1', '24.bj1', '24.bt1'], 'core': '96.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9122, -1, 7324, -1], 'generators': [1083180097, 1083098168, 1085750593, 1074830054, 1080656934, 668673292], 'label': '768.1090187.12.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.g1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633465
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fc2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bk2', '24.de1', '24.df1', '24.eb1', '24.ec1'], 'contains': ['96.cv1', '96.cz1', '96.dg1', '96.dj2', '96.ds2', '96.ee1', '96.ej2', '96.fo1', '96.fy2'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6826, -1, 4930, -1], 'generators': [1083180097, 1078860511, 1083098168, 1080656934], 'label': '768.1090187.48.fc2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fc2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fc2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633466
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fd1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bg1', '24.cy1', '24.ea1', '24.ee1', '24.eg1'], 'contains': ['96.cw1', '96.cx1', '96.dc1', '96.dk1', '96.dq1', '96.dw1', '96.dy2', '96.ek1', '96.er1', '96.gd1', '96.gp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1858, -1, 821, -1], 'generators': [1076429862, 1087290726, 1083180097, 1083202278], 'label': '768.1090187.48.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fd1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633467
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fd2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bg1', '24.cz1', '24.db1', '24.ea1', '24.ed1'], 'contains': ['96.cw1', '96.cy1', '96.db1', '96.dk1', '96.dn1', '96.dw1', '96.ea2', '96.ek2', '96.ep1', '96.gd2', '96.gm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1711, -1, 754, -1], 'generators': [1076429862, 1087290726, 1083180097, 1078860511], 'label': '768.1090187.48.fd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fd2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fd2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633468
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fe1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.bl1', '24.dd1', '24.de1', '24.ea1', '24.eb2', '24.ed1', '24.ee1'], 'contains': ['96.cv1', '96.cw1', '96.cy1', '96.cz2', '96.da1', '96.dc1', '96.dd1', '96.ds2', '96.dv1', '96.eb1', '96.ee4', '96.el2', '96.eq1', '96.es1', '96.fa1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4255, -1, 3323, -1], 'generators': [1083180097, 1083063654, 1089985272, 1078887480], 'label': '768.1090187.48.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fe1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fe1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633469
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fe2', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.bl1', '24.dd1', '24.de2', '24.ea1', '24.eb1', '24.ed1', '24.ee1'], 'contains': ['96.cv1', '96.cw1', '96.cy1', '96.cz1', '96.da2', '96.dc1', '96.dd1', '96.ds1', '96.dv2', '96.eb1', '96.ee2', '96.el4', '96.eq1', '96.es2', '96.fa2'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4584, -1, 3289, -1], 'generators': [1083180097, 1083063654, 1089067713, 1078887480], 'label': '768.1090187.48.fe2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fe2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fe2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633470
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ff1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.bl1', '24.dd1', '24.df1', '24.ea1', '24.ec1', '24.ee1', '24.ef1'], 'contains': ['96.cv1', '96.cx1', '96.cz1', '96.cz2', '96.db1', '96.di1', '96.ds1', '96.ds2', '96.dz1', '96.ee2', '96.ee4', '96.eo1', '96.et1', '96.fu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4126, -1, 3053, -1], 'generators': [1076429862, 1083180097, 1081574431, 1089985272], 'label': '768.1090187.48.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ff1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ff1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633471
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fg1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.bl1', '24.dc1', '24.dd1', '24.dz1', '24.ea1', '24.ed1', '24.eg1'], 'contains': ['96.cw1', '96.cx1', '96.da1', '96.da2', '96.db1', '96.dm1', '96.dv1', '96.dv2', '96.dz1', '96.el2', '96.el4', '96.eo1', '96.eu1', '96.gj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3860, -1, 2714, -1], 'generators': [1076429862, 1083180097, 1089985272, 1087421791], 'label': '768.1090187.48.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633472
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fh1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bm1', '24.cy1', '24.cz1', '24.ed1', '24.ee1'], 'contains': ['96.cx1', '96.cy1', '96.db1', '96.dc1', '96.do1', '96.dy1', '96.ea1', '96.ep1', '96.er1', '96.ev1', '96.gn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1725, -1, 686, -1], 'generators': [1076429862, 1084833144, 1083180097, 1076468417], 'label': '768.1090187.48.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fh1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633473
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fi1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.bm1', '24.da1', '24.db1', '24.ef1', '24.eg1'], 'contains': ['96.cx1', '96.db1', '96.dp1', '96.dy1', '96.ep1', '96.ew1', '96.go1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [800, -1, 348, -1], 'generators': [1083180097, 1078860511, 1087390721, 1083229185], 'label': '768.1090187.48.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fi1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633474
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fj1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bn1', '24.dc1', '24.df1', '24.ed1', '24.ef1'], 'contains': ['96.cz1', '96.cz2', '96.db1', '96.df1', '96.ee1', '96.ee3', '96.eo1', '96.ex1', '96.fk1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5103, -1, 4068, -1], 'generators': [1083180097, 1081574431, 1089985272, 1077347359], 'label': '768.1090187.48.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fj1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633475
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.a1', '6.b1', '6.c1'], 'contains': ['24.a1', '24.d1', '24.g1', '24.h1', '24.k1', '24.t1', '24.w1', '24.w2', '24.bd1', '24.bk1', '24.bk2', '24.bl1', '24.bn1', '24.bu1', '24.dc1', '24.dd1', '24.de1', '24.de2', '24.df1'], 'core': '24.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7447, -1, 4523, -1], 'generators': [1083180097, 1074660408, 1085750593, 1081547512, 1081574431, 1083229185], 'label': '768.1090187.12.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.h1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633476
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fk1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bn1', '24.de1', '24.de2', '24.ee1'], 'contains': ['96.cz1', '96.cz2', '96.dc1', '96.dh1', '96.ee1', '96.ee3', '96.eq1', '96.ey1', '96.fp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7328, -1, 4490, -1], 'generators': [1084833144, 1083180097, 1087298271, 1078887480], 'label': '768.1090187.48.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fk1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633477
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fl1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bn1', '24.dd1', '24.ed1', '24.ee1', '24.eg1'], 'contains': ['96.da1', '96.da2', '96.db1', '96.dc1', '96.dk1', '96.el1', '96.el3', '96.eo1', '96.eq1', '96.ez1', '96.ge1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3102, -1, 2292, -1], 'generators': [1076429862, 1087290726, 1083180097, 1089985272], 'label': '768.1090187.48.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fl1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633478
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.fm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bq1', '24.cy1', '24.ed1', '24.eh1', '24.ei1'], 'contains': ['96.dd1', '96.df1', '96.dk1', '96.dm1', '96.do1', '96.fb1', '96.fc1', '96.fj1', '96.gd1', '96.gk1', '96.gn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1911, -1, 957, -1], 'generators': [1078860511, 1083063654, 1081574431, 1077347359], 'label': '768.1090187.48.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fm1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633479
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.fn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bu1', '24.dc1', '24.dz1', '24.eh1'], 'contains': ['96.de1', '96.de2', '96.df1', '96.dm1', '96.fd1', '96.fd3', '96.fi1', '96.fk1', '96.gj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6168, -1, 4287, -1], 'generators': [1074724198, 1078860511, 1081574431, 1077347359], 'label': '768.1090187.48.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fn1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633480
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.fo1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.bq1', '24.cz1', '24.ee1', '24.ei1'], 'contains': ['96.dd1', '96.dh1', '96.di1', '96.dk1', '96.do1', '96.fb1', '96.fn1', '96.fs1', '96.fv1', '96.gd2', '96.gn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1945, -1, 1464, -1], 'generators': [1076429862, 1084833144, 1078860511, 1081574431], 'label': '768.1090187.48.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fo1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633481
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.fp1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bu1', '24.dd1', '24.ea1', '24.eh1', '24.ei1'], 'contains': ['96.dd1', '96.de1', '96.de2', '96.di1', '96.dk1', '96.dm1', '96.fa1', '96.fa2', '96.fd2', '96.fd4', '96.ft1', '96.fu1', '96.ge1', '96.gj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3962, -1, 3357, -1], 'generators': [1076429862, 1074724198, 1081574431, 1078991590], 'label': '768.1090187.48.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fp1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633482
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.fq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bu1', '24.de1', '24.eb1', '24.ei1'], 'contains': ['96.dd1', '96.de1', '96.dh1', '96.dj2', '96.fa1', '96.fd1', '96.fp1', '96.fw1', '96.fy2'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7194, -1, 4862, -1], 'generators': [1083098168, 1074830054, 1087421791, 1080656934], 'label': '768.1090187.48.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fq1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633483
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.fq2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bu1', '24.de2', '24.eb2', '24.ei1'], 'contains': ['96.dd1', '96.de2', '96.dh1', '96.dj1', '96.fa2', '96.fd3', '96.fp1', '96.fw2', '96.fy1'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [7252, -1, 4963, -1], 'generators': [1083098168, 1081574431, 1089985272, 1077411137], 'label': '768.1090187.48.fq2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fq2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fq2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633484
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.fr1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bq1', '24.da1', '24.ef1', '24.eh1', '24.ej1'], 'contains': ['96.df1', '96.di1', '96.dp1', '96.fj1', '96.fv1', '96.fx1', '96.go1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1533, -1, 855, -1], 'generators': [1076429862, 1074660408, 1078860511, 1081574431], 'label': '768.1090187.48.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fr1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633485
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.fs1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bu1', '24.df1', '24.ec1', '24.ei1', '24.ej1'], 'contains': ['96.df1', '96.di1', '96.dj1', '96.dj2', '96.fk1', '96.fu1', '96.fy1', '96.fy2', '96.gc1'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [5075, -1, 4523, -1], 'generators': [1074660408, 1081547512, 1081574431, 1083229185], 'label': '768.1090187.48.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fs1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633486
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4608.dp', 'aut_weyl_index': 4, 'centralizer': '192.a1', 'complements': ['384.c1', '384.h1', '384.i1', '384.l1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '6.g1', '8.f1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4837, 3665, 5457, 2785], 'generators': [1074660408, 1081574431, 1076429862, 1084867622, 669132075, 506952305, 2150763522, 1085750593], 'label': '768.1090187.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '192.1538', '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': '192.1538'}
  • id: 59633487
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 72, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1'], 'contains': ['24.k1', '24.l1', '24.m1', '24.p1', '24.q1', '24.r1', '24.s1', '24.cm1', '24.cn1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9453, -1, 8012, -1], 'generators': [1076429862, 1085750593, 1089985272, 1078871160, 658250892, 1080656934], 'label': '768.1090187.12.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.i1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633488
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.ft1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bq1', '24.db1', '24.eg1', '24.eh1'], 'contains': ['96.dk1', '96.dm1', '96.dp1', '96.gd2', '96.gk1', '96.gl1', '96.go1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1546, -1, 449, -1], 'generators': [1081547512, 1087390721, 1089060216, 1083229185], 'label': '768.1090187.48.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ft1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ft1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633489
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fu1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.bv1', '24.dg1', '24.dj1', '24.ea1', '24.eb1', '24.eb2'], 'contains': ['96.dr1', '96.ds1', '96.ds2', '96.dv1', '96.dv2', '96.ea2', '96.eb1', '96.fa1', '96.fa2', '96.fm1', '96.fo1', '96.gf1', '96.gi1', '96.gp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3455, -1, 2883, -1], 'generators': [1083063654, 1089985272, 1076479078, 1078887480], 'label': '768.1090187.48.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fu1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633490
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fv1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bv1', '24.dj1', '24.dk1', '24.ea1', '24.ec1'], 'contains': ['96.ds1', '96.ds2', '96.du1', '96.dy2', '96.dz1', '96.fm1', '96.fo1', '96.fu1', '96.gm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2765, -1, 2443, -1], 'generators': [1076429862, 1081574431, 1089985272, 1076479078], 'label': '768.1090187.48.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fv1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633491
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fw1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bv1', '24.dg1', '24.dl1', '24.dz1', '24.ea1'], 'contains': ['96.dv1', '96.dv2', '96.dx1', '96.dy2', '96.dz1', '96.gf1', '96.gi1', '96.gj1', '96.gm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2529, -1, 1785, -1], 'generators': [1076429862, 1089985272, 1076479078, 1087421791], 'label': '768.1090187.48.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fw1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633492
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fx1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ca1', '24.dm1', '24.dq1', '24.ea1'], 'contains': ['96.dv2', '96.dw1', '96.ec1', '96.ee4', '96.fd2', '96.fm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5966, -1, 3560, -1], 'generators': [1074724198, 1078860511, 1078887480, 1084818534], 'label': '768.1090187.48.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fx1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633493
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fx2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.ca1', '24.dp1', '24.dz1', '24.ea1', '24.eb1'], 'contains': ['96.ds2', '96.dt1', '96.dv2', '96.dw1', '96.ec2', '96.el4', '96.fd1', '96.fd2', '96.gf1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4677, -1, 3459, -1], 'generators': [1074724198, 1081547512, 1078887480, 1084818534], 'label': '768.1090187.48.fx2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fx2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fx2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633494
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fx3', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.ca2', '24.dm1', '24.dq2', '24.ea1', '24.ek1'], 'contains': ['96.dv1', '96.dw1', '96.ec3', '96.ee2', '96.fd4', '96.fm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6027, -1, 3763, -1], 'generators': [1078860511, 1074855263, 1078887480, 1084818534], 'label': '768.1090187.48.fx3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fx3', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fx3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633495
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.fx4', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.ca2', '24.dp1', '24.dz1', '24.ea1', '24.eb2'], 'contains': ['96.ds1', '96.dt1', '96.dv1', '96.dw1', '96.ec4', '96.el2', '96.fd3', '96.fd4', '96.gf1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4633, -1, 3492, -1], 'generators': [1081547512, 1074855263, 1078887480, 1084818534], 'label': '768.1090187.48.fx4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fx4', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fx4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633497
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.fy2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cb2', '24.dn1', '24.dr1', '24.ek1'], 'contains': ['96.ec3', '96.eg1', '96.ff1', '96.fg1', '96.fq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8909, -1, 8819, -1], 'generators': [1087290726, 660749132, 1087249055, 1089946655], 'label': '768.1090187.48.fy2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.fy2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fy2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633498
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 384, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1'], 'contains': ['24.j1', '24.k1', '24.t1', '24.v1', '24.be1', '24.bv1', '24.bw1', '24.cg1', '24.co1', '24.dg1', '24.dj1', '24.dk1', '24.dl1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2700, -1, 1971, -1], 'generators': [1076429862, 1074660408, 1085750593, 1081574431, 1089985272, 1076479078], 'label': '768.1090187.12.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.j1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633499
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.fz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ce1', '24.do1', '24.dt1', '24.ek1'], 'contains': ['96.ec3', '96.fh1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8508, -1, 6696, -1], 'generators': [508566806, 1074855263, 1078887480, 515340849], 'label': '768.1090187.48.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.fz1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633500
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.ga1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bw1', '24.dg1', '24.dk1', '24.dz1', '24.ec1', '24.ed1', '24.ef1'], 'contains': ['96.ds1', '96.ds2', '96.dy1', '96.dz1', '96.ed1', '96.eo1', '96.fj1', '96.fk1', '96.gm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2328, -1, 1634, -1], 'generators': [1081574431, 1089985272, 1077347359, 1084818534], 'label': '768.1090187.48.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ga1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ga1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633501
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gb1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bw1', '24.dj1', '24.eb1', '24.eb2', '24.ee1'], 'contains': ['96.ds1', '96.ds2', '96.ea1', '96.eb1', '96.ef1', '96.eq1', '96.fn1', '96.fp1', '96.gp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2817, -1, 2376, -1], 'generators': [1084833144, 1087298271, 1078887480, 1084818534], 'label': '768.1090187.48.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gb1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633502
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gc1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ca1', '24.dq2', '24.du1', '24.eb2', '24.ec1'], 'contains': ['96.ds2', '96.dt1', '96.ee4', '96.ej1', '96.fm1', '96.fy1'], 'core': '192.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [5635, -1, 4185, -1], 'generators': [1074840641, 1078860511, 1083098168, 1081574431], 'label': '768.1090187.48.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gc1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633503
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gc2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ca2', '24.dq1', '24.du1', '24.eb1', '24.ec1'], 'contains': ['96.ds1', '96.dt1', '96.ee2', '96.ej2', '96.fm1', '96.fy2'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5647, -1, 4000, -1], 'generators': [1078860511, 1083098168, 1089963103, 1080656934], 'label': '768.1090187.48.gc2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gc2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gc2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633504
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.gd1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cb1', '24.dr1', '24.dv1'], 'contains': ['96.eh1', '96.ei1', '96.ej1', '96.fq1', '96.fz1'], 'core': '192.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [8866, -1, 9110, -1], 'generators': [1083098168, 1081574431, 658250892, 1089936056], 'label': '768.1090187.48.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '48.gd1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633505
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.gd2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cb2', '24.dr2', '24.dv1', '24.el1', '24.em1'], 'contains': ['96.eg1', '96.ej2', '96.fq1', '96.ga1', '96.gb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8419, -1, 8649, -1], 'generators': [1083098168, 1080656934, 668673292, 1087249055], 'label': '768.1090187.48.gd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.gd2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gd2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633506
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.ge1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cc1', '24.ds1', '24.dw1', '24.el1', '24.em1'], 'contains': ['96.ej2', '96.gb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8273, -1, 7103, -1], 'generators': [1083098168, 1084856961, 1080656934, 668673292], 'label': '768.1090187.48.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ge1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ge1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633507
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gf1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bw1', '24.dg1', '24.ea1', '24.ee1', '24.eg1'], 'contains': ['96.dv1', '96.dv2', '96.dy1', '96.dz1', '96.ek1', '96.eq1', '96.gd2', '96.ge1', '96.gp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2316, -1, 1160, -1], 'generators': [1076429862, 1087290726, 1089963103, 1089985272], 'label': '768.1090187.48.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gf1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633508
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gf2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.bw1', '24.dj1', '24.dl1', '24.ea1', '24.ed1'], 'contains': ['96.dv1', '96.dv2', '96.ea1', '96.eb1', '96.ek2', '96.eo1', '96.gd1', '96.ge1', '96.gm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2014, -1, 1126, -1], 'generators': [1076429862, 1087290726, 1089985272, 1076479078], 'label': '768.1090187.48.gf2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gf2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gf2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633509
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 72, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1'], 'contains': ['24.n1', '24.o1', '24.p1', '24.s1', '24.w1', '24.x1', '24.ba1', '24.bx1', '24.cp1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9528, -1, 8115, -1], 'generators': [1074840641, 1083098168, 1081547512, 1085750593, 1081574431, 658250892], 'label': '768.1090187.12.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.k1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633510
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '48.gg1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.by1', '24.dh1'], 'contains': ['96.el3', '96.em1', '96.en1', '96.gg1', '96.gh1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [9100, -1, 7379, -1], 'generators': [1087290726, 1077396575, 1076468417, 658250892], 'label': '768.1090187.48.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '48.gg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633511
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gh1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.cf1', '24.dp1', '24.dq1', '24.ea1', '24.eb2', '24.ed1', '24.ee1'], 'contains': ['96.ds1', '96.dt1', '96.dv2', '96.dw1', '96.ea1', '96.ea2', '96.ee3', '96.ee4', '96.el1', '96.el2', '96.eq1', '96.er1', '96.es1', '96.fa2', '96.fb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3759, -1, 2917, -1], 'generators': [1083063654, 1089067713, 1078887480, 1083049080], 'label': '768.1090187.48.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gh1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633512
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gh2', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.cf1', '24.dp1', '24.dq2', '24.ea1', '24.eb1', '24.ed1', '24.ee1'], 'contains': ['96.ds2', '96.dt1', '96.dv1', '96.dw1', '96.ea1', '96.ea2', '96.ee1', '96.ee2', '96.el3', '96.el4', '96.eq1', '96.er1', '96.es2', '96.fa1', '96.fb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3813, -1, 2951, -1], 'generators': [1083063654, 1089985272, 1078887480, 1083049080], 'label': '768.1090187.48.gh2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gh2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gh2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633513
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gi1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.cf1', '24.dp1', '24.du1', '24.ea1', '24.ec1', '24.ee1', '24.ef1'], 'contains': ['96.ds1', '96.ds2', '96.dt1', '96.dy1', '96.dy2', '96.ee1', '96.ee2', '96.ee3', '96.ee4', '96.eo1', '96.ep1', '96.et1', '96.fu1', '96.fv1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3629, -1, 2782, -1], 'generators': [1076429862, 1081574431, 1089985272, 1083049080], 'label': '768.1090187.48.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gi1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633514
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gj1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.cf1', '24.dm1', '24.dp1', '24.dz1', '24.ea1', '24.ed1', '24.eg1'], 'contains': ['96.dv1', '96.dv2', '96.dw1', '96.dy1', '96.dy2', '96.el1', '96.el2', '96.el3', '96.el4', '96.eo1', '96.ep1', '96.eu1', '96.gj1', '96.gk1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3065, -1, 2477, -1], 'generators': [1076429862, 1089985272, 1087421791, 1083049080], 'label': '768.1090187.48.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gj1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633515
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gk1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.cg1', '24.dg1', '24.dj1', '24.ed1', '24.ee1'], 'contains': ['96.dy2', '96.dz1', '96.ea2', '96.eb1', '96.eo1', '96.eq1', '96.ev1', '96.gn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1846, -1, 1092, -1], 'generators': [1076429862, 1084833144, 1089963103, 1089985272], 'label': '768.1090187.48.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gk1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633516
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.cg1', '24.dk1', '24.dl1', '24.ef1', '24.eg1'], 'contains': ['96.dy2', '96.dz1', '96.eo1', '96.ew1', '96.go1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1521, -1, 517, -1], 'generators': [1078860511, 1087390721, 1087276152, 1083229185], 'label': '768.1090187.48.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gl1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633517
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.gm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.ck1', '24.dx1', '24.dz1'], 'contains': ['96.dx1', '96.ec2', '96.ec4', '96.ed1', '96.eu1', '96.fi1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4619, -1, 3696, -1], 'generators': [1074724198, 1081574431, 1077347359, 1089936056], 'label': '768.1090187.48.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gm1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633518
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ch1', '24.dm1', '24.du1', '24.ed1', '24.ef1'], 'contains': ['96.ee2', '96.ee4', '96.eo1', '96.ep1', '96.ex1', '96.fj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4230, -1, 2579, -1], 'generators': [1087298271, 1081574431, 1077347359, 1084818534], 'label': '768.1090187.48.gn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gn1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633519
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.go1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ci1', '24.dn1', '24.dv1'], 'contains': ['96.eg1', '96.eh1', '96.ei1', '96.ex1', '96.fl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8651, -1, 9054, -1], 'generators': [1076429862, 1081596600, 658250892, 1080656934], 'label': '768.1090187.48.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '48.go1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.go1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633520
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '512.7536911', 'aut_weyl_index': 36, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '6.d1'], 'contains': ['24.n1', '24.q1', '24.w2', '24.y1', '24.bc1', '24.by1', '24.cq1', '24.dh1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9019, -1, 6780, -1], 'generators': [1078860511, 660749132, 1083098168, 1085750593, 1087276152, 1080656934], 'label': '768.1090187.12.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.l1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633521
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gp1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ch1', '24.dq1', '24.dq2', '24.ee1'], 'contains': ['96.ee2', '96.ee4', '96.eq1', '96.er1', '96.ey1', '96.fn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5557, -1, 3086, -1], 'generators': [1084833144, 1089985272, 1078887480, 1084818534], 'label': '768.1090187.48.gp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gp1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633522
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '48.gq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ci1', '24.dr1', '24.dr2'], 'contains': ['96.eg1', '96.eh1', '96.ei1', '96.ey1', '96.fr1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8930, -1, 9280, -1], 'generators': [1085774520, 668673292, 1089946655, 1083194719], 'label': '768.1090187.48.gq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '48.gq1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633523
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.gr1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ck1', '24.dx1', '24.dy1', '24.ea1'], 'contains': ['96.dr1', '96.du1', '96.dx1', '96.ec1', '96.ec2', '96.ec3', '96.ec4', '96.ek1', '96.ek2', '96.es1', '96.es2', '96.et1', '96.eu1', '96.ft1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3826, -1, 3662, -1], 'generators': [1076429862, 1074724198, 1081574431, 1087249055], 'label': '768.1090187.48.gr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gr1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633524
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.gs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ck1', '24.dy1', '24.eb1', '24.el1'], 'contains': ['96.dr1', '96.ec2', '96.ef1', '96.ej2', '96.es2', '96.fw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5941, -1, 4726, -1], 'generators': [1083098168, 1087421791, 1080656934, 1087249055], 'label': '768.1090187.48.gs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gs1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633525
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.gs2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.ck1', '24.dy1', '24.eb2'], 'contains': ['96.dr1', '96.ec4', '96.ef1', '96.ej1', '96.es1', '96.fw2'], 'core': '192.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [5623, -1, 4422, -1], 'generators': [1083098168, 1081574431, 1087249055, 1077411137], 'label': '768.1090187.48.gs2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gs2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gs2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633526
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.gt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.c1', '24.ck1', '24.dy1', '24.ec1', '24.em1'], 'contains': ['96.du1', '96.ed1', '96.ej1', '96.ej2', '96.et1', '96.gc1'], 'core': '192.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [5514, -1, 5200, -1], 'generators': [1074660408, 1081574431, 1083229185, 1087249055], 'label': '768.1090187.48.gt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gt1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gt1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633527
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '48.gu1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.ch1', '24.dp1', '24.ed1', '24.ee1', '24.eg1'], 'contains': ['96.el2', '96.el4', '96.eo1', '96.ep1', '96.eq1', '96.er1', '96.ez1', '96.gd1', '96.gd2'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2585, -1, 1295, -1], 'generators': [1076429862, 1087290726, 1089963103, 1083202278], 'label': '768.1090187.48.gu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gu1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633528
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.gv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cl1', '24.dx1', '24.dy1', '24.ed1'], 'contains': ['96.ed1', '96.ek2', '96.es1', '96.es2', '96.eu1', '96.ev1', '96.ex1', '96.ez1', '96.fc1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2542, -1, 2123, -1], 'generators': [1083063654, 1081574431, 1081596600, 1077347359], 'label': '768.1090187.48.gv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gv1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633529
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.gw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cl1', '24.dy1', '24.ee1'], 'contains': ['96.ef1', '96.ek1', '96.es1', '96.es2', '96.et1', '96.ev1', '96.ey1', '96.ez1', '96.fs1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2616, -1, 2816, -1], 'generators': [1076429862, 1084833144, 1081574431, 1081596600], 'label': '768.1090187.48.gw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gw1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633530
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.gx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.cl1', '24.dx1', '24.ef1'], 'contains': ['96.ed1', '96.et1', '96.ew1', '96.ex1', '96.fx1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1699, -1, 2055, -1], 'generators': [1076429862, 1074660408, 1081574431, 1081596600], 'label': '768.1090187.48.gx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gx1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633585
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.s2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.j2', '48.y2', '48.bi1', '48.bm1', '48.bn1', '48.bp2', '48.bx1'], 'contains': ['192.d1', '192.h1', '192.be2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7527, -1, 5696, -1], 'generators': [1089963103, 1085750593, 1087429350], 'label': '768.1090187.96.s2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.s2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633531
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '512.7536911', 'aut_weyl_index': 36, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '6.e1'], 'contains': ['24.o1', '24.r1', '24.w2', '24.z1', '24.bb1', '24.bz1', '24.cr1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9564, -1, 8422, -1], 'generators': [1078860511, 1083098168, 1085750593, 1087276152, 1080656934, 668673292], 'label': '768.1090187.12.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.m1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633532
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '48.gy1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cl1', '24.dx1', '24.eg1'], 'contains': ['96.ek1', '96.eu1', '96.ew1', '96.ez1', '96.gl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1813, -1, 788, -1], 'generators': [1087390721, 1089060216, 1083229185, 1087249055], 'label': '768.1090187.48.gy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gy1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633533
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.gz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.co1', '24.dg1', '24.ed1', '24.eh1', '24.ei1'], 'contains': ['96.fa1', '96.fa2', '96.fc1', '96.fj1', '96.fk1', '96.gd2', '96.ge1', '96.gj1', '96.gn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2269, -1, 1532, -1], 'generators': [1083063654, 1081574431, 1089985272, 1077347359], 'label': '768.1090187.48.gz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gz1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633534
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '48.ha1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.cq1', '24.dh1', '24.ek1', '24.en1', '24.eo1'], 'contains': ['96.fd4', '96.ff1', '96.fh1', '96.gg1', '96.gh1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [8992, -1, 6940, -1], 'generators': [1074855263, 1078887480, 1084818534, 504259697], 'label': '768.1090187.48.ha1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.ha1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ha1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633535
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '48.hb1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['24.cs1', '24.di1', '24.ek1', '24.en1', '24.eo1'], 'contains': ['96.fd4', '96.fg1', '96.fh1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [8595, -1, 6888, -1], 'generators': [1074855263, 1078887480, 1084818534, 515340849], 'label': '768.1090187.48.hb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.hb1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633536
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.hc1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ct1', '24.dm1', '24.dz1', '24.eh1', '24.en1'], 'contains': ['96.fd2', '96.fd4', '96.fi1', '96.fj1', '96.gj1', '96.gk1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5569, -1, 3391, -1], 'generators': [1074724198, 1081547512, 1081574431, 1077347359], 'label': '768.1090187.48.hc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.hc1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633537
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.hd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cu1', '24.dn1', '24.en1'], 'contains': ['96.fe1', '96.ff1', '96.fg1', '96.fi1', '96.fl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8679, -1, 8423, -1], 'generators': [1076429862, 1087390721, 504396399, 1087421791], 'label': '768.1090187.48.hd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.hd1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633538
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.he1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cx1', '24.do1', '24.en1'], 'contains': ['96.fh1', '96.fi1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8321, -1, 6649, -1], 'generators': [1076429862, 1087390721, 1087421791, 512648241], 'label': '768.1090187.48.he1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.he1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.he1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633539
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.hf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.co1', '24.dj1', '24.ee1', '24.ei1'], 'contains': ['96.fa1', '96.fa2', '96.fn1', '96.fp1', '96.fs1', '96.fu1', '96.gd1', '96.ge1', '96.gn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2354, -1, 2022, -1], 'generators': [1076429862, 1084833144, 1081574431, 1089985272], 'label': '768.1090187.48.hf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.hf1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633540
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.hg1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.ct1', '24.dp1', '24.ea1', '24.eh1', '24.ei1'], 'contains': ['96.fa1', '96.fa2', '96.fb1', '96.fd1', '96.fd2', '96.fd3', '96.fd4', '96.ft1', '96.fu1', '96.fv1', '96.gd1', '96.gd2', '96.gj1', '96.gk1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3380, -1, 2985, -1], 'generators': [1076429862, 1074724198, 1078860511, 1081574431], 'label': '768.1090187.48.hg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.hg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633541
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.hh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ct1', '24.dq1', '24.eb1', '24.ei1'], 'contains': ['96.fa2', '96.fb1', '96.fd2', '96.fn1', '96.fw1', '96.fy2'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5660, -1, 3966, -1], 'generators': [1078860511, 1083098168, 1087421791, 1080656934], 'label': '768.1090187.48.hh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.hh1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633542
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 72, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.c1', '6.d1', '6.e1'], 'contains': ['24.w2', '24.z1', '24.bc1', '24.cs1', '24.di1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8681, -1, 6216, -1], 'generators': [1089963103, 1083098168, 1081547512, 1085750593, 1080656934, 668673292], 'label': '768.1090187.12.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.n1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633543
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.hh2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ct1', '24.dq2', '24.eb2', '24.ei1', '24.eo1'], 'contains': ['96.fa1', '96.fb1', '96.fd4', '96.fn1', '96.fw2', '96.fy1'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [6156, -1, 4219, -1], 'generators': [1078860511, 1083098168, 1081574431, 1077411137], 'label': '768.1090187.48.hh2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.hh2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hh2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633544
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.hi1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cu1', '24.dr1', '24.eo1'], 'contains': ['96.ff1', '96.fg1', '96.fr1', '96.fw2', '96.fz1'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [8951, -1, 8367, -1], 'generators': [1083098168, 1083063654, 1081574431, 504396399], 'label': '768.1090187.48.hi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.hi1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633545
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.hi2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cu1', '24.dr2', '24.el1', '24.ep1'], 'contains': ['96.fe1', '96.fr1', '96.fw1', '96.ga1', '96.gb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8465, -1, 8480, -1], 'generators': [504396399, 1087421791, 1078887480, 1085785119], 'label': '768.1090187.48.hi2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.hi2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hi2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633546
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.hj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cv1', '24.ds1', '24.el1', '24.ep1'], 'contains': ['96.fw1', '96.gb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8304, -1, 7206, -1], 'generators': [1087421791, 1078887480, 1085785119, 514417711], 'label': '768.1090187.48.hj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.hj1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633547
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.hk1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cx1', '24.dt1', '24.eo1'], 'contains': ['96.fh1', '96.fw2'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [8624, -1, 6742, -1], 'generators': [1083098168, 1083063654, 1081574431, 512648241], 'label': '768.1090187.48.hk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.hk1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633548
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '48.hl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.dx1', '24.eh1'], 'contains': ['96.fc1', '96.fi1', '96.ft1', '96.fx1', '96.gl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2303, -1, 2646, -1], 'generators': [1076429862, 1074724198, 1074660408, 1081574431], 'label': '768.1090187.48.hl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.hl1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633549
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.hm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.co1', '24.dk1', '24.ef1', '24.eh1', '24.ej1'], 'contains': ['96.fj1', '96.fk1', '96.fu1', '96.fx1', '96.go1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1570, -1, 1431, -1], 'generators': [1076429862, 1074660408, 1081574431, 1089985272], 'label': '768.1090187.48.hm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.hm1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633550
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '48.hn1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.b1', '24.dy1', '24.ei1', '24.ep1'], 'contains': ['96.fc1', '96.fs1', '96.ft1', '96.fw1', '96.fw2', '96.gc1'], 'core': '192.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [5247, -1, 5166, -1], 'generators': [1074660408, 1083063654, 1081574431, 1083229185], 'label': '768.1090187.48.hn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.hn1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633551
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.ho1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ct1', '24.du1', '24.ec1', '24.ei1', '24.ej1'], 'contains': ['96.fj1', '96.fu1', '96.fv1', '96.fy1', '96.fy2', '96.gc1'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [4280, -1, 3932, -1], 'generators': [1074660408, 1078860511, 1081574431, 1083229185], 'label': '768.1090187.48.ho1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ho1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ho1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633552
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.hp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cu1', '24.dv1', '24.em1', '24.ep1', '24.eq1'], 'contains': ['96.fl1', '96.fz1', '96.ga1', '96.gb1', '96.gc1'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [8254, -1, 7958, -1], 'generators': [1076429862, 1081574431, 504396399, 1085785119], 'label': '768.1090187.48.hp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.hp1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633553
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.a1', '6.d1', '6.e1'], 'contains': ['24.j1', '24.t1', '24.u1', '24.w1', '24.w2', '24.bd1', '24.ca1', '24.ca2', '24.cf1', '24.ch1', '24.ct1', '24.dm1', '24.dp1', '24.dq1', '24.dq2', '24.du1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5718, -1, 4048, -1], 'generators': [1074660408, 1078860511, 1085750593, 1081574431, 1083229185, 1084818534], 'label': '768.1090187.12.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.o1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633554
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '48.hq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cv1', '24.dw1', '24.em1', '24.ep1', '24.eq1'], 'contains': ['96.gb1', '96.gc1'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [7829, -1, 7056, -1], 'generators': [1076429862, 1081574431, 1085785119, 514417711], 'label': '768.1090187.48.hq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.hq1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633555
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '48.hr1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.co1', '24.dl1', '24.eg1', '24.eh1'], 'contains': ['96.gd1', '96.ge1', '96.gj1', '96.gl1', '96.go1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1661, -1, 585, -1], 'generators': [1078860511, 1087390721, 1089060216, 1083229185], 'label': '768.1090187.48.hr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.hr1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633556
    {'ambient': '768.1090187', 'aut_centralizer_order': 288, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '16.d1', '32.a1', '32.b1', '32.c1'], 'contains': ['128.a1', '128.b1', '192.a1'], 'core': '192.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [115, -1, 6197, -1], 'generators': [2148207653, 3229953892, 1085750593], 'label': '768.1090187.64.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '64.a1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633557
    {'ambient': '768.1090187', 'aut_centralizer_order': 144, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '16.f1', '32.a1', '32.d1'], 'contains': ['128.a1', '128.c1', '192.b1'], 'core': '192.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [95, -1, 5550, -1], 'generators': [2148207653, 1085750593, 3234148260], 'label': '768.1090187.64.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '64.b1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633558
    {'ambient': '768.1090187', 'aut_centralizer_order': 48, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.g1', '32.b1', '32.d1'], 'contains': ['128.a1', '128.d1', '192.j1'], 'core': '384.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5292, -1, 6482, -1], 'generators': [1085750593, 2148863004, 504396399], 'label': '768.1090187.64.c1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '64.c1', 'projective_image': '384.20163', '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': '12.4'}
  • id: 59633559
    {'ambient': '768.1090187', 'aut_centralizer_order': 48, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.h1', '32.c1', '32.d1'], 'contains': ['128.a1', '192.k1'], 'core': '384.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5507, -1, 6522, -1], 'generators': [1085750593, 506952305, 2148863004], 'label': '768.1090187.64.d1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '64.d1', 'projective_image': '384.20163', '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': '12.4'}
  • id: 59633560
    {'ambient': '768.1090187', 'aut_centralizer_order': 72, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.i1', '16.j1', '32.a1'], 'contains': ['128.b1', '128.c1', '192.l1'], 'core': '384.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [34, -1, 1503, -1], 'generators': [2148207653, 1083180097, 3234148260], 'label': '768.1090187.64.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1', 'old_label': '64.e1', 'projective_image': '384.20100', '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': '1.1'}
  • id: 59633561
    {'ambient': '768.1090187', 'aut_centralizer_order': 24, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.k1', '32.b1'], 'contains': ['128.b1', '128.d1', '192.s1'], 'core': '384.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [1404, -1, 6432, -1], 'generators': [2148207653, 660749132, 3229953892], 'label': '768.1090187.64.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1', 'old_label': '64.f1', 'projective_image': '384.20100', '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': '6.1'}
  • id: 59633562
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.a1', '32.e1', '32.g1', '32.i1', '32.k1'], 'contains': ['192.c1', '256.a1'], 'core': '192.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [79, -1, 6307, -1], 'generators': [2150763522, 1083098168, 1081574431], 'label': '768.1090187.64.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '64.g1', 'projective_image': '768.1090187', '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': '24.12'}
  • id: 59633563
    {'ambient': '768.1090187', 'aut_centralizer_order': 96, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '32.f1', '32.h1', '32.j1'], 'contains': ['192.ck1', '256.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7, -1, 169, -1], 'generators': [2150763522, 1087390721, 1083229185], 'label': '768.1090187.64.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '64.h1', 'projective_image': '768.1090187', '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': '12.3'}
  • id: 59633564
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '6.d1', '6.f1'], 'contains': ['24.l1', '24.x1', '24.y1', '24.z1', '24.bd1', '24.cb1', '24.cb2', '24.ci1', '24.cu1', '24.dn1', '24.dr1', '24.dr2', '24.dv1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8709, -1, 9027, -1], 'generators': [1074660408, 1085750593, 1081574431, 670833676, 1083229185, 1089936056], 'label': '768.1090187.12.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.p1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633565
    {'ambient': '768.1090187', 'aut_centralizer_order': 2304, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '2.a1', 'complements': ['8.i1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.d1', '48.e1', '48.f1'], 'contains': ['192.a1', '192.b1', '192.l1'], 'core': '96.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7490, 8377, 5595, 9332], 'generators': [1083180097, 1085750593, 1080629953], 'label': '768.1090187.96.a1', 'mobius_quo': 0, 'mobius_sub': 96, 'normal_closure': '96.a1', 'normal_contained_in': ['24.a1'], 'normal_contains': ['192.a1', '192.b1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '192.1538', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.50', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633566
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '96.b1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['32.e1', '48.a1', '48.b1', '48.bw1', '48.ct1', '48.cu1', '48.cx1', '48.da1'], 'contains': ['192.c1', '192.e1', '192.bm1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8325, 5389, 6373, 7273], 'generators': [1083098168, 1085750593, 1081574431], 'label': '768.1090187.96.b1', 'mobius_quo': 1, 'mobius_sub': -96, 'normal_closure': '96.b1', 'normal_contained_in': ['24.b1', '48.a1', '48.b1'], 'normal_contains': ['192.c1', '384.a1'], 'normalizer': '1.a1', 'old_label': '96.b1', 'projective_image': '384.20163', 'quotient_action_image': '6.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '96.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633567
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.c1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': ['8.g1'], 'conjugacy_class_count': 6, 'contained_in': ['32.g1', '48.a1', '48.dk1', '48.el1', '48.em1', '48.es2', '48.et1'], 'contains': ['192.c1', '192.m1', '192.bh1'], 'core': '96.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [7453, 6206, 6152, 8144], 'generators': [1083098168, 1081574431, 1081596600], 'label': '768.1090187.96.c1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.c1', 'normal_contained_in': ['24.c1', '48.a1'], 'normal_contains': ['192.c1', '384.b1'], 'normalizer': '1.a1', 'old_label': '96.c1', 'projective_image': '384.20100', 'quotient_action_image': '6.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '96.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633568
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.a1', '48.d1', '48.g1', '48.h1', '48.i1', '48.j1', '48.j2', '48.k1', '48.l1', '48.m1', '48.n1', '48.o1', '48.p1'], 'contains': ['192.a1', '192.d1', '192.e1', '192.m1', '192.n1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8582, -1, 6276, -1], 'generators': [1089018497, 1085750593, 1078887480], 'label': '768.1090187.96.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.d1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633569
    {'ambient': '768.1090187', 'aut_centralizer_order': 1536, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '48.g1', '48.o1', '48.q1', '48.r1', '48.s1', '48.t1'], 'contains': ['192.a1', '192.f1', '192.i1', '192.o1', '192.r1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4626, -1, 1733, -1], 'generators': [1076429862, 1087380134, 1085750593], 'label': '768.1090187.96.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.e1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633570
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '48.h1', '48.i1', '48.q1', '48.r1'], 'contains': ['192.a1', '192.g1', '192.p1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5568, -1, 3120, -1], 'generators': [1085750593, 1078991590, 1084818534], 'label': '768.1090187.96.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.f1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633571
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.d1', '48.h1', '48.j1', '48.j2', '48.q1', '48.s1', '48.u1'], 'contains': ['192.a1', '192.h1', '192.q1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8283, -1, 5662, -1], 'generators': [1089963103, 1085750593, 1074698975], 'label': '768.1090187.96.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.g1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633572
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1', '48.f1', '48.k1', '48.u1'], 'contains': ['192.a1', '192.j1', '192.s1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9660, -1, 9200, -1], 'generators': [1089018497, 1085750593, 658250892], 'label': '768.1090187.96.h1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '96.h1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633573
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1', '48.f1', '48.m1', '48.u1'], 'contains': ['192.a1', '192.k1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9780, -1, 9155, -1], 'generators': [516831830, 1085750593, 506952305], 'label': '768.1090187.96.i1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '96.i1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633574
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.d1', '48.v1', '48.w1', '48.x1', '48.y1', '48.y2', '48.z1'], 'contains': ['192.b1', '192.d1', '192.h1', '192.t1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8060, -1, 5628, -1], 'generators': [1083180097, 1085750593, 1074830054], 'label': '768.1090187.96.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.j1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633575
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.c1', '6.e1', '6.f1'], 'contains': ['24.z1', '24.bd1', '24.cc1', '24.cv1', '24.ds1', '24.dw1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8523, -1, 6601, -1], 'generators': [1074660408, 1085750593, 1081574431, 1083229185, 668673292, 1089936056], 'label': '768.1090187.12.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.q1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633576
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.b1', '48.d1', '48.v1', '48.y1', '48.y2', '48.ba1', '48.bb1', '48.bc1', '48.bd1', '48.be1', '48.bf1'], 'contains': ['192.b1', '192.e1', '192.h1', '192.u1', '192.v1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8349, -1, 6001, -1], 'generators': [1085750593, 1080629953, 1078887480], 'label': '768.1090187.96.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.k1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633577
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.e1', '48.w1', '48.z1', '48.ba1', '48.be1', '48.bg1', '48.bh1'], 'contains': ['192.b1', '192.f1', '192.g1', '192.w1', '192.y1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [4638, -1, 1356, -1], 'generators': [1076429862, 1085750593, 1078991590], 'label': '768.1090187.96.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.l1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633578
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.e1', '48.v1', '48.w1', '48.bb1', '48.bg1'], 'contains': ['192.b1', '192.g1', '192.i1', '192.x1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5121, -1, 3086, -1], 'generators': [1083180097, 1078860511, 1085750593], 'label': '768.1090187.96.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.m1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633579
    {'ambient': '768.1090187', 'aut_centralizer_order': 96, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.d1', '48.f1', '48.x1', '48.bc1'], 'contains': ['192.b1', '192.j1', '192.k1'], 'core': '192.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [9764, -1, 9232, -1], 'generators': [1083180097, 1085750593, 506952305], 'label': '768.1090187.96.n1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '96.n1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633580
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.o1', '48.v1', '48.bi1', '48.bi2', '48.bj1', '48.bk1', '48.bo1', '48.bw1', '48.bw2', '48.bz1'], 'contains': ['192.d1', '192.e1', '192.i1', '192.z1', '192.ba1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6500, -1, 4930, -1], 'generators': [1085750593, 1078887480, 1087249055], 'label': '768.1090187.96.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.o1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633581
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.g1', '48.w1', '48.bk1', '48.bl1', '48.bl2', '48.bm1', '48.bo1', '48.bz1', '48.ca1'], 'contains': ['192.d1', '192.f1', '192.i1', '192.bb1', '192.bf1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3160, -1, 2206, -1], 'generators': [1076429862, 1085750593, 1084856961], 'label': '768.1090187.96.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.p1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633582
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.h1', '48.v1', '48.z1', '48.bi1', '48.bi2', '48.bj1', '48.bl1', '48.bl2', '48.bp1', '48.bp2', '48.bp3', '48.bp4', '48.bx1', '48.by1'], 'contains': ['192.d1', '192.g1', '192.h1', '192.bc1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6603, -1, 4659, -1], 'generators': [1085750593, 1077385976, 1084818534], 'label': '768.1090187.96.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.q1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633583
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.i1', '48.w1', '48.bj1', '48.bp2', '48.bp4', '48.by1'], 'contains': ['192.d1', '192.g1', '192.bd1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5581, -1, 4523, -1], 'generators': [1085750593, 1076468417, 1084818534], 'label': '768.1090187.96.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.r1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633584
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.j1', '48.y1', '48.bi2', '48.bm1', '48.bp4', '48.bx1'], 'contains': ['192.d1', '192.h1', '192.be1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7263, -1, 5302, -1], 'generators': [1089963103, 1085750593, 1089985272], 'label': '768.1090187.96.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.s1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633586
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '6.e1', '6.g1'], 'contains': ['24.m1', '24.ba1', '24.bb1', '24.bc1', '24.bd1', '24.cd1', '24.cd2', '24.cj1', '24.cw1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9323, -1, 7098, -1], 'generators': [1076429862, 1085750593, 506952305, 508566806, 1081574431, 1085785119], 'label': '768.1090187.12.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.r1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633587
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.k1', '48.x1', '48.bn1', '48.br1'], 'contains': ['192.d1', '192.j1', '192.bg1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9796, -1, 9783, -1], 'generators': [1083218598, 1085750593, 658250892], 'label': '768.1090187.96.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '96.t1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633588
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.m1', '48.x1', '48.bn1', '48.bu1'], 'contains': ['192.d1', '192.k1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9968, -1, 9526, -1], 'generators': [1085750593, 506952305, 506930390], 'label': '768.1090187.96.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '96.u1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633589
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.a1', '48.y1', '48.bp1', '48.bp2', '48.bq1', '48.bt1', '48.bw2', '48.bz1', '48.cb1'], 'contains': ['192.d1', '192.e1', '192.bh1', '192.bi1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8249, -1, 6118, -1], 'generators': [1085750593, 1078887480, 1079040678], 'label': '768.1090187.96.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.v1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633590
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.v2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.p1', '48.y2', '48.bp3', '48.bp4', '48.br1', '48.bs1', '48.bu1', '48.bv1', '48.bw1', '48.bz1', '48.cb1'], 'contains': ['192.d1', '192.e1', '192.bh2', '192.bi2'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8392, -1, 6339, -1], 'generators': [1085750593, 1078909599, 1078887480], 'label': '768.1090187.96.v2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.v2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633591
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.o1', '48.z1', '48.bo1', '48.bx1', '48.by1', '48.bz1', '48.ca1', '48.cb1'], 'contains': ['192.d1', '192.f1', '192.bj1', '192.bk1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4750, -1, 2240, -1], 'generators': [1076429862, 1085774520, 1085750593], 'label': '768.1090187.96.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.w1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633592
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.g1', '48.ba1', '48.bo1', '48.cb1', '48.cc1', '48.cd1', '48.ce1', '48.cf1', '48.cs1', '48.da1'], 'contains': ['192.e1', '192.f1', '192.bn1', '192.bs1', '192.bx1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7188, -1, 4320, -1], 'generators': [1085750593, 1081574431, 1077347359], 'label': '768.1090187.96.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.x1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633593
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.h1', '48.v1', '48.be1', '48.bi1', '48.bi2', '48.bj1', '48.bp2', '48.bp4', '48.cc1', '48.cg1', '48.cq1', '48.cr1', '48.ct1', '48.ct2'], 'contains': ['192.e1', '192.g1', '192.h1', '192.bo1', '192.by1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6615, -1, 4692, -1], 'generators': [1078860511, 1085750593, 1078887480], 'label': '768.1090187.96.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.y1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633594
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.i1', '48.ba1', '48.bb1', '48.bj1', '48.bp1', '48.bp3', '48.ch1', '48.ci1', '48.cr1', '48.ct1', '48.ct2'], 'contains': ['192.e1', '192.g1', '192.bp1', '192.bz1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8047, -1, 5437, -1], 'generators': [1085750593, 1081547512, 1078887480], 'label': '768.1090187.96.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.z1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633595
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.b1', '48.j1', '48.y1', '48.bi1', '48.bp3', '48.cd1', '48.ck1', '48.cl1', '48.cn1', '48.cq1', '48.ct2'], 'contains': ['192.e1', '192.h1', '192.bq1', '192.ca1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8270, -1, 5967, -1], 'generators': [1085750593, 1087429350, 1078887480], 'label': '768.1090187.96.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ba1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633596
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ba2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.j2', '48.y2', '48.bf1', '48.bi2', '48.bp1', '48.cd1', '48.cj1', '48.cm1', '48.cn1', '48.cq1', '48.ct1'], 'contains': ['192.e1', '192.h1', '192.bq2', '192.ca2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8337, -1, 6084, -1], 'generators': [1085750593, 1087298271, 1078887480], 'label': '768.1090187.96.ba2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ba2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633597
    {'ambient': '768.1090187', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2304.hr', 'aut_weyl_index': 8, 'centralizer': '192.a1', 'complements': ['384.b1', '384.c1', '384.d1', '384.h1', '384.i1', '384.j1', '384.l1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.d1', '6.i1', '8.g1'], 'core': '2.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [4809, 5528, 5380, 801], 'generators': [1074660408, 1081574431, 1076429862, 1084867622, 506952305, 1083180097, 2150763522, 1085750593], 'label': '768.1090187.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '384.20163', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 59633598
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.c1', '6.d1', '6.g1'], 'contains': ['24.bc1', '24.bd1', '24.ce1', '24.cx1', '24.do1', '24.dt1'], 'core': '48.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8555, -1, 5579, -1], 'generators': [1076429862, 1085750593, 1081574431, 512648241, 518587222, 1085785119], 'label': '768.1090187.12.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.s1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633599
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.g1', '48.bb1', '48.bk1', '48.bw1', '48.bw2', '48.cg1', '48.cn1', '48.co1', '48.cp1'], 'contains': ['192.e1', '192.i1', '192.br1', '192.cb1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7478, -1, 5764, -1], 'generators': [1085750593, 1078887480, 1089936056], 'label': '768.1090187.96.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.bb1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633600
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.k1', '48.bc1', '48.bq1', '48.br1', '48.ce1', '48.ch1', '48.cj1', '48.ck1', '48.co1', '48.cu1', '48.cv1'], 'contains': ['192.e1', '192.j1', '192.bt1', '192.cc1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9647, -1, 8860, -1], 'generators': [1085750593, 504396399, 1078887480], 'label': '768.1090187.96.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bc1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633601
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.l1', '48.bd1', '48.bq1', '48.bs1', '48.ce1', '48.ci1', '48.cl1', '48.cm1', '48.co1', '48.cu1', '48.cw1'], 'contains': ['192.e1', '192.bu1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9589, -1, 8297, -1], 'generators': [1085750593, 1078887480, 514417711], 'label': '768.1090187.96.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bd1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633602
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.m1', '48.bc1', '48.bt1', '48.bu1', '48.cf1', '48.ci1', '48.cj1', '48.cl1', '48.cp1', '48.cx1', '48.cy1'], 'contains': ['192.e1', '192.k1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9890, -1, 8747, -1], 'generators': [1085750593, 506952305, 1078887480], 'label': '768.1090187.96.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.be1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633603
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.n1', '48.bd1', '48.bt1', '48.bv1', '48.cf1', '48.ch1', '48.ck1', '48.cm1', '48.cp1', '48.cx1', '48.cz1'], 'contains': ['192.e1', '192.cd1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9748, -1, 7542, -1], 'generators': [1085750593, 512648241, 1078887480], 'label': '768.1090187.96.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bf1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633604
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.o1', '48.be1', '48.bk1', '48.bz1', '48.cq1', '48.cr1', '48.cs1', '48.da1'], 'contains': ['192.e1', '192.f1', '192.bl1', '192.bv1', '192.ce1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4763, -1, 3222, -1], 'generators': [1076429862, 1085750593, 1081574431], 'label': '768.1090187.96.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bg1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633605
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1', '48.bf1', '48.bw2', '48.ct2', '48.cv1', '48.cw1', '48.cy1', '48.cz1', '48.da1'], 'contains': ['192.e1', '192.bm2', '192.bw1'], 'core': '384.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9061, -1, 6558, -1], 'generators': [1083098168, 1085750593, 1080656934], 'label': '768.1090187.96.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.bh1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633606
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.q1', '48.w1', '48.ba1', '48.bl2', '48.bx1', '48.by1', '48.cc1', '48.cq1', '48.cr1', '48.db1', '48.dc1'], 'contains': ['192.f1', '192.g1', '192.h1', '192.cf1', '192.cm1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4064, -1, 1699, -1], 'generators': [1076429862, 1085750593, 1076468417], 'label': '768.1090187.96.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bi1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633607
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '96.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.r1', '48.bg1', '48.bh1', '48.bl1', '48.by1', '48.cc1', '48.cr1'], 'contains': ['192.f1', '192.g1', '192.cg1', '192.co1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1209, -1, 646, -1], 'generators': [1076429862, 1078860511, 1085750593], 'label': '768.1090187.96.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bj1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633608
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.bk1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.s1', '48.z1', '48.be1', '48.bl1', '48.bm1', '48.bx1', '48.cc1', '48.cd1', '48.cq1', '48.db1', '48.dc1'], 'contains': ['192.f1', '192.h1', '192.ch1', '192.cq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4701, -1, 1767, -1], 'generators': [1076429862, 1085750593, 1077385976], 'label': '768.1090187.96.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bk1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633609
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.b1'], 'contains': ['24.bi1', '24.bj1', '24.bk1', '24.bp1', '24.br1', '24.by1', '24.bz1', '24.cb1', '24.cd1', '24.cn1', '24.cp1'], 'core': '48.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9491, -1, 8320, -1], 'generators': [1083180097, 1083098168, 1081547512, 1085750593, 1081574431, 658250892], 'label': '768.1090187.12.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.t1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633610
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '96.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1', '48.bg1', '48.bk1', '48.bo1', '48.db1'], 'contains': ['192.f1', '192.i1', '192.ci1', '192.cr1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1032, -1, 680, -1], 'generators': [1076429862, 1085750593, 1087249055], 'label': '768.1090187.96.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bl1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633611
    {'ambient': '768.1090187', 'aut_centralizer_order': 1536, 'aut_label': '96.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1', '48.t1', '48.bh1', '48.ca1', '48.cs1', '48.dc1'], 'contains': ['192.f1', '192.cj1', '192.ck1'], 'core': '384.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [285, -1, 375, -1], 'generators': [1085750593, 1087390721, 1083229185], 'label': '768.1090187.96.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '96.bm1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bm1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633612
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.q1', '48.w1', '48.bb1', '48.bi1', '48.bi2', '48.bj1', '48.bl1', '48.cg1', '48.db1'], 'contains': ['192.g1', '192.h1', '192.i1', '192.cl1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5069, -1, 4000, -1], 'generators': [1085750593, 1074830054, 1084818534], 'label': '768.1090187.96.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bn1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633613
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '96.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.r1', '48.bg1', '48.bj1', '48.bl2', '48.cg1'], 'contains': ['192.g1', '192.i1', '192.cn1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1369, -1, 2342, -1], 'generators': [1078860511, 1085750593, 1084818534], 'label': '768.1090187.96.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bo1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633614
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '96.bp1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.u1', '48.x1', '48.bc1', '48.bn1', '48.cj1'], 'contains': ['192.h1', '192.j1', '192.k1'], 'core': '384.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9928, -1, 9709, -1], 'generators': [1085750593, 506952305, 1087276152], 'label': '768.1090187.96.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '96.bp1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633615
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.bq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.s1', '48.v1', '48.bi1', '48.bi2', '48.bl2', '48.bm1', '48.cg1', '48.cn1', '48.db1'], 'contains': ['192.h1', '192.i1', '192.cp1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5137, -1, 4034, -1], 'generators': [1089963103, 1085750593, 1074830054], 'label': '768.1090187.96.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bq1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633616
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.br1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.d1', '48.dd1', '48.de1', '48.dg1', '48.dh1', '48.dj1', '48.dj2', '48.dk1', '48.dk2'], 'contains': ['192.l1', '192.m1', '192.q1', '192.t1', '192.u1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6993, -1, 4388, -1], 'generators': [1083180097, 1080629953, 1078887480], 'label': '768.1090187.96.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.br1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.br1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633617
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.bs1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.d1', '48.df1', '48.dg1', '48.di1', '48.dj1', '48.dj2'], 'contains': ['192.l1', '192.n1', '192.q1', '192.t1', '192.v1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5605, -1, 4185, -1], 'generators': [1083180097, 1080629953, 1087421791], 'label': '768.1090187.96.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bs1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633618
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '96.bt1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.dd1', '48.df1', '48.dh1', '48.di1', '48.dl1', '48.dm1'], 'contains': ['192.l1', '192.o1', '192.p1', '192.w1', '192.x1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2772, -1, 1086, -1], 'generators': [1076429862, 1083180097, 1078991590], 'label': '768.1090187.96.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bt1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bt1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633619
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '96.bu1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.de1', '48.df1', '48.dg1', '48.dl1'], 'contains': ['192.l1', '192.p1', '192.r1', '192.x1', '192.y1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [4571, -1, 1800, -1], 'generators': [1083180097, 1083063654, 1078991590], 'label': '768.1090187.96.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bu1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633620
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.t2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.b1', '6.h1'], 'contains': ['24.bh1', '24.bk2', '24.bp1', '24.bs1', '24.bt1', '24.bx1', '24.cb2', '24.cd2', '24.cn1', '24.cq1', '24.cr1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9250, -1, 7704, -1], 'generators': [1083180097, 1078860511, 1083098168, 1085750593, 1080656934, 668673292], 'label': '768.1090187.12.t2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.t2', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t2', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633621
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.bv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.g1', '48.dd1', '48.dn1', '48.do1', '48.dp1', '48.ed1', '48.ek1', '48.eq1', '48.et1'], 'contains': ['192.m1', '192.o1', '192.bb1', '192.bn1', '192.br1'], 'core': '384.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [4900, -1, 3797, -1], 'generators': [1081574431, 1077347359, 1087249055], 'label': '768.1090187.96.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.bv1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633622
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.h1', '48.dg1', '48.dh1', '48.dn1', '48.dq1', '48.dx1', '48.dx2', '48.dy1', '48.dz1', '48.ea1', '48.ee2', '48.ee4', '48.el1', '48.el2'], 'contains': ['192.m1', '192.p1', '192.q1', '192.bc1', '192.bo1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [4831, -1, 3560, -1], 'generators': [1078991590, 1078887480, 1084818534], 'label': '768.1090187.96.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bw1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633623
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.i1', '48.dd1', '48.de1', '48.dy1', '48.ea1', '48.ee1', '48.ee3', '48.el1', '48.el2'], 'contains': ['192.m1', '192.p1', '192.bd1', '192.bp1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6654, -1, 4101, -1], 'generators': [1081547512, 1078887480, 1083049080], 'label': '768.1090187.96.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bx1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633624
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.by1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.j1', '48.dj1', '48.dk1', '48.do1', '48.dr1', '48.dx2', '48.dz1', '48.ee3', '48.el2'], 'contains': ['192.m1', '192.q1', '192.be1', '192.bq1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6951, -1, 5031, -1], 'generators': [1076479078, 1087429350, 1078887480], 'label': '768.1090187.96.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.by1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.by1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633625
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.by2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.j2', '48.dj2', '48.dk2', '48.do1', '48.dr1', '48.dx1', '48.dz1', '48.ee1', '48.el1'], 'contains': ['192.m1', '192.q1', '192.be2', '192.bq2'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6981, -1, 5099, -1], 'generators': [1077396575, 1087298271, 1078887480], 'label': '768.1090187.96.by2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.by2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.by2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633626
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.bz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.g1', '48.de1', '48.dq1', '48.dr1', '48.ds1', '48.ej1', '48.es1', '48.es2'], 'contains': ['192.m1', '192.r1', '192.bf1', '192.br1', '192.bs1'], 'core': '384.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7006, -1, 4456, -1], 'generators': [1084833144, 1078887480, 1089936056], 'label': '768.1090187.96.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.bz1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633627
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ca1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.k1', '48.dp1', '48.ds1', '48.ef1', '48.eg1', '48.em1', '48.en1'], 'contains': ['192.m1', '192.s1', '192.bg1', '192.bt1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9258, -1, 8997, -1], 'generators': [1089018497, 660749132, 1089946655], 'label': '768.1090187.96.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.ca1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ca1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633628
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.cb1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.l1', '48.dp1', '48.ds1', '48.ef1', '48.eh1', '48.em1', '48.eo1'], 'contains': ['192.m1', '192.bu1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9024, -1, 8449, -1], 'generators': [1089018497, 668673292, 1089946655], 'label': '768.1090187.96.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.cb1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633629
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.cc1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.g1', '48.df1', '48.dt1', '48.dt2', '48.du1', '48.ed1', '48.ej1', '48.ep1', '48.er1'], 'contains': ['192.n1', '192.o1', '192.r1', '192.bb1', '192.bf1', '192.bx1', '192.cb1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [1603, -1, 1322, -1], 'generators': [1076429862, 1087290726, 1084856961], 'label': '768.1090187.96.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cc1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633630
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.cd1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.h1', '48.dg1', '48.di1', '48.dt1', '48.dt2', '48.dx1', '48.dx2', '48.dy1', '48.eb1', '48.ec1', '48.ee1', '48.ee2', '48.ee3', '48.ee4'], 'contains': ['192.n1', '192.p1', '192.q1', '192.bc1', '192.by1'], 'core': '384.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [4738, -1, 3188, -1], 'generators': [1078991590, 1087421791, 1084818534], 'label': '768.1090187.96.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cd1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633631
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.c1', '6.h1'], 'contains': ['24.bk2', '24.bt1', '24.cc1', '24.ce1', '24.cs1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8746, -1, 6149, -1], 'generators': [1083180097, 1083098168, 1085750593, 1076468417, 1080656934, 668673292], 'label': '768.1090187.12.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.u1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633632
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.ce1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.i1', '48.df1', '48.dv1', '48.dy1', '48.ec1', '48.ee2', '48.ee4'], 'contains': ['192.n1', '192.p1', '192.bd1', '192.bz1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5175, -1, 3662, -1], 'generators': [1078860511, 1087421791, 1085736031], 'label': '768.1090187.96.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ce1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ce1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633633
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.cf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.j1', '48.dj1', '48.du1', '48.dw1', '48.dx1', '48.eb1', '48.ee4'], 'contains': ['192.n1', '192.q1', '192.be1', '192.ca1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6716, -1, 4726, -1], 'generators': [1089985272, 1074709624, 1087421791], 'label': '768.1090187.96.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.cf1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633634
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.cf2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.j2', '48.dj2', '48.du1', '48.dx2', '48.eb1', '48.ee2'], 'contains': ['192.n1', '192.q1', '192.be2', '192.ca2'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5304, -1, 4557, -1], 'generators': [1076479078, 1087421791, 1087429350], 'label': '768.1090187.96.cf2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cf2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cf2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633635
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.cg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.k1', '48.dv1', '48.dw1', '48.eg1'], 'contains': ['192.n1', '192.s1', '192.bg1', '192.cc1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9405, -1, 8702, -1], 'generators': [1089018497, 1076493688, 658250892], 'label': '768.1090187.96.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '96.cg1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633636
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ch1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.n1', '48.dv1', '48.dw1', '48.ei1'], 'contains': ['192.n1', '192.cd1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [9311, -1, 7141, -1], 'generators': [1078885734, 508566806, 508576689], 'label': '768.1090187.96.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '96.ch1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ch1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633637
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ci1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.o1', '48.dg1', '48.dx1', '48.dx2', '48.dy1', '48.ed1', '48.ej1', '48.er1', '48.es1', '48.es2'], 'contains': ['192.m1', '192.n1', '192.r1', '192.z1', '192.ba1', '192.bk1', '192.bl1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [4713, -1, 3831, -1], 'generators': [1087380134, 1083063654, 1078887480], 'label': '768.1090187.96.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ci1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ci1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633672
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.dj2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bf1', '48.dk2', '48.fc2', '48.fq1', '48.fs1'], 'contains': ['192.u1', '192.bq2', '192.bw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7213, -1, 5369, -1], 'generators': [1083098168, 1074830054, 1080656934], 'label': '768.1090187.96.dj2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dj2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dj2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633638
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.cj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.o1', '48.dh1', '48.dz1', '48.ea1', '48.ej1', '48.ek1', '48.er1', '48.et1'], 'contains': ['192.m1', '192.o1', '192.z1', '192.bj1', '192.bv1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [3391, -1, 2816, -1], 'generators': [1076429862, 1087380134, 1081574431], 'label': '768.1090187.96.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cj1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633639
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ck1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.o1', '48.di1', '48.eb1', '48.ec1', '48.ed1', '48.ep1', '48.eq1', '48.er1'], 'contains': ['192.n1', '192.o1', '192.ba1', '192.bj1', '192.ce1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [3375, -1, 2410, -1], 'generators': [1076429862, 1087380134, 1087421791], 'label': '768.1090187.96.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ck1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ck1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633640
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.cl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.a1', '48.dj1', '48.ee1', '48.ee2', '48.ef1', '48.eq1', '48.er1', '48.es1'], 'contains': ['192.m1', '192.n1', '192.bh1', '192.bi1', '192.bm1'], 'core': '384.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7275, -1, 5471, -1], 'generators': [1089018497, 1074724198, 1078887480], 'label': '768.1090187.96.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.cl1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633641
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.cl2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.p1', '48.dj2', '48.ee3', '48.ee4', '48.eg1', '48.eh1', '48.ei1', '48.eq1', '48.er1', '48.es2'], 'contains': ['192.m1', '192.n1', '192.bh2', '192.bi2', '192.bm2'], 'core': '384.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7825, -1, 6050, -1], 'generators': [1089018497, 1074855263, 1078887480], 'label': '768.1090187.96.cl2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.cl2', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cl2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633642
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.b1'], 'contains': ['24.bh1', '24.bi1', '24.bj1', '24.bn1', '24.bo1', '24.bx1', '24.by1', '24.bz1', '24.ci1', '24.cj1', '24.cm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9377, -1, 8217, -1], 'generators': [1083180097, 1076429862, 1085750593, 1089985272, 658250892, 1080656934], 'label': '768.1090187.12.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.v1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633643
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.cm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.p1', '48.dk2', '48.el2', '48.en1', '48.eo1', '48.es1', '48.et1'], 'contains': ['192.m1', '192.bh2', '192.bw1'], 'core': '384.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8077, -1, 6242, -1], 'generators': [1083218598, 1083098168, 1080656934], 'label': '768.1090187.96.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.cm1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633644
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.cn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.q1', '48.dd1', '48.df1', '48.dn1', '48.dt1', '48.dz1', '48.ea1', '48.eb1', '48.ec1', '48.eu1', '48.ev1'], 'contains': ['192.o1', '192.p1', '192.q1', '192.cf1', '192.cl1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [2324, -1, 1221, -1], 'generators': [1076429862, 1089045606, 1076468417], 'label': '768.1090187.96.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cn1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633645
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '96.co1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.r1', '48.dl1', '48.dm1', '48.dn1', '48.dt2', '48.ea1', '48.ec1'], 'contains': ['192.o1', '192.p1', '192.cg1', '192.cn1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [784, -1, 578, -1], 'generators': [1076429862, 1078860511, 1083049080], 'label': '768.1090187.96.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.co1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.co1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633646
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.cp1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.s1', '48.dh1', '48.di1', '48.dn1', '48.do1', '48.dt2', '48.du1', '48.dz1', '48.eb1', '48.eu1', '48.ev1'], 'contains': ['192.o1', '192.q1', '192.ch1', '192.cp1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3249, -1, 1458, -1], 'generators': [1076429862, 1089963103, 1077385976], 'label': '768.1090187.96.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cp1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633647
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '96.cq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.t1', '48.dl1', '48.ed1', '48.ej1', '48.eu1'], 'contains': ['192.o1', '192.r1', '192.ci1', '192.cj1', '192.cr1'], 'core': '384.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [708, -1, 476, -1], 'generators': [1076429862, 1084833144, 1087249055], 'label': '768.1090187.96.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cq1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633648
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '96.cr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.h1', '48.t1', '48.dm1', '48.ek1', '48.ep1', '48.ev1'], 'contains': ['192.o1', '192.ci1', '192.ck1'], 'core': '384.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [193, -1, 341, -1], 'generators': [1084856961, 1087390721, 1083229185], 'label': '768.1090187.96.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '96.cr1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cr1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633649
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.cs1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.q1', '48.de1', '48.df1', '48.dq1', '48.dt2', '48.dx1', '48.dx2', '48.dy1', '48.eu1'], 'contains': ['192.p1', '192.q1', '192.r1', '192.cl1', '192.cm1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3218, -1, 2071, -1], 'generators': [1083063654, 1089045606, 1076468417], 'label': '768.1090187.96.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cs1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633650
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '96.ct1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.r1', '48.dl1', '48.dq1', '48.dt1', '48.dy1'], 'contains': ['192.p1', '192.r1', '192.cn1', '192.co1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1221, -1, 781, -1], 'generators': [1078860511, 1083063654, 1083049080], 'label': '768.1090187.96.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ct1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ct1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633651
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.cu1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.s1', '48.dg1', '48.dq1', '48.dr1', '48.dt1', '48.du1', '48.dx1', '48.dx2', '48.eu1'], 'contains': ['192.q1', '192.r1', '192.cp1', '192.cq1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [4162, -1, 2443, -1], 'generators': [1089963103, 1083063654, 1077385976], 'label': '768.1090187.96.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cu1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633652
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.cv1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.v1', '48.dg1', '48.dh1', '48.ew1', '48.ex1', '48.ez2', '48.ez4', '48.fa1', '48.fb1', '48.fc1', '48.fc2', '48.fe1', '48.fe2', '48.ff1'], 'contains': ['192.t1', '192.u1', '192.x1', '192.z1', '192.bc1', '192.bo1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4496, -1, 3289, -1], 'generators': [1083180097, 1078860511, 1078887480], 'label': '768.1090187.96.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cv1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633653
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.a1', '6.h1'], 'contains': ['24.bf1', '24.bg1', '24.bk1', '24.bk2', '24.bl1', '24.bu1', '24.bv1', '24.bw1', '24.ca1', '24.ca2', '24.cf1', '24.ck1', '24.ct1', '24.dz1', '24.ea1', '24.eb1', '24.eb2', '24.ec1'], 'core': '48.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [5661, -1, 4014, -1], 'generators': [1083180097, 1074660408, 1078860511, 1085750593, 1081574431, 1083229185], 'label': '768.1090187.12.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.w1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633654
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.cw1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.v1', '48.dg1', '48.di1', '48.ew1', '48.ey1', '48.ez1', '48.ez2', '48.ez3', '48.ez4', '48.fd1', '48.fd2', '48.fe1', '48.fe2', '48.fg1'], 'contains': ['192.t1', '192.v1', '192.x1', '192.ba1', '192.bc1', '192.by1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4277, -1, 3019, -1], 'generators': [1083180097, 1081547512, 1087421791], 'label': '768.1090187.96.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cw1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633655
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.cx1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.w1', '48.dd1', '48.df1', '48.ex1', '48.ey1', '48.fa1', '48.fd1', '48.ff1', '48.fg1', '48.fh1', '48.fi1'], 'contains': ['192.t1', '192.w1', '192.x1', '192.bb1', '192.bd1', '192.cf1', '192.cl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2292, -1, 1153, -1], 'generators': [1076429862, 1083180097, 1076468417], 'label': '768.1090187.96.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cx1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633656
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.cy1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.w1', '48.de1', '48.df1', '48.ew1', '48.fb1', '48.fd2', '48.fe1', '48.fe2', '48.fh1'], 'contains': ['192.t1', '192.x1', '192.y1', '192.bd1', '192.bf1', '192.cl1', '192.cm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2968, -1, 1868, -1], 'generators': [1083180097, 1083063654, 1076468417], 'label': '768.1090187.96.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cy1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633657
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.cz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.y1', '48.dj1', '48.dk1', '48.ez3', '48.fc2', '48.fe2', '48.ff1', '48.fj1', '48.fk1'], 'contains': ['192.t1', '192.u1', '192.be1', '192.bh1', '192.bq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6788, -1, 5065, -1], 'generators': [1083180097, 1087429350, 1078887480], 'label': '768.1090187.96.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cz1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633658
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.cz2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.y2', '48.dj2', '48.dk2', '48.ez1', '48.fc1', '48.fe1', '48.ff1', '48.fj1', '48.fk1'], 'contains': ['192.t1', '192.u1', '192.be2', '192.bh2', '192.bq2'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6873, -1, 5133, -1], 'generators': [1083180097, 1087298271, 1078887480], 'label': '768.1090187.96.cz2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cz2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cz2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633659
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.da1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.y1', '48.dj1', '48.ez4', '48.fe1', '48.fg1', '48.fl1'], 'contains': ['192.t1', '192.v1', '192.be1', '192.bi1', '192.ca1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5208, -1, 4287, -1], 'generators': [1083180097, 1089985272, 1087421791], 'label': '768.1090187.96.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.da1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.da1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633660
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.da2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.y2', '48.dj2', '48.ez2', '48.fe2', '48.fg1', '48.fl1'], 'contains': ['192.t1', '192.v1', '192.be2', '192.bi2', '192.ca2'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5221, -1, 4354, -1], 'generators': [1083180097, 1087421791, 1087429350], 'label': '768.1090187.96.da2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.da2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.da2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633661
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.db1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.z1', '48.dh1', '48.di1', '48.fa1', '48.fd2', '48.ff1', '48.fg1', '48.fh1', '48.fi1', '48.fj1', '48.fl1'], 'contains': ['192.t1', '192.w1', '192.bc1', '192.bj1', '192.ch1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2802, -1, 1424, -1], 'generators': [1076429862, 1083180097, 1077385976], 'label': '768.1090187.96.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.db1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.db1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633662
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.dc1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.z1', '48.dg1', '48.fb1', '48.fd1', '48.fe1', '48.fe2', '48.fh1', '48.fk1', '48.fl1'], 'contains': ['192.t1', '192.y1', '192.bc1', '192.bk1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4175, -1, 2274, -1], 'generators': [1083180097, 1083063654, 1077385976], 'label': '768.1090187.96.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dc1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633663
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.dd1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.be1', '48.dg1', '48.ew1', '48.fe1', '48.fe2', '48.fm1', '48.fo1', '48.fp1', '48.fq1', '48.fq2'], 'contains': ['192.u1', '192.v1', '192.y1', '192.bl1', '192.bo1', '192.by1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4583, -1, 3255, -1], 'generators': [1083063654, 1078991590, 1078887480], 'label': '768.1090187.96.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dd1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633664
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 768, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1'], 'contains': ['24.bg1', '24.bl1', '24.bm1', '24.bn1', '24.bq1', '24.bw1', '24.cf1', '24.cg1', '24.ch1', '24.cl1', '24.co1', '24.ed1', '24.ee1', '24.ef1', '24.eg1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2862, -1, 2114, -1], 'generators': [1083180097, 1076429862, 1074660408, 1085750593, 1081574431, 1089985272], 'label': '768.1090187.12.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.x1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633665
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.de1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.b1', '48.dj1', '48.ez1', '48.ez2', '48.fn1', '48.fp1', '48.fq1'], 'contains': ['192.u1', '192.v1', '192.bm1', '192.bq1', '192.ca1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6678, -1, 5166, -1], 'generators': [1074724198, 1080629953, 1078887480], 'label': '768.1090187.96.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.de1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.de1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633666
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.de2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bf1', '48.dj2', '48.ez3', '48.ez4', '48.fn1', '48.fp1', '48.fq2'], 'contains': ['192.u1', '192.v1', '192.bm2', '192.bq2', '192.ca2'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6776, -1, 5200, -1], 'generators': [1080629953, 1074855263, 1078887480], 'label': '768.1090187.96.de2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.de2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.de2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633667
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.df1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ba1', '48.dd1', '48.fa1', '48.fj1', '48.fm1', '48.fn1', '48.fr1', '48.fs1'], 'contains': ['192.u1', '192.w1', '192.bn1', '192.bp1', '192.cf1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4558, -1, 2613, -1], 'generators': [1078860511, 1081574431, 1077347359], 'label': '768.1090187.96.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.df1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.df1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633668
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.dg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bb1', '48.dd1', '48.de1', '48.ew1', '48.ex1', '48.ez1', '48.ez3', '48.fc1', '48.fc2'], 'contains': ['192.u1', '192.x1', '192.bp1', '192.br1', '192.cl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5543, -1, 4135, -1], 'generators': [1083180097, 1081547512, 1078887480], 'label': '768.1090187.96.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633669
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.dh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ba1', '48.de1', '48.fb1', '48.fk1', '48.fo1', '48.fq1', '48.fq2'], 'contains': ['192.u1', '192.y1', '192.bp1', '192.bs1', '192.cm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6628, -1, 3763, -1], 'generators': [1084833144, 1081547512, 1078887480], 'label': '768.1090187.96.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dh1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633670
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.di1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.be1', '48.dh1', '48.ex1', '48.ff1', '48.fo1', '48.fp1', '48.fr1', '48.fs1'], 'contains': ['192.u1', '192.w1', '192.bo1', '192.bv1', '192.ch1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3301, -1, 2511, -1], 'generators': [1076429862, 1081574431, 1078991590], 'label': '768.1090187.96.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.di1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.di1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633671
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.dj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['32.i1', '48.b1', '48.dk1', '48.fc1', '48.fq2', '48.fs1'], 'contains': ['192.c1', '192.u1', '192.bq1'], 'core': '192.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [6763, -1, 5403, -1], 'generators': [1083098168, 1081574431, 1089985272], 'label': '768.1090187.96.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '96.dj1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dj1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633673
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.dk1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.ba1', '48.df1', '48.fd1', '48.fd2', '48.fl1', '48.fm1', '48.fo1', '48.fp1', '48.ft1'], 'contains': ['192.v1', '192.w1', '192.y1', '192.bx1', '192.bz1', '192.cf1', '192.cm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1823, -1, 1018, -1], 'generators': [1076429862, 1087290726, 1076468417], 'label': '768.1090187.96.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dk1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633674
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.dl1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bb1', '48.df1', '48.ew1', '48.ey1', '48.ez2', '48.ez4'], 'contains': ['192.v1', '192.x1', '192.bz1', '192.cb1', '192.cl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3692, -1, 3053, -1], 'generators': [1083180097, 1078860511, 1087421791], 'label': '768.1090187.96.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dl1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633675
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.b1', '6.h1', '6.i1'], 'contains': ['24.bo1', '24.br1', '24.bs1', '24.bt1', '24.bu1', '24.cm1', '24.cp1', '24.cq1', '24.cr1', '24.cu1', '24.cw1'], 'core': '48.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9211, -1, 7601, -1], 'generators': [1076429862, 1083180097, 1085750593, 506952305, 1081574431, 1085785119], 'label': '768.1090187.12.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.y1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633676
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.dm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.be1', '48.di1', '48.ey1', '48.fg1', '48.fm1', '48.fn1', '48.fp1', '48.ft1'], 'contains': ['192.v1', '192.w1', '192.by1', '192.ce1', '192.ch1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3261, -1, 1936, -1], 'generators': [1076429862, 1078991590, 1087421791], 'label': '768.1090187.96.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dm1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633677
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '96.dn1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.bg1', '48.dl1', '48.dm1', '48.ex1', '48.ey1', '48.fa1', '48.fd2'], 'contains': ['192.w1', '192.x1', '192.cg1', '192.ci1', '192.cn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [758, -1, 510, -1], 'generators': [1076429862, 1083180097, 1078860511], 'label': '768.1090187.96.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dn1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633678
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '96.do1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bh1', '48.dl1', '48.fh1', '48.fm1', '48.fo1'], 'contains': ['192.w1', '192.y1', '192.cg1', '192.cj1', '192.co1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [770, -1, 443, -1], 'generators': [1076429862, 1084833144, 1078860511], 'label': '768.1090187.96.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.do1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.do1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633679
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '96.dp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.j1', '48.bh1', '48.dm1', '48.fi1', '48.fr1', '48.ft1'], 'contains': ['192.w1', '192.cg1', '192.ck1'], 'core': '768.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [256, -1, 307, -1], 'generators': [1087390721, 1076468417, 1083229185], 'label': '768.1090187.96.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '96.dp1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dp1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633680
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '96.dq1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.bg1', '48.dl1', '48.ew1', '48.fb1', '48.fd1'], 'contains': ['192.x1', '192.y1', '192.cn1', '192.co1', '192.cr1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1044, -1, 713, -1], 'generators': [1083180097, 1078860511, 1083063654], 'label': '768.1090187.96.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dq1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633681
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.dr1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bk1', '48.ed1', '48.ej1', '48.ew1', '48.fu1', '48.gr1', '48.gs1', '48.gs2'], 'contains': ['192.z1', '192.ba1', '192.bf1', '192.bl1', '192.br1', '192.cb1', '192.cr1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3230, -1, 3154, -1], 'generators': [1083063654, 1078887480, 1087249055], 'label': '768.1090187.96.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dr1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633682
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ds1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.bi1', '48.dx2', '48.dz1', '48.ez2', '48.fc1', '48.fe2', '48.ff1', '48.fu1', '48.fv1', '48.fx4', '48.ga1', '48.gb1', '48.gc2', '48.gh1', '48.gi1'], 'contains': ['192.z1', '192.bc1', '192.be2', '192.bo1', '192.bq1', '192.cl1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4126, -1, 3391, -1], 'generators': [1087429350, 1078887480, 1084818534], 'label': '768.1090187.96.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ds1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ds1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633683
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ds2', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.bi2', '48.dx1', '48.dz1', '48.ez4', '48.fc2', '48.fe1', '48.ff1', '48.fu1', '48.fv1', '48.fx2', '48.ga1', '48.gb1', '48.gc1', '48.gh2', '48.gi1'], 'contains': ['192.z1', '192.bc1', '192.be1', '192.bo1', '192.bq2', '192.cl1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4138, -1, 3425, -1], 'generators': [1087298271, 1078887480, 1084818534], 'label': '768.1090187.96.ds2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ds2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ds2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633684
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.dt1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.bj1', '48.dy1', '48.ea1', '48.ew1', '48.ex1', '48.fa1', '48.fb1', '48.fx2', '48.fx4', '48.gc1', '48.gc2', '48.gh1', '48.gh2', '48.gi1'], 'contains': ['192.z1', '192.bc1', '192.bd1', '192.bo1', '192.bp1', '192.cl1', '192.cn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3338, -1, 2849, -1], 'generators': [1081547512, 1078887480, 1084818534], 'label': '768.1090187.96.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dt1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dt1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633685
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.du1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bk1', '48.ej1', '48.ek1', '48.ex1', '48.fv1', '48.gr1', '48.gt1'], 'contains': ['192.z1', '192.bb1', '192.br1', '192.bv1', '192.ci1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2337, -1, 2646, -1], 'generators': [1076429862, 1081574431, 1087249055], 'label': '768.1090187.96.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.du1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.du1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633686
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.c1', '6.h1', '6.i1'], 'contains': ['24.bt1', '24.bu1', '24.cs1', '24.cv1', '24.cx1'], 'core': '48.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8618, -1, 6103, -1], 'generators': [1076429862, 1083180097, 1085750593, 1081574431, 512648241, 1085785119], 'label': '768.1090187.12.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.z1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633687
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.dv1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.bi1', '48.dx1', '48.eb1', '48.ez1', '48.ez2', '48.fe1', '48.fg1', '48.fu1', '48.fw1', '48.fx3', '48.fx4', '48.gf1', '48.gf2', '48.gh2', '48.gj1'], 'contains': ['192.ba1', '192.bc1', '192.be2', '192.by1', '192.ca1', '192.cl1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4077, -1, 2951, -1], 'generators': [1089985272, 1087421791, 1084818534], 'label': '768.1090187.96.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dv1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633688
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.dv2', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.bi2', '48.dx2', '48.eb1', '48.ez3', '48.ez4', '48.fe2', '48.fg1', '48.fu1', '48.fw1', '48.fx1', '48.fx2', '48.gf1', '48.gf2', '48.gh1', '48.gj1'], 'contains': ['192.ba1', '192.bc1', '192.be1', '192.by1', '192.ca2', '192.cl1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4089, -1, 2917, -1], 'generators': [1087421791, 1087429350, 1084818534], 'label': '768.1090187.96.dv2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dv2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dv2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633689
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.dw1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.bj1', '48.dy1', '48.ec1', '48.ew1', '48.ey1', '48.fd1', '48.fd2', '48.fx1', '48.fx2', '48.fx3', '48.fx4', '48.gh1', '48.gh2', '48.gj1'], 'contains': ['192.ba1', '192.bc1', '192.bd1', '192.by1', '192.bz1', '192.cl1', '192.cn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3326, -1, 2579, -1], 'generators': [1078860511, 1087421791, 1084818534], 'label': '768.1090187.96.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dw1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633690
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.dx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bk1', '48.ed1', '48.ep1', '48.ey1', '48.fw1', '48.gm1', '48.gr1'], 'contains': ['192.ba1', '192.bb1', '192.cb1', '192.ce1', '192.ci1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2112, -1, 1970, -1], 'generators': [1076429862, 1087421791, 1087249055], 'label': '768.1090187.96.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dx1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633691
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.dy1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bl1', '48.dn1', '48.dt2', '48.ex1', '48.ey1', '48.fh1', '48.fi1', '48.ga1', '48.gf1', '48.gi1', '48.gj1'], 'contains': ['192.bb1', '192.bc1', '192.cg1', '192.ch1', '192.cl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1515, -1, 916, -1], 'generators': [1076429862, 1078860511, 1089963103], 'label': '768.1090187.96.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dy1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633692
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.dy2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bl2', '48.dn1', '48.dt1', '48.fa1', '48.fd1', '48.fv1', '48.fw1', '48.gi1', '48.gj1', '48.gk1', '48.gl1'], 'contains': ['192.bb1', '192.bc1', '192.cf1', '192.cn1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1503, -1, 1052, -1], 'generators': [1076429862, 1089045606, 1083202278], 'label': '768.1090187.96.dy2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dy2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dy2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633693
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.dz1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bm1', '48.do1', '48.du1', '48.ff1', '48.fg1', '48.fv1', '48.fw1', '48.ga1', '48.gf1', '48.gk1', '48.gl1'], 'contains': ['192.bb1', '192.be1', '192.be2', '192.ch1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2549, -1, 2037, -1], 'generators': [1076429862, 1089963103, 1089985272], 'label': '768.1090187.96.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.dz1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.dz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633694
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ea1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bl1', '48.dq1', '48.dt1', '48.ew1', '48.fh1', '48.gb1', '48.gf2', '48.gh1', '48.gh2'], 'contains': ['192.bc1', '192.bf1', '192.cl1', '192.co1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2084, -1, 1390, -1], 'generators': [1078860511, 1089963103, 1083063654], 'label': '768.1090187.96.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ea1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ea1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633695
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ea2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bl2', '48.dq1', '48.dt2', '48.fb1', '48.fd2', '48.fu1', '48.gh1', '48.gh2', '48.gk1'], 'contains': ['192.bc1', '192.bf1', '192.cm1', '192.cn1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1591, -1, 1563, -1], 'generators': [1083063654, 1089045606, 1083202278], 'label': '768.1090187.96.ea2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ea2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ea2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633696
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.eb1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bm1', '48.dr1', '48.du1', '48.fe1', '48.fe2', '48.fu1', '48.gb1', '48.gf2', '48.gk1'], 'contains': ['192.be1', '192.be2', '192.bf1', '192.cp1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3313, -1, 2545, -1], 'generators': [1089963103, 1083063654, 1089985272], 'label': '768.1090187.96.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.eb1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633697
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.d1', '6.h1'], 'contains': ['24.ca2', '24.cb2', '24.ce1', '24.cq1', '24.cs1', '24.ek1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8646, -1, 6028, -1], 'generators': [1083098168, 1089963103, 1085750593, 1076468417, 1080656934, 668673292], 'label': '768.1090187.12.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.ba1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633698
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ec1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bw1', '48.eq1', '48.es1', '48.ez1', '48.fx1', '48.fy1', '48.gr1'], 'contains': ['192.ba1', '192.bh2', '192.bm1', '192.br1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7238, -1, 5505, -1], 'generators': [1074724198, 1078887480, 1089936056], 'label': '768.1090187.96.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ec1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ec1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633699
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ec2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bw1', '48.er1', '48.ez2', '48.fx2', '48.gm1', '48.gr1', '48.gs1'], 'contains': ['192.z1', '192.ba1', '192.bi2', '192.bm1', '192.cb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4940, -1, 4490, -1], 'generators': [1074724198, 1078887480, 1087249055], 'label': '768.1090187.96.ec2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ec2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ec2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633700
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ec3', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bw2', '48.eq1', '48.es2', '48.ez3', '48.fx3', '48.fy2', '48.fz1', '48.gr1'], 'contains': ['192.ba1', '192.bh1', '192.bm2', '192.br1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7465, -1, 5798, -1], 'generators': [1074855263, 1078887480, 1089936056], 'label': '768.1090187.96.ec3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ec3', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ec3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633701
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ec4', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bw2', '48.er1', '48.ez4', '48.fx4', '48.gm1', '48.gr1', '48.gs2'], 'contains': ['192.z1', '192.ba1', '192.bi1', '192.bm2', '192.cb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4920, -1, 4591, -1], 'generators': [1074855263, 1078887480, 1087249055], 'label': '768.1090187.96.ec4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ec4', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ec4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633702
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ed1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bo1', '48.ed1', '48.ek1', '48.fa1', '48.ga1', '48.gm1', '48.gt1', '48.gv1', '48.gx1'], 'contains': ['192.z1', '192.bb1', '192.bj1', '192.bn1', '192.ci1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1628, -1, 2003, -1], 'generators': [1081574431, 1077347359, 1089936056], 'label': '768.1090187.96.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ed1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ed1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633703
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ee1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bp1', '48.ee1', '48.el1', '48.ez3', '48.fc2', '48.fj1', '48.fk1', '48.gh2', '48.gi1'], 'contains': ['192.bc1', '192.bh1', '192.bp1', '192.bq2'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6751, -1, 4963, -1], 'generators': [1087298271, 1078887480, 1083049080], 'label': '768.1090187.96.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ee1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ee1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633704
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ee2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bp2', '48.ee2', '48.el1', '48.fe2', '48.ff1', '48.fx3', '48.gc2', '48.gh2', '48.gi1', '48.gn1', '48.gp1'], 'contains': ['192.bc1', '192.bd1', '192.be2', '192.bh1', '192.bo1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4965, -1, 3696, -1], 'generators': [1089067713, 1078887480, 1084818534], 'label': '768.1090187.96.ee2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ee2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ee2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633705
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ee3', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bp3', '48.ee3', '48.el2', '48.ez1', '48.fc1', '48.fj1', '48.fk1', '48.gh1', '48.gi1'], 'contains': ['192.bc1', '192.bh2', '192.bp1', '192.bq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6476, -1, 4760, -1], 'generators': [1087429350, 1078887480, 1083049080], 'label': '768.1090187.96.ee3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ee3', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ee3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633706
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ee4', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bp4', '48.ee4', '48.el2', '48.fe1', '48.ff1', '48.fx1', '48.gc1', '48.gh1', '48.gi1', '48.gn1', '48.gp1'], 'contains': ['192.bc1', '192.bd1', '192.be1', '192.bh2', '192.bo1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4952, -1, 3729, -1], 'generators': [1089985272, 1078887480, 1084818534], 'label': '768.1090187.96.ee4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ee4', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ee4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633707
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ef1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bo1', '48.ej1', '48.fb1', '48.gb1', '48.gs1', '48.gs2', '48.gw1'], 'contains': ['192.z1', '192.bf1', '192.bk1', '192.bs1', '192.cr1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2831, -1, 2680, -1], 'generators': [1084833144, 1078887480, 1087249055], 'label': '768.1090187.96.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ef1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ef1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633708
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1536.408634201', 'aut_weyl_index': 12, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '6.d1', '6.e1', '6.f1', '6.g1', '6.h1', '6.i1'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8569, -1, 6079, -1], 'generators': [1083180097, 1076429862, 1074660408, 1084867622, 1078860511, 1085750593, 1081574431, 668673292], 'label': '768.1090187.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633709
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.e1', '6.h1'], 'contains': ['24.ca2', '24.cc1', '24.cd2', '24.cr1', '24.cs1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8781, -1, 6534, -1], 'generators': [1078860511, 1089963103, 1083098168, 1085750593, 1080656934, 668673292], 'label': '768.1090187.12.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bb1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633710
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '96.eg1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bq1', '48.ef1', '48.em1', '48.fy2', '48.gd2', '48.go1', '48.gq1'], 'contains': ['192.bh1', '192.bt1', '192.bu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [8987, -1, 8641, -1], 'generators': [1085774520, 668673292, 1089946655], 'label': '768.1090187.96.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.eg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633711
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '96.eh1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.br1', '48.eg1', '48.en1', '48.fy1', '48.gd1', '48.go1', '48.gq1'], 'contains': ['192.bg1', '192.bh2', '192.bt1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9163, -1, 9110, -1], 'generators': [1083218598, 660749132, 1089946655], 'label': '768.1090187.96.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.eh1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633712
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '96.ei1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bs1', '48.eh1', '48.eo1', '48.fy1', '48.gd1', '48.go1', '48.gq1'], 'contains': ['192.bh2', '192.bu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9003, -1, 8505, -1], 'generators': [1083218598, 668673292, 1089946655], 'label': '768.1090187.96.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.ei1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ei1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633713
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ej1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bw1', '48.es2', '48.et1', '48.fc1', '48.gc1', '48.gd1', '48.gs2', '48.gt1'], 'contains': ['192.c1', '192.z1', '192.bh2', '192.br1'], 'core': '192.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [7032, -1, 5866, -1], 'generators': [1083098168, 1081574431, 1087249055], 'label': '768.1090187.96.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ej1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ej1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633714
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ej2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bw2', '48.es1', '48.et1', '48.fc2', '48.gc2', '48.gd2', '48.ge1', '48.gs1', '48.gt1'], 'contains': ['192.z1', '192.bh1', '192.br1', '192.bw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7201, -1, 5933, -1], 'generators': [1083098168, 1080656934, 1087249055], 'label': '768.1090187.96.ej2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ej2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ej2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633715
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ek1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bo1', '48.ed1', '48.fd1', '48.gf1', '48.gr1', '48.gw1', '48.gy1'], 'contains': ['192.ba1', '192.bb1', '192.bk1', '192.bx1', '192.cr1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1653, -1, 1255, -1], 'generators': [1076429862, 1087290726, 1074813606], 'label': '768.1090187.96.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ek1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ek1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633716
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ek2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bo1', '48.ej1', '48.ep1', '48.fd2', '48.gf2', '48.gr1', '48.gv1'], 'contains': ['192.ba1', '192.bf1', '192.bj1', '192.bx1', '192.ci1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1234, -1, 1119, -1], 'generators': [1076429862, 1087290726, 1087249055], 'label': '768.1090187.96.ek2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ek2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ek2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633717
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.el1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bp1', '48.ee2', '48.ez4', '48.fl1', '48.gh1', '48.gj1'], 'contains': ['192.bc1', '192.bi1', '192.bz1', '192.ca2'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4725, -1, 3628, -1], 'generators': [1087421791, 1087429350, 1085736031], 'label': '768.1090187.96.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.el1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.el1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633718
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.el2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bp2', '48.ee1', '48.ee2', '48.fe1', '48.fg1', '48.fx4', '48.gh1', '48.gj1', '48.gu1'], 'contains': ['192.bc1', '192.bd1', '192.be2', '192.bi1', '192.by1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4651, -1, 3459, -1], 'generators': [1087298271, 1087421791, 1084818534], 'label': '768.1090187.96.el2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.el2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.el2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633719
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.el3', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bp3', '48.ee4', '48.ez2', '48.fl1', '48.gg1', '48.gh2', '48.gj1'], 'contains': ['192.bc1', '192.bi2', '192.bz1', '192.ca1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5149, -1, 4219, -1], 'generators': [1089985272, 1087421791, 1085736031], 'label': '768.1090187.96.el3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.el3', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.el3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633720
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1', '6.h1'], 'contains': ['24.cb2', '24.cc1', '24.ck1', '24.cu1', '24.cv1', '24.el1', '24.em1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8489, -1, 6695, -1], 'generators': [1074660408, 1085750593, 1081574431, 1083229185, 668673292, 1087249055], 'label': '768.1090187.12.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bc1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633721
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.el4', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.bp4', '48.ee3', '48.ee4', '48.fe2', '48.fg1', '48.fx2', '48.gh2', '48.gj1', '48.gu1'], 'contains': ['192.bc1', '192.bd1', '192.be1', '192.bi2', '192.by1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4847, -1, 3594, -1], 'generators': [1089067713, 1087421791, 1084818534], 'label': '768.1090187.96.el4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.el4', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.el4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633722
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '96.em1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.br1', '48.eg1', '48.gg1'], 'contains': ['192.bg1', '192.bi2', '192.cc1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9420, -1, 8826, -1], 'generators': [1076493688, 658250892, 1074682527], 'label': '768.1090187.96.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '96.em1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.em1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633723
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '96.en1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bv1', '48.ei1', '48.gg1'], 'contains': ['192.bi2', '192.cd1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9331, -1, 7198, -1], 'generators': [1074855263, 518587222, 518610417], 'label': '768.1090187.96.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '96.en1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.en1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633724
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.eo1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.bx1', '48.dz1', '48.eb1', '48.ff1', '48.fg1', '48.fj1', '48.fl1', '48.ga1', '48.gf2', '48.gi1', '48.gj1', '48.gk1', '48.gl1', '48.gn1', '48.gu1'], 'contains': ['192.bc1', '192.be1', '192.be2', '192.bj1', '192.cf1', '192.ch1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3102, -1, 2139, -1], 'generators': [1076429862, 1089963103, 1083202278], 'label': '768.1090187.96.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.eo1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633725
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ep1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.by1', '48.ea1', '48.ec1', '48.fa1', '48.fd2', '48.fh1', '48.fi1', '48.gi1', '48.gj1', '48.gn1', '48.gu1'], 'contains': ['192.bc1', '192.bd1', '192.bj1', '192.cf1', '192.cg1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1879, -1, 984, -1], 'generators': [1076429862, 1076468417, 1083049080], 'label': '768.1090187.96.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ep1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ep1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633726
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.eq1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['48.bx1', '48.dx1', '48.dx2', '48.fe1', '48.fe2', '48.fk1', '48.fl1', '48.gb1', '48.gf1', '48.gh1', '48.gh2', '48.gk1', '48.gp1', '48.gu1'], 'contains': ['192.bc1', '192.be1', '192.be2', '192.bk1', '192.cm1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3667, -1, 2782, -1], 'generators': [1089963103, 1083063654, 1083202278], 'label': '768.1090187.96.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.eq1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633727
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.er1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.by1', '48.dy1', '48.fb1', '48.fd1', '48.fh1', '48.gh1', '48.gh2', '48.gp1', '48.gu1'], 'contains': ['192.bc1', '192.bd1', '192.bk1', '192.cm1', '192.co1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2994, -1, 1631, -1], 'generators': [1083063654, 1076468417, 1083049080], 'label': '768.1090187.96.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.er1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.er1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633728
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.es1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bz1', '48.er1', '48.es1', '48.fe1', '48.gh1', '48.gr1', '48.gs2', '48.gv1', '48.gw1'], 'contains': ['192.z1', '192.ba1', '192.bf1', '192.bh2', '192.bi1', '192.bk1', '192.bl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4412, -1, 3898, -1], 'generators': [1083063654, 1081596600, 1078887480], 'label': '768.1090187.96.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.es1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.es1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633729
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.es2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bz1', '48.er1', '48.es2', '48.fe2', '48.gh2', '48.gr1', '48.gs1', '48.gv1', '48.gw1'], 'contains': ['192.z1', '192.ba1', '192.bf1', '192.bh1', '192.bi2', '192.bk1', '192.bl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4361, -1, 4068, -1], 'generators': [1080679041, 1083063654, 1078887480], 'label': '768.1090187.96.es2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.es2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.es2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633730
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.et1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bz1', '48.er1', '48.et1', '48.ff1', '48.gi1', '48.gr1', '48.gt1', '48.gw1', '48.gx1'], 'contains': ['192.z1', '192.bb1', '192.bh1', '192.bh2', '192.bj1', '192.bv1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4028, -1, 3865, -1], 'generators': [1076429862, 1081574431, 1081596600], 'label': '768.1090187.96.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.et1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.et1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633731
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.g1', '6.h1'], 'contains': ['24.cd2', '24.ce1', '24.ck1', '24.cw1', '24.cx1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8729, -1, 5851, -1], 'generators': [1076429862, 1085750593, 508566806, 1081574431, 512648241, 1085785119], 'label': '768.1090187.12.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bd1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633732
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.eu1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bz1', '48.eq1', '48.er1', '48.fg1', '48.gj1', '48.gm1', '48.gr1', '48.gv1', '48.gy1'], 'contains': ['192.ba1', '192.bb1', '192.bi1', '192.bi2', '192.bj1', '192.ce1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3679, -1, 3357, -1], 'generators': [1076429862, 1081596600, 1087421791], 'label': '768.1090187.96.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.eu1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.eu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633733
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ev1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ca1', '48.ed1', '48.ej1', '48.fh1', '48.gk1', '48.gv1', '48.gw1'], 'contains': ['192.bb1', '192.bf1', '192.bj1', '192.bk1', '192.cj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1056, -1, 950, -1], 'generators': [1076429862, 1084833144, 1084856961], 'label': '768.1090187.96.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ev1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ev1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633734
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ew1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ca1', '48.ek1', '48.ep1', '48.fi1', '48.gl1', '48.gx1', '48.gy1'], 'contains': ['192.bb1', '192.bj1', '192.ck1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [382, -1, 544, -1], 'generators': [1087390721, 1083229185, 1087249055], 'label': '768.1090187.96.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ew1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ew1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633735
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ex1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cb1', '48.eq1', '48.et1', '48.fj1', '48.gn1', '48.go1', '48.gv1', '48.gx1'], 'contains': ['192.bh1', '192.bh2', '192.bj1', '192.bn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5556, -1, 4896, -1], 'generators': [1081574431, 1081596600, 1077347359], 'label': '768.1090187.96.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ex1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ex1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633736
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ey1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cb1', '48.es1', '48.es2', '48.fk1', '48.gp1', '48.gq1', '48.gw1'], 'contains': ['192.bh1', '192.bh2', '192.bk1', '192.bs1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7250, -1, 5268, -1], 'generators': [1084833144, 1078909599, 1078887480], 'label': '768.1090187.96.ey1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ey1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ey1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633737
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '96.ez1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cb1', '48.er1', '48.fl1', '48.gu1', '48.gv1', '48.gw1', '48.gy1'], 'contains': ['192.bi1', '192.bi2', '192.bj1', '192.bk1', '192.bx1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3054, -1, 2477, -1], 'generators': [1076429862, 1087290726, 1081596600], 'label': '768.1090187.96.ez1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ez1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ez1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633738
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fa1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.cq1', '48.dx1', '48.fe1', '48.fp1', '48.fq1', '48.fu1', '48.gh2', '48.gz1', '48.hf1', '48.hg1', '48.hh2'], 'contains': ['192.bl1', '192.bo1', '192.bq2', '192.by1', '192.ca1', '192.cm1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3836, -1, 3492, -1], 'generators': [1083063654, 1089985272, 1078887480], 'label': '768.1090187.96.fa1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fa1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fa1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633739
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fa2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.cq1', '48.dx2', '48.fe2', '48.fp1', '48.fq2', '48.fu1', '48.gh1', '48.gz1', '48.hf1', '48.hg1', '48.hh1'], 'contains': ['192.bl1', '192.bo1', '192.bq1', '192.by1', '192.ca2', '192.cm1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3929, -1, 3323, -1], 'generators': [1083063654, 1089067713, 1078887480], 'label': '768.1090187.96.fa2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fa2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fa2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633794
    {'ambient': '768.1090187', 'aut_centralizer_order': 144, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.i1', '32.j1', '64.b1', '64.e1'], 'contains': ['256.a1', '384.c1'], 'core': '768.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [38, -1, 3087, -1], 'generators': [2148207653, 3234148260], 'label': '768.1090187.128.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1', 'old_label': '128.c1', 'projective_image': '768.1090187', '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: 59633740
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fb1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.cr1', '48.dy1', '48.ew1', '48.fm1', '48.fo1', '48.gh1', '48.gh2', '48.hg1', '48.hh1', '48.hh2'], 'contains': ['192.bl1', '192.bo1', '192.bp1', '192.by1', '192.bz1', '192.cm1', '192.co1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3351, -1, 2714, -1], 'generators': [1078860511, 1083063654, 1078887480], 'label': '768.1090187.96.fb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fb1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633741
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.fc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.cs1', '48.ed1', '48.fm1', '48.gv1', '48.gz1', '48.hl1', '48.hn1'], 'contains': ['192.bl1', '192.bn1', '192.bx1', '192.ce1', '192.cj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1671, -1, 1834, -1], 'generators': [1083063654, 1081574431, 1077347359], 'label': '768.1090187.96.fc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fc1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633742
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.d1', '6.h1', '6.i1'], 'contains': ['24.cq1', '24.cs1', '24.ct1', '24.cu1', '24.cx1', '24.en1', '24.eo1'], 'core': '96.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8590, -1, 5925, -1], 'generators': [1076429862, 1085750593, 1081574431, 1076479078, 512648241, 1085785119], 'label': '768.1090187.12.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.be1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633743
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ct1', '48.ee1', '48.ez1', '48.fn1', '48.fq1', '48.fx2', '48.hg1'], 'contains': ['192.bm1', '192.bp1', '192.bq2', '192.by1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6640, -1, 4794, -1], 'generators': [1074724198, 1081547512, 1078887480], 'label': '768.1090187.96.fd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fd1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633744
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fd2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.ct1', '48.ee2', '48.ez2', '48.fp1', '48.fx1', '48.fx2', '48.hc1', '48.hg1', '48.hh1'], 'contains': ['192.bm1', '192.bo1', '192.by1', '192.bz1', '192.ca2'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5163, -1, 3932, -1], 'generators': [1074724198, 1078860511, 1078887480], 'label': '768.1090187.96.fd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fd2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fd2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633745
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fd3', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ct2', '48.ee3', '48.ez3', '48.fn1', '48.fq2', '48.fx4', '48.hg1'], 'contains': ['192.bm2', '192.bp1', '192.bq1', '192.by1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6691, -1, 4997, -1], 'generators': [1081547512, 1074855263, 1078887480], 'label': '768.1090187.96.fd3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fd3', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fd3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633746
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fd4', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.ct2', '48.ee4', '48.ez4', '48.fp1', '48.fx3', '48.fx4', '48.ha1', '48.hb1', '48.hc1', '48.hg1', '48.hh2'], 'contains': ['192.bm2', '192.bo1', '192.by1', '192.bz1', '192.ca1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6512, -1, 4422, -1], 'generators': [1078860511, 1074855263, 1078887480], 'label': '768.1090187.96.fd4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.fd4', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fd4', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633747
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.fe1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cu1', '48.ef1', '48.fy1', '48.hd1', '48.hi2'], 'contains': ['192.bm1', '192.bt1', '192.bu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8976, -1, 8611, -1], 'generators': [1074724198, 1078887480, 514417711], 'label': '768.1090187.96.fe1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.fe1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fe1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633748
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ff1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cv1', '48.eg1', '48.fy2', '48.ha1', '48.hd1', '48.hi1'], 'contains': ['192.bm2', '192.bt1', '192.cc1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9294, -1, 8579, -1], 'generators': [504396399, 1074855263, 1078887480], 'label': '768.1090187.96.ff1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '96.ff1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ff1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633749
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.fg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cw1', '48.eh1', '48.fy2', '48.hb1', '48.hd1', '48.hi1'], 'contains': ['192.bm2', '192.bu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9044, -1, 8241, -1], 'generators': [1074855263, 1078887480, 514417711], 'label': '768.1090187.96.fg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '96.fg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633750
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.fh1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cz1', '48.ei1', '48.fz1', '48.ha1', '48.hb1', '48.he1', '48.hk1'], 'contains': ['192.bm2', '192.cd1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8866, -1, 6832, -1], 'generators': [1074855263, 1078887480, 504259697], 'label': '768.1090187.96.fh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '96.fh1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633751
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.fi1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.da1', '48.eq1', '48.fn1', '48.gm1', '48.hc1', '48.hd1', '48.he1', '48.hl1'], 'contains': ['192.bm1', '192.bm2', '192.bn1', '192.ce1'], 'core': '768.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7018, -1, 5335, -1], 'generators': [1074724198, 1081574431, 1077347359], 'label': '768.1090187.96.fi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.fi1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633752
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fj1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cc1', '48.dn1', '48.fa1', '48.fm1', '48.fr1', '48.ga1', '48.gn1', '48.gz1', '48.hc1', '48.hm1', '48.ho1'], 'contains': ['192.bn1', '192.bo1', '192.cf1', '192.cg1', '192.ch1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1616, -1, 1289, -1], 'generators': [1081547512, 1081574431, 1077347359], 'label': '768.1090187.96.fj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fj1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633753
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.e1', '6.h1', '6.i1'], 'contains': ['24.cr1', '24.cs1', '24.ct1', '24.cv1', '24.cw1'], 'core': '96.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [8764, -1, 6282, -1], 'generators': [1076429862, 1085750593, 506952305, 1081574431, 1076479078, 1085785119], 'label': '768.1090187.12.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bf1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633754
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fk1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cd1', '48.do1', '48.fj1', '48.fn1', '48.fs1', '48.ga1', '48.gz1', '48.hm1'], 'contains': ['192.bn1', '192.bq1', '192.bq2', '192.ch1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4688, -1, 3966, -1], 'generators': [1081574431, 1089985272, 1077347359], 'label': '768.1090187.96.fk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fk1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633755
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.fl1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ce1', '48.dp1', '48.go1', '48.hd1', '48.hp1'], 'contains': ['192.bn1', '192.bt1', '192.bu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8936, -1, 8406, -1], 'generators': [1076429862, 1087390721, 504396399], 'label': '768.1090187.96.fl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.fl1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633756
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.fm1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.cg1', '48.dn1', '48.dq1', '48.ew1', '48.ex1', '48.fu1', '48.fv1', '48.fx1', '48.fx3', '48.gc1', '48.gc2'], 'contains': ['192.bo1', '192.br1', '192.cl1', '192.cn1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3646, -1, 2883, -1], 'generators': [1078860511, 1078887480, 1084818534], 'label': '768.1090187.96.fm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fm1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633757
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cc1', '48.dq1', '48.fb1', '48.fo1', '48.gb1', '48.gp1', '48.hf1', '48.hh1', '48.hh2'], 'contains': ['192.bo1', '192.bs1', '192.cm1', '192.co1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3007, -1, 2173, -1], 'generators': [1084833144, 1078860511, 1078887480], 'label': '768.1090187.96.fn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fn1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633758
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.fo1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cn1', '48.do1', '48.dr1', '48.ez1', '48.ez3', '48.fc1', '48.fc2', '48.fu1', '48.fv1'], 'contains': ['192.bq1', '192.bq2', '192.br1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6448, -1, 4862, -1], 'generators': [1087298271, 1076479078, 1078887480], 'label': '768.1090187.96.fo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fo1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633759
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cd1', '48.dr1', '48.fk1', '48.fq1', '48.fq2', '48.gb1', '48.hf1'], 'contains': ['192.bq1', '192.bq2', '192.bs1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6703, -1, 4625, -1], 'generators': [1084833144, 1087298271, 1078887480], 'label': '768.1090187.96.fp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fp1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633760
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '96.fq1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.co1', '48.dp1', '48.ds1', '48.fy1', '48.fy2', '48.gd1', '48.gd2'], 'contains': ['192.br1', '192.bt1', '192.bu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9120, -1, 8671, -1], 'generators': [668673292, 1087249055, 1089946655], 'label': '768.1090187.96.fq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.fq1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633761
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.fr1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ce1', '48.ds1', '48.gq1', '48.hi1', '48.hi2'], 'contains': ['192.bs1', '192.bt1', '192.bu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9178, -1, 8548, -1], 'generators': [1084833144, 1078887480, 514417711], 'label': '768.1090187.96.fr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.fr1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633762
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.fs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.cs1', '48.ej1', '48.fo1', '48.gw1', '48.hf1', '48.hn1'], 'contains': ['192.bl1', '192.bs1', '192.bv1', '192.bx1', '192.cj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1641, -1, 2376, -1], 'generators': [1076429862, 1084833144, 1081574431], 'label': '768.1090187.96.fs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fs1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633763
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.ft1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.da1', '48.er1', '48.fp1', '48.gr1', '48.hg1', '48.hl1', '48.hn1'], 'contains': ['192.bl1', '192.bm1', '192.bm2', '192.bv1', '192.bx1', '192.ce1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3959, -1, 4253, -1], 'generators': [1076429862, 1074724198, 1081574431], 'label': '768.1090187.96.ft1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ft1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ft1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633764
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 192, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.f1', '6.i1'], 'contains': ['24.b1', '24.cu1', '24.cv1', '24.ep1', '24.eq1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8038, -1, 6460, -1], 'generators': [1076429862, 1074660408, 1084867622, 1085750593, 1081574431, 504396399], 'label': '768.1090187.12.bg1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bg1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633765
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fu1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.cq1', '48.dz1', '48.ff1', '48.fp1', '48.fs1', '48.fv1', '48.gi1', '48.hf1', '48.hg1', '48.hm1', '48.ho1'], 'contains': ['192.bo1', '192.bq1', '192.bq2', '192.bv1', '192.cf1', '192.ch1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3634, -1, 2985, -1], 'generators': [1076429862, 1081574431, 1089985272], 'label': '768.1090187.96.fu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fu1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633766
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fv1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cr1', '48.ea1', '48.ex1', '48.fo1', '48.fr1', '48.gi1', '48.hg1', '48.ho1'], 'contains': ['192.bo1', '192.bp1', '192.bv1', '192.cf1', '192.cg1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2437, -1, 2105, -1], 'generators': [1076429862, 1078860511, 1081574431], 'label': '768.1090187.96.fv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fv1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633767
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.fw1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.da1', '48.es1', '48.fq1', '48.gs1', '48.hh1', '48.hi2', '48.hj1', '48.hn1'], 'contains': ['192.bl1', '192.bm1', '192.bs1', '192.bw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7226, -1, 5832, -1], 'generators': [1083098168, 1087421791, 1080656934], 'label': '768.1090187.96.fw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.fw1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633768
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.fw2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.da1', '48.es2', '48.fq2', '48.gs2', '48.hh2', '48.hi1', '48.hk1', '48.hn1'], 'contains': ['192.c1', '192.bl1', '192.bm2', '192.bs1'], 'core': '192.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [7288, -1, 5899, -1], 'generators': [1083098168, 1081574431, 1077411137], 'label': '768.1090187.96.fw2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.fw2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fw2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633769
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.fx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '48.cs1', '48.ek1', '48.fr1', '48.gx1', '48.hl1', '48.hm1'], 'contains': ['192.bn1', '192.bv1', '192.ck1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [497, -1, 1902, -1], 'generators': [1076429862, 1074660408, 1081574431], 'label': '768.1090187.96.fx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fx1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633770
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fy1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ct1', '48.el1', '48.fc1', '48.fq2', '48.fs1', '48.gc1', '48.hh2', '48.ho1'], 'contains': ['192.c1', '192.bo1', '192.bp1', '192.bq2'], 'core': '192.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [6666, -1, 5234, -1], 'generators': [1078860511, 1083098168, 1081574431], 'label': '768.1090187.96.fy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fy1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633771
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.fy2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ct2', '48.el2', '48.fc2', '48.fq1', '48.fs1', '48.gc2', '48.hh1', '48.ho1'], 'contains': ['192.bo1', '192.bp1', '192.bq1', '192.bw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6153, -1, 4828, -1], 'generators': [1078860511, 1083098168, 1080656934], 'label': '768.1090187.96.fy2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.fy2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fy2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633772
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.fz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['32.k1', '48.cu1', '48.em1', '48.gd1', '48.hi1', '48.hp1'], 'contains': ['192.c1', '192.bt1', '192.bu1'], 'core': '192.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [8947, -1, 8376, -1], 'generators': [1083098168, 1081574431, 504396399], 'label': '768.1090187.96.fz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '96.fz1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.fz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633773
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.ga1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 768, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cv1', '48.en1', '48.gd2', '48.hi2', '48.hp1'], 'contains': ['192.bt1', '192.bw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8808, -1, 8792, -1], 'generators': [504396399, 1078887480, 1085785119], 'label': '768.1090187.96.ga1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '96.ga1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ga1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633774
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.gb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2304, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cw1', '48.eo1', '48.gd2', '48.ge1', '48.hi2', '48.hj1', '48.hp1', '48.hq1'], 'contains': ['192.bu1', '192.bw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8756, -1, 7778, -1], 'generators': [511132591, 1078887480, 1085785119], 'label': '768.1090187.96.gb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '96.gb1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633775
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 192, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.g1', '6.i1'], 'contains': ['24.b1', '24.cw1', '24.cx1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8461, -1, 5512, -1], 'generators': [1076429862, 1074660408, 1084867622, 1085750593, 506952305, 1081574431], 'label': '768.1090187.12.bh1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bh1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59633776
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.gc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.c1', '48.da1', '48.et1', '48.fs1', '48.gt1', '48.hn1', '48.ho1', '48.hp1', '48.hq1'], 'contains': ['192.c1', '192.bn1', '192.bv1', '192.bw1'], 'core': '192.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [5593, -1, 5730, -1], 'generators': [1074660408, 1081574431, 1083229185], 'label': '768.1090187.96.gc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.gc1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633777
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.gd1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cc1', '48.dt1', '48.fd1', '48.fm1', '48.gf2', '48.gu1', '48.hf1', '48.hg1', '48.hr1'], 'contains': ['192.bx1', '192.by1', '192.cf1', '192.co1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1381, -1, 815, -1], 'generators': [1076429862, 1087290726, 1083202278], 'label': '768.1090187.96.gd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gd1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633778
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.gd2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cc1', '48.dt2', '48.fd2', '48.fo1', '48.ft1', '48.gf1', '48.gu1', '48.gz1', '48.hg1'], 'contains': ['192.bx1', '192.by1', '192.cg1', '192.ch1', '192.cm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1246, -1, 849, -1], 'generators': [1076429862, 1087290726, 1078860511], 'label': '768.1090187.96.gd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gd2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gd2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633779
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.ge1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cd1', '48.du1', '48.fl1', '48.fp1', '48.gf1', '48.gf2', '48.gz1', '48.hf1', '48.hr1'], 'contains': ['192.bx1', '192.ca1', '192.ca2', '192.ch1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2305, -1, 1665, -1], 'generators': [1076429862, 1087290726, 1089985272], 'label': '768.1090187.96.ge1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ge1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ge1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633780
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.gf1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.cg1', '48.dt1', '48.dt2', '48.ew1', '48.ey1', '48.fu1', '48.fw1', '48.fx2', '48.fx4'], 'contains': ['192.by1', '192.cb1', '192.cl1', '192.cn1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2982, -1, 2308, -1], 'generators': [1081547512, 1087421791, 1084818534], 'label': '768.1090187.96.gf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gf1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633781
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '96.gg1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.ch1', '48.dv1', '48.gg1', '48.ha1'], 'contains': ['192.bz1', '192.cc1', '192.cd1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [9439, -1, 7270, -1], 'generators': [1074840641, 1074855263, 518610417], 'label': '768.1090187.96.gg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '96.gg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633782
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '96.gh1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.ck1', '48.dw1', '48.gg1', '48.ha1'], 'contains': ['192.ca1', '192.cc1', '192.cd1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [9353, -1, 7240, -1], 'generators': [1078885734, 1089963103, 508576689], 'label': '768.1090187.96.gh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '96.gh1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59633783
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.gi1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cn1', '48.du1', '48.ez2', '48.ez4', '48.fu1', '48.fw1'], 'contains': ['192.ca1', '192.ca2', '192.cb1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4309, -1, 3526, -1], 'generators': [1089985272, 1076479078, 1087421791], 'label': '768.1090187.96.gi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gi1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633784
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.gj1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.cq1', '48.eb1', '48.fg1', '48.fn1', '48.fp1', '48.fw1', '48.gj1', '48.gz1', '48.hc1', '48.hg1', '48.hr1'], 'contains': ['192.by1', '192.ca1', '192.ca2', '192.ce1', '192.cf1', '192.ch1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3363, -1, 2748, -1], 'generators': [1076429862, 1089985272, 1087421791], 'label': '768.1090187.96.gj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gj1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633785
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.gk1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cr1', '48.ec1', '48.ey1', '48.fm1', '48.ft1', '48.gj1', '48.hc1', '48.hg1'], 'contains': ['192.by1', '192.bz1', '192.ce1', '192.cf1', '192.cg1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2350, -1, 1597, -1], 'generators': [1076429862, 1078860511, 1087421791], 'label': '768.1090187.96.gk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gk1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633786
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1'], 'contains': ['24.cy1', '24.da1', '24.db1', '24.dc1', '24.dd1', '24.dg1', '24.dk1', '24.dl1', '24.dm1', '24.dp1', '24.dx1', '24.dz1', '24.ea1', '24.ed1', '24.ef1', '24.eg1', '24.eh1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2726, -1, 2072, -1], 'generators': [1083180097, 1074724198, 1076429862, 1074660408, 1078860511, 1081574431], 'label': '768.1090187.12.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.bi1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633787
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '96.gl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cs1', '48.ep1', '48.ft1', '48.gy1', '48.hl1', '48.hr1'], 'contains': ['192.bx1', '192.ce1', '192.ck1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [485, -1, 612, -1], 'generators': [1087390721, 1089060216, 1083229185], 'label': '768.1090187.96.gl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gl1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633788
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.gm1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.db1', '48.eu1', '48.ev1', '48.ex1', '48.ey1', '48.fa1', '48.fd2', '48.fv1', '48.fw1', '48.ga1', '48.gf2'], 'contains': ['192.cf1', '192.ch1', '192.ci1', '192.cl1', '192.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1413, -1, 883, -1], 'generators': [1076429862, 1089963103, 1076468417], 'label': '768.1090187.96.gm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gm1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633789
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.gn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.dc1', '48.eu1', '48.fh1', '48.fm1', '48.fo1', '48.gk1', '48.gz1', '48.hf1'], 'contains': ['192.cf1', '192.ch1', '192.cj1', '192.cm1', '192.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [796, -1, 747, -1], 'generators': [1076429862, 1084833144, 1076468417], 'label': '768.1090187.96.gn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gn1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633790
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '96.go1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.dc1', '48.ev1', '48.fi1', '48.fr1', '48.ft1', '48.gl1', '48.hm1', '48.hr1'], 'contains': ['192.cf1', '192.ch1', '192.ck1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [337, -1, 409, -1], 'generators': [1078860511, 1087390721, 1083229185], 'label': '768.1090187.96.go1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.go1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.go1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633791
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '96.gp1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['48.db1', '48.eu1', '48.ew1', '48.fb1', '48.fd1', '48.fu1', '48.gb1', '48.gf1'], 'contains': ['192.cl1', '192.cm1', '192.cp1', '192.cq1', '192.cr1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1835, -1, 1187, -1], 'generators': [1089963103, 1083063654, 1076468417], 'label': '768.1090187.96.gp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.gp1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.gp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633792
    {'ambient': '768.1090187', 'aut_centralizer_order': 576, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1', '32.f1', '64.a1', '64.b1', '64.c1', '64.d1'], 'contains': ['256.a1', '384.a1'], 'core': '384.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [202, -1, 5907, -1], 'generators': [2150763522, 1085750593], 'label': '768.1090187.128.a1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '128.a1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633793
    {'ambient': '768.1090187', 'aut_centralizer_order': 288, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.g1', '32.h1', '64.a1', '64.e1', '64.f1'], 'contains': ['256.a1', '384.b1'], 'core': '384.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [52, -1, 4709, -1], 'generators': [2148207653, 3229953892], 'label': '768.1090187.128.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '128.b1', 'projective_image': '384.20100', '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': '2.1'}
  • id: 59633796
    {'ambient': '768.1090187', 'aut_centralizer_order': 9216, 'aut_label': '192.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '96.a1', '96.d1', '96.e1', '96.f1', '96.g1', '96.h1', '96.i1'], 'contains': ['384.a1', '384.b1'], 'core': '192.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7328, 8785, 5628, 9661], 'generators': [1089018497, 1085750593], 'label': '768.1090187.192.a1', 'mobius_quo': 2, 'mobius_sub': -192, 'normal_closure': '192.a1', 'normal_contained_in': ['48.a1', '96.a1'], 'normal_contains': ['384.a1', '384.b1'], 'normalizer': '1.a1', 'old_label': '192.a1', 'projective_image': '192.1538', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.1538', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633797
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.a1'], 'contains': ['24.cy1', '24.cz1', '24.dd1', '24.de1', '24.de2', '24.df1', '24.dg1', '24.dj1', '24.dp1', '24.dq1', '24.dq2', '24.du1', '24.dy1', '24.ea1', '24.eb1', '24.eb2', '24.ec1', '24.ed1', '24.ee1', '24.ei1'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [4201, -1, 3656, -1], 'generators': [1083180097, 1074660408, 1078860511, 1083063654, 1081574431, 1083229185], 'label': '768.1090187.12.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.bj1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633798
    {'ambient': '768.1090187', 'aut_centralizer_order': 4608, 'aut_label': '192.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '2.a1', 'complements': ['4.g1'], 'conjugacy_class_count': 2, 'contained_in': ['64.b1', '96.a1', '96.j1', '96.k1', '96.l1', '96.m1', '96.n1'], 'contains': ['384.a1', '384.c1'], 'core': '192.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7234, 7968, 5268, 8791], 'generators': [1085750593, 1080629953], 'label': '768.1090187.192.b1', 'mobius_quo': 0, 'mobius_sub': -192, 'normal_closure': '192.b1', 'normal_contained_in': ['48.b1', '96.a1'], 'normal_contains': ['384.a1'], 'normalizer': '1.a1', 'old_label': '192.b1', 'projective_image': '384.20163', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.229', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633799
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': ['4.e1'], 'conjugacy_class_count': 3, 'contained_in': ['64.g1', '96.b1', '96.c1', '96.dj1', '96.ej1', '96.fw2', '96.fy1', '96.fz1', '96.gc1'], 'contains': ['384.e1'], 'core': '192.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6872, 5797, 5860, 7708], 'generators': [1083098168, 1081574431], 'label': '768.1090187.192.c1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.c1', 'normal_contained_in': ['48.c1', '96.b1', '96.c1'], 'normal_contains': ['768.a1'], 'normalizer': '1.a1', 'old_label': '192.c1', 'projective_image': '768.1090187', 'quotient_action_image': '6.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '192.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633800
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.d1', '96.j1', '96.o1', '96.p1', '96.q1', '96.r1', '96.s1', '96.s2', '96.t1', '96.u1', '96.v1', '96.v2', '96.w1'], 'contains': ['384.a1', '384.d1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7385, -1, 5369, -1], 'generators': [1083218598, 1085750593], 'label': '768.1090187.192.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.d1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633801
    {'ambient': '768.1090187', 'aut_centralizer_order': 2048, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.b1', '96.d1', '96.k1', '96.o1', '96.v1', '96.v2', '96.x1', '96.y1', '96.z1', '96.ba1', '96.ba2', '96.bb1', '96.bc1', '96.bd1', '96.be1', '96.bf1', '96.bg1', '96.bh1'], 'contains': ['384.a1', '384.e1', '384.f1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8278, -1, 6001, -1], 'generators': [1085750593, 1078887480], 'label': '768.1090187.192.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.e1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633802
    {'ambient': '768.1090187', 'aut_centralizer_order': 3072, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1', '96.l1', '96.p1', '96.w1', '96.x1', '96.bg1', '96.bi1', '96.bj1', '96.bk1', '96.bl1', '96.bm1'], 'contains': ['384.a1', '384.g1', '384.k1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4163, -1, 1750, -1], 'generators': [1076429862, 1085750593], 'label': '768.1090187.192.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.f1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633803
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.f1', '96.l1', '96.m1', '96.q1', '96.r1', '96.y1', '96.z1', '96.bi1', '96.bj1', '96.bn1', '96.bo1'], 'contains': ['384.a1', '384.h1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5080, -1, 3254, -1], 'generators': [1078860511, 1085750593], 'label': '768.1090187.192.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.g1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633804
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.g1', '96.j1', '96.k1', '96.q1', '96.s1', '96.s2', '96.y1', '96.ba1', '96.ba2', '96.bi1', '96.bk1', '96.bn1', '96.bp1', '96.bq1'], 'contains': ['384.a1', '384.i1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7250, -1, 5302, -1], 'generators': [1085750593, 1074830054], 'label': '768.1090187.192.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.h1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633805
    {'ambient': '768.1090187', 'aut_centralizer_order': 1536, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1', '96.m1', '96.o1', '96.p1', '96.bb1', '96.bl1', '96.bn1', '96.bo1', '96.bq1'], 'contains': ['384.a1', '384.j1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4879, -1, 3288, -1], 'generators': [1085750593, 1087249055], 'label': '768.1090187.192.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.i1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633806
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.c1', '96.h1', '96.n1', '96.t1', '96.bc1', '96.bp1'], 'contains': ['384.a1', '384.l1'], 'core': '384.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9653, -1, 9194, -1], 'generators': [1085750593, 504396399], 'label': '768.1090187.192.j1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '192.j1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633807
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '24.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.d1', '96.i1', '96.n1', '96.u1', '96.be1', '96.bp1'], 'contains': ['384.a1'], 'core': '384.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9781, -1, 9155, -1], 'generators': [1085750593, 506952305], 'label': '768.1090187.192.k1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '192.k1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633808
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 256, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.f1', '6.a1'], 'contains': ['24.c1', '24.da1', '24.df1', '24.dk1', '24.du1', '24.ec1', '24.ef1', '24.ej1'], 'core': '24.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1866, -1, 3622, -1], 'generators': [1076429862, 1083180097, 1074660408, 1084867622, 1078860511, 1081574431], 'label': '768.1090187.12.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.bk1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633809
    {'ambient': '768.1090187', 'aut_centralizer_order': 2304, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.e1', '96.a1', '96.br1', '96.bs1', '96.bt1', '96.bu1'], 'contains': ['384.b1', '384.c1'], 'core': '384.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5148, -1, 3119, -1], 'generators': [1083180097, 1080629953], 'label': '768.1090187.192.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '192.l1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633810
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.c1', '96.d1', '96.br1', '96.bv1', '96.bw1', '96.bx1', '96.by1', '96.by2', '96.bz1', '96.ca1', '96.cb1', '96.ci1', '96.cj1', '96.cl1', '96.cl2', '96.cm1'], 'contains': ['384.b1', '384.d1', '384.e1'], 'core': '384.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7014, -1, 4828, -1], 'generators': [1089018497, 1078887480], 'label': '768.1090187.192.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.m1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633811
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.d1', '96.bs1', '96.cc1', '96.cd1', '96.ce1', '96.cf1', '96.cf2', '96.cg1', '96.ch1', '96.ci1', '96.ck1', '96.cl1', '96.cl2'], 'contains': ['384.b1', '384.d1', '384.f1'], 'core': '384.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [6618, -1, 4405, -1], 'generators': [1089018497, 1087421791], 'label': '768.1090187.192.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.n1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633812
    {'ambient': '768.1090187', 'aut_centralizer_order': 1536, 'aut_label': '192.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.e1', '96.bt1', '96.bv1', '96.cc1', '96.cj1', '96.ck1', '96.cn1', '96.co1', '96.cp1', '96.cq1', '96.cr1'], 'contains': ['384.b1', '384.g1', '384.j1'], 'core': '384.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2873, -1, 1545, -1], 'generators': [1076429862, 1087380134], 'label': '768.1090187.192.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.o1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633813
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '192.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.f1', '96.bt1', '96.bu1', '96.bw1', '96.bx1', '96.cd1', '96.ce1', '96.cn1', '96.co1', '96.cs1', '96.ct1'], 'contains': ['384.b1', '384.h1'], 'core': '384.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [4175, -1, 2410, -1], 'generators': [1078991590, 1084818534], 'label': '768.1090187.192.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.p1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633814
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.g1', '96.br1', '96.bs1', '96.bw1', '96.by1', '96.by2', '96.cd1', '96.cf1', '96.cf2', '96.cn1', '96.cp1', '96.cs1', '96.cu1'], 'contains': ['384.b1', '384.i1'], 'core': '384.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5243, -1, 3696, -1], 'generators': [1089963103, 1074698975], 'label': '768.1090187.192.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.q1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633815
    {'ambient': '768.1090187', 'aut_centralizer_order': 1536, 'aut_label': '192.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.e1', '96.bu1', '96.bz1', '96.cc1', '96.ci1', '96.cq1', '96.cs1', '96.ct1', '96.cu1'], 'contains': ['384.b1', '384.j1', '384.k1'], 'core': '384.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3844, -1, 2088, -1], 'generators': [1087380134, 1083063654], 'label': '768.1090187.192.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.r1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633816
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '192.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.f1', '96.h1', '96.ca1', '96.cg1'], 'contains': ['384.b1', '384.l1'], 'core': '384.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [9258, -1, 8682, -1], 'generators': [1089018497, 658250892], 'label': '768.1090187.192.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1', 'old_label': '192.s1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633817
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.t1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.j1', '96.br1', '96.bs1', '96.cv1', '96.cw1', '96.cx1', '96.cy1', '96.cz1', '96.cz2', '96.da1', '96.da2', '96.db1', '96.dc1'], 'contains': ['384.c1', '384.d1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5105, -1, 3526, -1], 'generators': [1083180097, 1074830054], 'label': '768.1090187.192.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.t1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633818
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.k1', '96.br1', '96.cv1', '96.cz1', '96.cz2', '96.dd1', '96.de1', '96.de2', '96.df1', '96.dg1', '96.dh1', '96.di1', '96.dj1', '96.dj2'], 'contains': ['384.c1', '384.e1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6568, -1, 4371, -1], 'generators': [1080629953, 1078887480], 'label': '768.1090187.192.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.u1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633819
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 16, 'centralizer': '96.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.b1', '12.a1', '16.c1', '16.d1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1848, 1544, 3953, 6838], 'generators': [1076429862, 2150763522, 1074660408, 1084867622, 3229953892, 1085750593, 1081574431], 'label': '768.1090187.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.b1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '192.1538', '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': '96.227'}
  • id: 59633820
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.d1'], 'contains': ['24.dh1', '24.di1', '24.dm1', '24.dn1', '24.do1', '24.ek1', '24.en1'], 'core': '384.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [8382, -1, 5673, -1], 'generators': [1076429862, 1078860511, 1080655224, 1076479078, 658250892, 1080656934], 'label': '768.1090187.12.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '12.bl1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633821
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.v1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.k1', '96.bs1', '96.cw1', '96.da1', '96.da2', '96.dd1', '96.de1', '96.de2', '96.dk1', '96.dl1', '96.dm1'], 'contains': ['384.c1', '384.f1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5093, -1, 3729, -1], 'generators': [1080629953, 1087421791], 'label': '768.1090187.192.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.v1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.v1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633822
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '192.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.l1', '96.bt1', '96.cx1', '96.db1', '96.df1', '96.di1', '96.dk1', '96.dm1', '96.dn1', '96.do1', '96.dp1'], 'contains': ['384.c1', '384.g1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2752, -1, 1390, -1], 'generators': [1076429862, 1078991590], 'label': '768.1090187.192.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.w1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633823
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '192.x1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['96.m1', '96.bt1', '96.bu1', '96.cv1', '96.cw1', '96.cx1', '96.cy1', '96.dg1', '96.dl1', '96.dn1', '96.dq1'], 'contains': ['384.c1', '384.h1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3657, -1, 2206, -1], 'generators': [1083180097, 1078860511], 'label': '768.1090187.192.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.x1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.x1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633824
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '192.y1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.l1', '96.bu1', '96.cy1', '96.dc1', '96.dd1', '96.dh1', '96.dk1', '96.do1', '96.dq1'], 'contains': ['384.c1', '384.h1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3888, -1, 1970, -1], 'generators': [1083063654, 1078991590], 'label': '768.1090187.192.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.y1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633825
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.z1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.o1', '96.ci1', '96.cj1', '96.cv1', '96.dr1', '96.ds1', '96.ds2', '96.dt1', '96.du1', '96.ec2', '96.ec4', '96.ed1', '96.ef1', '96.ej1', '96.ej2', '96.es1', '96.es2', '96.et1'], 'contains': ['384.d1', '384.e1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4473, -1, 3662, -1], 'generators': [1078887480, 1087249055], 'label': '768.1090187.192.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.z1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633826
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.ba1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.o1', '96.ci1', '96.ck1', '96.cw1', '96.dr1', '96.dv1', '96.dv2', '96.dw1', '96.dx1', '96.ec1', '96.ec2', '96.ec3', '96.ec4', '96.ek1', '96.ek2', '96.es1', '96.es2', '96.eu1'], 'contains': ['384.d1', '384.f1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4334, -1, 3391, -1], 'generators': [1087421791, 1089936056], 'label': '768.1090187.192.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.ba1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633827
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.bb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.p1', '96.bv1', '96.cc1', '96.cx1', '96.du1', '96.dx1', '96.dy1', '96.dy2', '96.dz1', '96.ed1', '96.ek1', '96.et1', '96.eu1', '96.ev1', '96.ew1'], 'contains': ['384.d1', '384.g1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2311, -1, 2003, -1], 'generators': [1076429862, 1084856961], 'label': '768.1090187.192.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bb1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633828
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '192.bc1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['96.q1', '96.bw1', '96.cd1', '96.cv1', '96.cw1', '96.db1', '96.dc1', '96.ds1', '96.ds2', '96.dt1', '96.dv1', '96.dv2', '96.dw1', '96.dy1', '96.dy2', '96.ea1', '96.ea2', '96.ee1', '96.ee2', '96.ee3', '96.ee4', '96.el1', '96.el2', '96.el3', '96.el4', '96.eo1', '96.ep1', '96.eq1', '96.er1'], 'contains': ['384.d1', '384.h1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3953, -1, 3021, -1], 'generators': [1077385976, 1084818534], 'label': '768.1090187.192.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bc1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633829
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.bd1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.r1', '96.bx1', '96.ce1', '96.cx1', '96.cy1', '96.dt1', '96.dw1', '96.ee2', '96.ee4', '96.el2', '96.el4', '96.ep1', '96.er1'], 'contains': ['384.d1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4602, -1, 3056, -1], 'generators': [1076468417, 1084818534], 'label': '768.1090187.192.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bd1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633830
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.be1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.s1', '96.by1', '96.cf1', '96.cz1', '96.da1', '96.ds2', '96.dv2', '96.dz1', '96.eb1', '96.ee4', '96.el4', '96.eo1', '96.eq1'], 'contains': ['384.d1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4956, -1, 3594, -1], 'generators': [1089963103, 1089985272], 'label': '768.1090187.192.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.be1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633831
    {'ambient': '768.1090187', 'aut_centralizer_order': 4, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '64.261', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.d1'], 'contains': ['24.dh1', '24.di1', '24.dq2', '24.dr1', '24.dt1', '24.ek1', '24.eo1'], 'core': '96.c1', 'coset_action_label': None, 'count': 72, 'diagramx': [8425, -1, 5776, -1], 'generators': [1083098168, 1087298271, 1081574431, 1076479078, 658250892, 1077411137], 'label': '768.1090187.12.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '12.bm1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633832
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.be2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.s2', '96.by2', '96.cf2', '96.cz2', '96.da2', '96.ds1', '96.dv1', '96.dz1', '96.eb1', '96.ee2', '96.el2', '96.eo1', '96.eq1'], 'contains': ['384.d1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4916, -1, 3628, -1], 'generators': [1089963103, 1087429350], 'label': '768.1090187.192.be2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.be2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.be2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633833
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.bf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.p1', '96.bz1', '96.cc1', '96.cy1', '96.dr1', '96.ea1', '96.ea2', '96.eb1', '96.ef1', '96.ek2', '96.es1', '96.es2', '96.ev1'], 'contains': ['384.d1', '384.j1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3021, -1, 2443, -1], 'generators': [1084856961, 1083063654], 'label': '768.1090187.192.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bf1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633834
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '192.bg1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.t1', '96.ca1', '96.cg1', '96.eh1', '96.em1'], 'contains': ['384.d1', '384.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9324, -1, 8826, -1], 'generators': [1083218598, 658250892], 'label': '768.1090187.192.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1', 'old_label': '192.bg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633835
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.c1', '96.v1', '96.cl1', '96.cz1', '96.ec3', '96.ee1', '96.ee2', '96.eg1', '96.ej2', '96.es2', '96.et1', '96.ex1', '96.ey1'], 'contains': ['384.d1', '384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6784, -1, 5065, -1], 'generators': [1078887480, 1079040678], 'label': '768.1090187.192.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.bh1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633836
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.bh2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.v2', '96.cl2', '96.cm1', '96.cz2', '96.ec1', '96.ee3', '96.ee4', '96.eh1', '96.ei1', '96.ej1', '96.es1', '96.et1', '96.ex1', '96.ey1'], 'contains': ['384.d1', '384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6953, -1, 5335, -1], 'generators': [1078909599, 1078887480], 'label': '768.1090187.192.bh2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.bh2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bh2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633837
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.bi1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.v1', '96.cl1', '96.da1', '96.ec4', '96.el1', '96.el2', '96.es1', '96.eu1', '96.ez1'], 'contains': ['384.d1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5040, -1, 3797, -1], 'generators': [1081596600, 1087421791], 'label': '768.1090187.192.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bi1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633838
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.bi2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.v2', '96.cl2', '96.da2', '96.ec2', '96.el3', '96.el4', '96.em1', '96.en1', '96.es2', '96.eu1', '96.ez1'], 'contains': ['384.d1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5556, -1, 4741, -1], 'generators': [1087421791, 1079040678], 'label': '768.1090187.192.bi2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.bi2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bi2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633839
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.bj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.w1', '96.cj1', '96.ck1', '96.db1', '96.ed1', '96.ek2', '96.eo1', '96.ep1', '96.et1', '96.eu1', '96.ev1', '96.ew1', '96.ex1', '96.ez1'], 'contains': ['384.d1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3114, -1, 2240, -1], 'generators': [1076429862, 1085774520], 'label': '768.1090187.192.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bj1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633840
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.bk1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.w1', '96.ci1', '96.dc1', '96.ef1', '96.ek1', '96.eq1', '96.er1', '96.es1', '96.es2', '96.ev1', '96.ey1', '96.ez1'], 'contains': ['384.d1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3901, -1, 2680, -1], 'generators': [1085774520, 1083063654], 'label': '768.1090187.192.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bk1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633841
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.bl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bg1', '96.ci1', '96.dd1', '96.dr1', '96.es1', '96.es2', '96.fa1', '96.fa2', '96.fb1', '96.fc1', '96.fs1', '96.ft1', '96.fw1', '96.fw2'], 'contains': ['384.e1', '384.f1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4277, -1, 3492, -1], 'generators': [1083063654, 1078887480], 'label': '768.1090187.192.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bl1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633842
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1'], 'contains': ['24.dr2', '24.ds1', '24.dv1', '24.dw1', '24.dy1', '24.el1', '24.em1', '24.ep1'], 'core': '96.c1', 'coset_action_label': None, 'count': 36, 'diagramx': [8093, -1, 6864, -1], 'generators': [1074660408, 1083063654, 1081574431, 1083229185, 668673292, 1087249055], 'label': '768.1090187.12.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.bn1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633843
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.bm1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.b1', '96.cl1', '96.de1', '96.ec1', '96.ec2', '96.fd1', '96.fd2', '96.fe1', '96.fi1', '96.ft1', '96.fw1'], 'contains': ['384.e1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6679, -1, 5166, -1], 'generators': [1074724198, 1078887480], 'label': '768.1090187.192.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.bm1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633844
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.bm2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.bh1', '96.cl2', '96.de2', '96.ec3', '96.ec4', '96.fd3', '96.fd4', '96.ff1', '96.fg1', '96.fh1', '96.fi1', '96.ft1', '96.fw2'], 'contains': ['384.e1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7263, -1, 5403, -1], 'generators': [1074855263, 1078887480], 'label': '768.1090187.192.bm2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.bm2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bm2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633845
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.bn1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.x1', '96.bv1', '96.df1', '96.ed1', '96.ex1', '96.fc1', '96.fi1', '96.fj1', '96.fk1', '96.fl1', '96.fx1', '96.gc1'], 'contains': ['384.e1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4891, -1, 3560, -1], 'generators': [1081574431, 1077347359], 'label': '768.1090187.192.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.bn1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633846
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.bo1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['96.y1', '96.bw1', '96.cv1', '96.dd1', '96.di1', '96.ds1', '96.ds2', '96.dt1', '96.ee2', '96.ee4', '96.fa1', '96.fa2', '96.fb1', '96.fd2', '96.fd4', '96.fj1', '96.fm1', '96.fn1', '96.fu1', '96.fv1', '96.fy1', '96.fy2'], 'contains': ['384.e1', '384.h1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4615, -1, 3357, -1], 'generators': [1078860511, 1078887480], 'label': '768.1090187.192.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bo1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633847
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.bp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.z1', '96.bx1', '96.df1', '96.dg1', '96.dh1', '96.dt1', '96.ee1', '96.ee3', '96.fb1', '96.fd1', '96.fd3', '96.fv1', '96.fy1', '96.fy2'], 'contains': ['384.e1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5543, -1, 4211, -1], 'generators': [1081547512, 1078887480], 'label': '768.1090187.192.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bp1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633848
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.bq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.ba1', '96.by1', '96.cz1', '96.de1', '96.dj1', '96.ds1', '96.ee3', '96.fa2', '96.fd3', '96.fk1', '96.fo1', '96.fp1', '96.fu1', '96.fy2'], 'contains': ['384.e1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6468, -1, 4644, -1], 'generators': [1087429350, 1078887480], 'label': '768.1090187.192.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bq1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633849
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.bq2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.ba2', '96.by2', '96.cz2', '96.de2', '96.dj2', '96.ds2', '96.ee1', '96.fa1', '96.fd1', '96.fk1', '96.fo1', '96.fp1', '96.fu1', '96.fy1'], 'contains': ['384.e1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6581, -1, 4794, -1], 'generators': [1087298271, 1078887480], 'label': '768.1090187.192.bq2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bq2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bq2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633850
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.br1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bb1', '96.bv1', '96.bz1', '96.dg1', '96.dr1', '96.du1', '96.ec1', '96.ec3', '96.ej1', '96.ej2', '96.fm1', '96.fo1', '96.fq1'], 'contains': ['384.e1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6593, -1, 4678, -1], 'generators': [1078887480, 1089936056], 'label': '768.1090187.192.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.br1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.br1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633851
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.bs1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.x1', '96.bz1', '96.dh1', '96.ef1', '96.ey1', '96.fn1', '96.fp1', '96.fr1', '96.fs1', '96.fw1', '96.fw2'], 'contains': ['384.e1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6606, -1, 4337, -1], 'generators': [1084833144, 1078887480], 'label': '768.1090187.192.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.bs1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633852
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.bt1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bc1', '96.ca1', '96.eg1', '96.eh1', '96.fe1', '96.ff1', '96.fl1', '96.fq1', '96.fr1', '96.fz1', '96.ga1'], 'contains': ['384.e1', '384.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9120, -1, 8634, -1], 'generators': [504396399, 1078887480], 'label': '768.1090187.192.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '192.bt1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bt1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633853
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.226', 'aut_weyl_index': 192, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.g1', '6.f1'], 'contains': ['24.c1', '24.dv1', '24.dw1', '24.em1', '24.eq1'], 'core': '24.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [4688, -1, 6357, -1], 'generators': [1076429862, 1074660408, 1084867622, 1081574431, 668673292, 1087249055], 'label': '768.1090187.12.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.bo1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633854
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.bu1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bd1', '96.cb1', '96.eg1', '96.ei1', '96.fe1', '96.fg1', '96.fl1', '96.fq1', '96.fr1', '96.fz1', '96.gb1'], 'contains': ['384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8996, -1, 8427, -1], 'generators': [1078887480, 514417711], 'label': '768.1090187.192.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.p1', 'old_label': '192.bu1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633855
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.bv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.bg1', '96.cj1', '96.di1', '96.du1', '96.et1', '96.fs1', '96.ft1', '96.fu1', '96.fv1', '96.fx1', '96.gc1'], 'contains': ['384.e1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3391, -1, 3153, -1], 'generators': [1076429862, 1081574431], 'label': '768.1090187.192.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bv1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633856
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.bw1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bh1', '96.cm1', '96.dj2', '96.ej2', '96.fw1', '96.fy2', '96.ga1', '96.gb1', '96.gc1'], 'contains': ['384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7403, -1, 5939, -1], 'generators': [1083098168, 1080656934], 'label': '768.1090187.192.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.bw1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633857
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '192.bx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.x1', '96.cc1', '96.dk1', '96.ek1', '96.ek2', '96.ez1', '96.fc1', '96.fs1', '96.ft1', '96.gd1', '96.gd2', '96.ge1', '96.gl1'], 'contains': ['384.f1', '384.g1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1706, -1, 1665, -1], 'generators': [1076429862, 1087290726], 'label': '768.1090187.192.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.bx1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633858
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.by1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['96.y1', '96.cd1', '96.cw1', '96.dd1', '96.dm1', '96.dv1', '96.dv2', '96.dw1', '96.el2', '96.el4', '96.fa1', '96.fa2', '96.fb1', '96.fd1', '96.fd2', '96.fd3', '96.fd4', '96.gd1', '96.gd2', '96.gf1', '96.gj1', '96.gk1'], 'contains': ['384.f1', '384.h1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4188, -1, 3187, -1], 'generators': [1081547512, 1087421791], 'label': '768.1090187.192.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.by1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.by1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633859
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.bz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.z1', '96.ce1', '96.dk1', '96.dl1', '96.dw1', '96.el1', '96.el3', '96.fb1', '96.fd2', '96.fd4', '96.gg1', '96.gk1'], 'contains': ['384.f1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4904, -1, 3459, -1], 'generators': [1078860511, 1087421791], 'label': '768.1090187.192.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.bz1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633860
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.ca1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.ba1', '96.cf1', '96.da1', '96.de1', '96.dv1', '96.el3', '96.fa1', '96.fd4', '96.ge1', '96.gh1', '96.gi1', '96.gj1'], 'contains': ['384.f1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5209, -1, 4004, -1], 'generators': [1089985272, 1087421791], 'label': '768.1090187.192.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.ca1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ca1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633861
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.ca2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.ba2', '96.cf2', '96.da2', '96.de2', '96.dv2', '96.el1', '96.fa2', '96.fd2', '96.ge1', '96.gi1', '96.gj1'], 'contains': ['384.f1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4968, -1, 3763, -1], 'generators': [1087421791, 1087429350], 'label': '768.1090187.192.ca2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.ca2', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ca2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633862
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.cb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.bb1', '96.cc1', '96.dl1', '96.dr1', '96.dx1', '96.ec2', '96.ec4', '96.gf1', '96.gi1'], 'contains': ['384.f1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3914, -1, 3220, -1], 'generators': [1087421791, 1087249055], 'label': '768.1090187.192.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cb1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633863
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.cc1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bc1', '96.cg1', '96.em1', '96.ff1', '96.gg1', '96.gh1'], 'contains': ['384.f1', '384.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9377, -1, 8586, -1], 'generators': [504396399, 1089060216], 'label': '768.1090187.192.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '192.cc1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633864
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 32, 'centralizer': '96.a1', 'complements': ['48.gg1', '48.dv1', '48.x1', '48.u1', '48.dw1', '48.bn1', '48.f1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.h1', '8.i1'], 'contains': ['48.c1', '64.g1', '64.h1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [185, 2420, 3931, 4642], 'generators': [1076429862, 1074660408, 2150763522, 1084867622, 1081574431], 'label': '768.1090187.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['48.c1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '768.1090187', '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': '96.227'}
  • id: 59633865
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.cd1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bf1', '96.ch1', '96.en1', '96.fh1', '96.gg1', '96.gh1'], 'contains': ['384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9312, -1, 7198, -1], 'generators': [1078885734, 508576689], 'label': '768.1090187.192.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '192.cd1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633866
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '192.ce1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.bg1', '96.ck1', '96.dm1', '96.dx1', '96.eu1', '96.fc1', '96.fi1', '96.ft1', '96.gj1', '96.gk1', '96.gl1'], 'contains': ['384.f1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3351, -1, 2511, -1], 'generators': [1076429862, 1087421791], 'label': '768.1090187.192.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.ce1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ce1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633867
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.cf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.bi1', '96.cn1', '96.cx1', '96.df1', '96.dk1', '96.dy2', '96.eo1', '96.ep1', '96.fj1', '96.fu1', '96.fv1', '96.gd1', '96.gj1', '96.gk1', '96.gm1', '96.gn1', '96.go1'], 'contains': ['384.g1', '384.h1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2505, -1, 1484, -1], 'generators': [1076429862, 1076468417], 'label': '768.1090187.192.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cf1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633868
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '192.cg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bj1', '96.co1', '96.dn1', '96.do1', '96.dp1', '96.dy1', '96.ep1', '96.fj1', '96.fv1', '96.gd2', '96.gk1'], 'contains': ['384.g1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1513, -1, 950, -1], 'generators': [1076429862, 1078860511], 'label': '768.1090187.192.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cg1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633869
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.ch1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.bk1', '96.cp1', '96.db1', '96.di1', '96.dm1', '96.dy1', '96.dz1', '96.eo1', '96.fj1', '96.fk1', '96.fu1', '96.gd2', '96.ge1', '96.gj1', '96.gm1', '96.gn1', '96.go1'], 'contains': ['384.g1', '384.i1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2859, -1, 1699, -1], 'generators': [1076429862, 1077385976], 'label': '768.1090187.192.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.ch1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ch1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633870
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '192.ci1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bl1', '96.cq1', '96.cr1', '96.dn1', '96.du1', '96.dx1', '96.ed1', '96.ek2', '96.gm1'], 'contains': ['384.g1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1413, -1, 1119, -1], 'generators': [1076429862, 1087249055], 'label': '768.1090187.192.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.ci1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ci1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633871
    {'ambient': '768.1090187', 'aut_centralizer_order': 1536, 'aut_label': '192.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bm1', '96.cq1', '96.do1', '96.ev1', '96.fc1', '96.fs1', '96.gn1'], 'contains': ['384.g1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1056, -1, 916, -1], 'generators': [1076429862, 1084833144], 'label': '768.1090187.192.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cj1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633872
    {'ambient': '768.1090187', 'aut_centralizer_order': 1536, 'aut_label': '192.ck1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1', '96.bm1', '96.cr1', '96.dp1', '96.ew1', '96.fx1', '96.gl1', '96.go1'], 'contains': ['384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [485, -1, 409, -1], 'generators': [1087390721, 1083229185], 'label': '768.1090187.192.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '192.ck1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.ck1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633873
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.cl1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['96.bn1', '96.cn1', '96.cs1', '96.cx1', '96.cy1', '96.dg1', '96.dl1', '96.ds1', '96.ds2', '96.dt1', '96.dv1', '96.dv2', '96.dw1', '96.dy1', '96.ea1', '96.fm1', '96.gf1', '96.gm1', '96.gp1'], 'contains': ['384.h1', '384.i1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3285, -1, 2477, -1], 'generators': [1074830054, 1084818534], 'label': '768.1090187.192.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cl1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633874
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '192.cm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.bi1', '96.cs1', '96.cy1', '96.dh1', '96.dk1', '96.ea2', '96.eq1', '96.er1', '96.fa1', '96.fa2', '96.fb1', '96.fn1', '96.gd2', '96.gn1', '96.gp1'], 'contains': ['384.h1', '384.i1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3102, -1, 2054, -1], 'generators': [1083063654, 1076468417], 'label': '768.1090187.192.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cm1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633875
    {'ambient': '768.1090187', 'aut_centralizer_order': 6, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 96, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1'], 'contains': ['32.a1', '32.b1', '32.c1', '32.d1', '48.f1'], 'core': '96.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4795, -1, 5332, -1], 'generators': [2148207653, 1083180097, 660749132, 1085750593, 3234148260], 'label': '768.1090187.16.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '16.b1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 59633876
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '192.cn1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['96.bo1', '96.co1', '96.ct1', '96.dn1', '96.dq1', '96.dt1', '96.dw1', '96.dy2', '96.ea2', '96.fm1', '96.gf1'], 'contains': ['384.h1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1659, -1, 1936, -1], 'generators': [1078860511, 1084818534], 'label': '768.1090187.192.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cn1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633877
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '192.co1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bj1', '96.ct1', '96.do1', '96.dq1', '96.ea1', '96.er1', '96.fb1', '96.fn1', '96.gd1'], 'contains': ['384.h1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1646, -1, 1356, -1], 'generators': [1078860511, 1083063654], 'label': '768.1090187.192.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.co1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.co1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633878
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '192.cp1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['96.bq1', '96.cp1', '96.cu1', '96.cv1', '96.cw1', '96.ds1', '96.ds2', '96.dv1', '96.dv2', '96.dy2', '96.dz1', '96.ea2', '96.eb1', '96.fm1', '96.fo1', '96.gf1', '96.gi1', '96.gm1', '96.gp1'], 'contains': ['384.i1', '384.j1'], 'core': '768.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3669, -1, 2646, -1], 'generators': [1089963103, 1074830054], 'label': '768.1090187.192.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cp1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633879
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '192.cq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.bk1', '96.cu1', '96.dc1', '96.dd1', '96.ea1', '96.eb1', '96.eq1', '96.fa1', '96.fa2', '96.fn1', '96.fp1', '96.gd1', '96.ge1', '96.gn1', '96.gp1'], 'contains': ['384.i1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3507, -1, 2274, -1], 'generators': [1083063654, 1077385976], 'label': '768.1090187.192.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cq1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633880
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '192.cr1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bl1', '96.cq1', '96.dq1', '96.dr1', '96.ef1', '96.ek1', '96.gp1'], 'contains': ['384.j1', '384.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1611, -1, 1424, -1], 'generators': [1083063654, 1087249055], 'label': '768.1090187.192.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.cr1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.cr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633881
    {'ambient': '768.1090187', 'aut_centralizer_order': 576, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9216, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.g1', '64.h1', '128.a1', '128.b1', '128.c1', '128.d1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [73, -1, 4709, -1], 'generators': [2150763522], 'label': '768.1090187.256.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '256.a1', 'projective_image': '768.1090187', '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': '2.1'}
  • id: 59633882
    {'ambient': '768.1090187', 'aut_centralizer_order': 18432, 'aut_label': '384.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['128.a1', '192.a1', '192.b1', '192.d1', '192.e1', '192.f1', '192.g1', '192.h1', '192.i1', '192.j1', '192.k1'], 'contains': ['768.a1'], 'core': '384.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7243, 8068, 5335, 8897], 'generators': [1085750593], 'label': '768.1090187.384.a1', 'mobius_quo': -1, 'mobius_sub': 768, 'normal_closure': '384.a1', 'normal_contained_in': ['96.b1', '192.a1', '192.b1'], 'normal_contains': ['768.a1'], 'normalizer': '1.a1', 'old_label': '384.a1', 'projective_image': '384.20163', 'quotient_action_image': '1.1', 'quotient_action_kernel': '384.20163', 'quotient_action_kernel_order': 384, 'quotient_fusion': None, 'short_label': '384.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633883
    {'ambient': '768.1090187', 'aut_centralizer_order': 9216, 'aut_label': '384.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '1.a1', 'complements': ['2.d1'], 'conjugacy_class_count': 2, 'contained_in': ['128.b1', '192.a1', '192.l1', '192.m1', '192.n1', '192.o1', '192.p1', '192.q1', '192.r1', '192.s1'], 'contains': ['768.a1'], 'core': '384.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5095, 8785, 3696, 9661], 'generators': [1089018497], 'label': '768.1090187.384.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '384.b1', 'normal_contained_in': ['96.c1', '192.a1'], 'normal_contains': ['768.a1'], 'normalizer': '1.a1', 'old_label': '384.b1', 'projective_image': '384.20100', 'quotient_action_image': '1.1', 'quotient_action_kernel': '384.20100', 'quotient_action_kernel_order': 384, 'quotient_fusion': None, 'short_label': '384.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633884
    {'ambient': '768.1090187', 'aut_centralizer_order': 4608, 'aut_label': '384.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.c1', '192.b1', '192.l1', '192.t1', '192.u1', '192.v1', '192.w1', '192.x1', '192.y1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4960, -1, 3322, -1], 'generators': [1080629953], 'label': '768.1090187.384.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '384.c1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633885
    {'ambient': '768.1090187', 'aut_centralizer_order': 1024, 'aut_label': '384.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['192.d1', '192.m1', '192.n1', '192.t1', '192.z1', '192.ba1', '192.bb1', '192.bc1', '192.bd1', '192.be1', '192.be2', '192.bf1', '192.bg1', '192.bh1', '192.bh2', '192.bi1', '192.bi2', '192.bj1', '192.bk1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4971, -1, 3628, -1], 'generators': [1083218598], 'label': '768.1090187.384.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '384.d1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633886
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '8.c1', '8.e1', '8.f1'], 'contains': ['32.e1', '32.g1', '48.a1', '64.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1592, -1, 5122, -1], 'generators': [1083098168, 3229953892, 1085750593, 1081574431, 2154597435], 'label': '768.1090187.16.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '16.c1', 'projective_image': '192.1538', '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': '24.12'}
  • id: 59633887
    {'ambient': '768.1090187', 'aut_centralizer_order': 2048, 'aut_label': '384.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['192.c1', '192.e1', '192.m1', '192.u1', '192.z1', '192.bh1', '192.bh2', '192.bl1', '192.bm1', '192.bm2', '192.bn1', '192.bo1', '192.bp1', '192.bq1', '192.bq2', '192.br1', '192.bs1', '192.bt1', '192.bu1', '192.bv1', '192.bw1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6590, -1, 4678, -1], 'generators': [1078887480], 'label': '768.1090187.384.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '384.e1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633888
    {'ambient': '768.1090187', 'aut_centralizer_order': 2048, 'aut_label': '384.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['192.e1', '192.n1', '192.v1', '192.ba1', '192.bi1', '192.bi2', '192.bl1', '192.bm1', '192.bm2', '192.bx1', '192.by1', '192.bz1', '192.ca1', '192.ca2', '192.cb1', '192.cc1', '192.cd1', '192.ce1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5106, -1, 3763, -1], 'generators': [1087421791], 'label': '768.1090187.384.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '384.f1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633889
    {'ambient': '768.1090187', 'aut_centralizer_order': 3072, 'aut_label': '384.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.f1', '192.o1', '192.w1', '192.bb1', '192.bj1', '192.bn1', '192.bv1', '192.bx1', '192.ce1', '192.cf1', '192.cg1', '192.ch1', '192.ci1', '192.cj1', '192.ck1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2775, -1, 1682, -1], 'generators': [1076429862], 'label': '768.1090187.384.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '384.g1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633890
    {'ambient': '768.1090187', 'aut_centralizer_order': 768, 'aut_label': '384.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.g1', '192.p1', '192.w1', '192.x1', '192.y1', '192.bc1', '192.bd1', '192.bo1', '192.bp1', '192.by1', '192.bz1', '192.cf1', '192.cg1', '192.cl1', '192.cm1', '192.cn1', '192.co1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3900, -1, 2420, -1], 'generators': [1078860511], 'label': '768.1090187.384.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '384.h1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633891
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '384.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['192.h1', '192.q1', '192.t1', '192.u1', '192.v1', '192.bc1', '192.be1', '192.be2', '192.bo1', '192.bq1', '192.bq2', '192.by1', '192.ca1', '192.ca2', '192.cf1', '192.ch1', '192.cl1', '192.cm1', '192.cp1', '192.cq1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4907, -1, 3594, -1], 'generators': [1074830054], 'label': '768.1090187.384.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '384.i1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633892
    {'ambient': '768.1090187', 'aut_centralizer_order': 1536, 'aut_label': '384.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.i1', '192.o1', '192.r1', '192.x1', '192.z1', '192.ba1', '192.bb1', '192.bf1', '192.br1', '192.cb1', '192.ci1', '192.cl1', '192.cn1', '192.cp1', '192.cr1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3661, -1, 2460, -1], 'generators': [1087249055], 'label': '768.1090187.384.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '384.j1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633893
    {'ambient': '768.1090187', 'aut_centralizer_order': 3072, 'aut_label': '384.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.f1', '192.r1', '192.y1', '192.bf1', '192.bk1', '192.bl1', '192.bs1', '192.bx1', '192.cj1', '192.cm1', '192.co1', '192.cq1', '192.cr1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3790, -1, 2071, -1], 'generators': [1083063654], 'label': '768.1090187.384.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '384.k1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633894
    {'ambient': '768.1090187', 'aut_centralizer_order': 384, 'aut_label': '384.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 18432, 'centralizer': '24.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.d1', '192.j1', '192.s1', '192.bg1', '192.bt1', '192.cc1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9258, -1, 8634, -1], 'generators': [504396399], 'label': '768.1090187.384.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1', 'old_label': '384.l1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633895
    {'ambient': '768.1090187', 'aut_centralizer_order': None, 'aut_label': '768.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['256.a1', '384.a1', '384.b1', '384.c1', '384.d1', '384.e1', '384.f1', '384.g1', '384.h1', '384.i1', '384.j1', '384.k1', '384.l1'], 'contains': [], 'core': '768.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4960, 8426, 3628, 9279], 'generators': [], 'label': '768.1090187.768.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '768.a1', 'normal_contained_in': ['192.c1', '384.a1', '384.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '768.a1', 'projective_image': '768.1090187', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633896
    {'ambient': '768.1090187', 'aut_centralizer_order': 48, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.d1'], 'contains': ['32.f1', '32.h1', '48.t1', '64.a1'], 'core': '192.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [68, -1, 335, -1], 'generators': [3229953892, 2160806949, 1085750593, 1087390721, 1083229185], 'label': '768.1090187.16.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '16.d1', 'projective_image': '192.1538', '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': '12.3'}
  • id: 59633897
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '8.c1', '8.g1'], 'contains': ['32.e1', '32.i1', '48.b1', '64.b1'], 'core': '48.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1901, -1, 5008, -1], 'generators': [1083098168, 1085750593, 1081574431, 3234148260, 2154597435], 'label': '768.1090187.16.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '16.e1', 'projective_image': '384.20163', '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': '24.12'}
  • id: 59633898
    {'ambient': '768.1090187', 'aut_centralizer_order': 24, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '8.d1'], 'contains': ['32.f1', '32.j1', '48.bh1', '64.b1'], 'core': '192.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [100, -1, 251, -1], 'generators': [2160806949, 1085750593, 1087390721, 3234148260, 1083229185], 'label': '768.1090187.16.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '16.f1', 'projective_image': '384.20163', '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': '12.3'}
  • id: 59633899
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 16, 'centralizer': '96.a1', 'complements': ['192.s1', '192.bg1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.a1', '8.h1', '12.b1', '16.e1', '16.f1'], 'core': '4.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1908, 7012, 3853, 4621], 'generators': [1076429862, 2150763522, 1074660408, 1084867622, 1085750593, 1081574431, 3234148260], 'label': '768.1090187.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.a1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '384.20163', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 59633900
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.c1', '8.e1', '8.g1'], 'contains': ['32.e1', '32.k1', '48.cu1', '64.c1'], 'core': '96.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [4714, -1, 5270, -1], 'generators': [1083098168, 1085750593, 1081574431, 504396399, 2154990594], 'label': '768.1090187.16.g1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '16.g1', 'projective_image': '384.20163', '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': '48.48'}
  • id: 59633901
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.d1', '8.f1', '8.g1'], 'contains': ['32.e1', '48.cx1', '64.d1'], 'core': '96.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [4879, -1, 5416, -1], 'generators': [1083098168, 1085750593, 506952305, 1081574431, 2154990594], 'label': '768.1090187.16.h1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '16.h1', 'projective_image': '384.20163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 59633902
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.f1', '8.c1'], 'contains': ['32.g1', '32.i1', '48.dk1', '64.e1'], 'core': '96.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [135, -1, 4743, -1], 'generators': [1083180097, 1083098168, 1081574431, 3234148260, 2154597435], 'label': '768.1090187.16.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '16.i1', 'projective_image': '384.20100', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 59633903
    {'ambient': '768.1090187', 'aut_centralizer_order': 12, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '8.d1'], 'contains': ['32.h1', '32.j1', '48.dm1', '64.e1'], 'core': '384.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [41, -1, 131, -1], 'generators': [1083180097, 2160806949, 1087390721, 3234148260, 1083229185], 'label': '768.1090187.16.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1', 'old_label': '16.j1', 'projective_image': '384.20100', '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': '12.3'}
  • id: 59633904
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 384, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.g1', '8.e1'], 'contains': ['32.g1', '32.k1', '48.em1', '64.f1'], 'core': '96.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [1614, -1, 5182, -1], 'generators': [1083098168, 3229953892, 1081574431, 670833676, 2154597435], 'label': '768.1090187.16.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '16.k1', 'projective_image': '384.20100', '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': '24.12'}
  • id: 59633905
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 384, 'centralizer': '6.a1', 'complements': ['32.k1'], 'conjugacy_class_count': 3, 'contained_in': ['8.c1', '12.e1', '12.h1'], 'contains': ['48.a1', '48.b1', '48.d1', '48.j1', '48.y1', '48.dj1', '48.dk1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8025, 5797, 4943, 7708], 'generators': [1083180097, 1083098168, 1085750593, 1081574431, 1089985272], 'label': '768.1090187.24.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['48.a1', '48.b1', '96.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '192.1538', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633906
    {'ambient': '768.1090187', 'aut_centralizer_order': 512, 'aut_label': '24.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 512, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.a1', '12.b1', '12.bg1', '12.bh1'], 'contains': ['48.c1', '48.cs1', '48.da1', '48.hl1', '48.hn1'], 'core': '24.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4663, 4243, 4354, 5682], 'generators': [1076429862, 1074660408, 1084867622, 1085750593, 1081574431], 'label': '768.1090187.24.b1', 'mobius_quo': -2, 'mobius_sub': 24, 'normal_closure': '24.b1', 'normal_contained_in': ['8.a1', '12.a1', '12.b1'], 'normal_contains': ['48.c1', '96.b1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '384.20163', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633907
    {'ambient': '768.1090187', 'aut_centralizer_order': 256, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '36.10', 'aut_weyl_index': 512, 'centralizer': '6.a1', 'complements': ['32.d1'], 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '12.a1', '12.bk1', '12.bo1'], 'contains': ['48.c1', '48.ek1', '48.et1', '48.gt1', '48.gx1'], 'core': '24.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [2218, 3427, 3972, 6838], 'generators': [1076429862, 1074660408, 1084867622, 1081574431, 1087249055], 'label': '768.1090187.24.c1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': ['8.b1', '12.a1'], 'normal_contains': ['48.c1', '96.c1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '384.20100', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 59633908
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.d1', '12.h1'], 'contains': ['48.d1', '48.e1', '48.g1', '48.i1', '48.q1', '48.w1', '48.ba1', '48.bb1', '48.dd1', '48.de1', '48.df1'], 'core': '96.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7348, -1, 3323, -1], 'generators': [1083180097, 1078860511, 1085750593, 1081574431, 1077347359], 'label': '768.1090187.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.d1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633909
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.e1', '12.f1'], 'contains': ['48.d1', '48.f1', '48.k1', '48.m1', '48.u1', '48.x1', '48.bc1'], 'core': '96.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9821, -1, 9680, -1], 'generators': [1083180097, 660749132, 1085750593, 1080629953, 1089946655], 'label': '768.1090187.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.e1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633910
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 16, 'centralizer': '192.a1', 'complements': ['192.l1', '192.bc1', '192.cl1', '192.t1', '192.be1', '192.cp1', '192.be2', '192.q1', '192.bd1', '192.x1', '192.cn1', '192.p1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.a1', '8.i1', '12.bg1', '16.g1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [4713, 3516, 5259, 2520], 'generators': [1076429862, 1074660408, 2150763522, 1084867622, 1085750593, 1081574431, 504396399], 'label': '768.1090187.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '384.20163', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 59633911
    {'ambient': '768.1090187', 'aut_centralizer_order': 16, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '64.202', 'aut_weyl_index': 288, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.e1', '12.g1'], 'contains': ['48.d1', '48.l1', '48.n1', '48.bd1'], 'core': '96.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9256, -1, 7324, -1], 'generators': [1083180097, 1085750593, 1080629953, 668673292, 1089946655], 'label': '768.1090187.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.f1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633912
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.d1', '12.h1'], 'contains': ['48.d1', '48.e1', '48.h1', '48.o1', '48.s1', '48.v1', '48.z1', '48.be1', '48.dg1', '48.dh1', '48.di1'], 'core': '96.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5880, -1, 3103, -1], 'generators': [1076429862, 1083180097, 1085750593, 1081574431, 1078991590], 'label': '768.1090187.24.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.g1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633913
    {'ambient': '768.1090187', 'aut_centralizer_order': 128, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 384, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.g1', '12.h1'], 'contains': ['48.d1', '48.j2', '48.p1', '48.y2', '48.bf1', '48.dj2', '48.dk2'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8619, -1, 5057, -1], 'generators': [1083180097, 1083098168, 1085750593, 1074830054, 1080656934], 'label': '768.1090187.24.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.h1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633914
    {'ambient': '768.1090187', 'aut_centralizer_order': 192, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.38', 'aut_weyl_index': 384, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '12.d1'], 'contains': ['48.e1', '48.r1', '48.t1', '48.bg1', '48.bh1', '48.dl1', '48.dm1'], 'core': '96.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1537, -1, 415, -1], 'generators': [1083180097, 1085750593, 1087390721, 1076468417, 1083229185], 'label': '768.1090187.24.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.i1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 59633915
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.d1', '12.j1', '12.o1'], 'contains': ['48.g1', '48.h1', '48.q1', '48.r1', '48.s1', '48.bl1', '48.bl2', '48.cc1', '48.cg1', '48.dn1', '48.dq1', '48.dt1', '48.dt2'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2746, -1, 1954, -1], 'generators': [1085750593, 1081547512, 1081574431, 1077347359, 1084818534], 'label': '768.1090187.24.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.j1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59633916
    {'ambient': '768.1090187', 'aut_centralizer_order': 64, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.h1', '12.i1', '12.j1'], 'contains': ['48.g1', '48.j1', '48.j2', '48.s1', '48.bm1', '48.cd1', '48.cn1', '48.do1', '48.dr1', '48.du1'], 'core': '192.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7440, -1, 4422, -1], 'generators': [1085750593, 1081574431, 1089985272, 1076479078, 1077347359], 'label': '768.1090187.24.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.k1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59633917
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.i1', '12.p1'], 'contains': ['48.g1', '48.k1', '48.l1', '48.ce1', '48.co1', '48.dp1', '48.ds1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9067, -1, 9125, -1], 'generators': [1076429862, 1085750593, 1084856961, 658250892, 1080656934], 'label': '768.1090187.24.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.l1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633918
    {'ambient': '768.1090187', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 576, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.i1', '12.r1'], 'contains': ['48.g1', '48.m1', '48.n1', '48.cf1', '48.cp1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9553, -1, 7401, -1], 'generators': [1076429862, 1085750593, 506952305, 1087390721, 506930390], 'label': '768.1090187.24.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.m1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633919
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.k1', '12.l1'], 'contains': ['48.i1', '48.k1', '48.n1', '48.ch1', '48.dv1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9282, -1, 7473, -1], 'generators': [1078860511, 660749132, 1085750593, 1085736031, 1089946655], 'label': '768.1090187.24.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.n1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59633920
    {'ambient': '768.1090187', 'aut_centralizer_order': 8, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 144, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.k1', '12.m1'], 'contains': ['48.i1', '48.l1', '48.m1', '48.ci1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9773, -1, 8715, -1], 'generators': [1078860511, 1085750593, 1085736031, 668673292, 1089946655], 'label': '768.1090187.24.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.o1', 'projective_image': '192.1538', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1', 'subgroup_fusion': None, 'weyl_group': '8.5'}