Abstract group data - 768.1090070

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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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [6, 4, 8, 4, 4], 'aut_gens': [[1508405, 40723320, 495363, 7, 16, 11291167, 14933656, 90842400, 135732240], [11370961, 212340360, 258371300, 262459463, 90842407, 243901463, 83589127, 262459440, 90842400], [262091522, 40723320, 261355688, 7, 23, 83589120, 243901440, 90842400, 262459440], [291811801, 212340360, 95081164, 135732256, 90842407, 255191776, 143354287, 135732240, 90842400], [83463966, 212340360, 95081179, 16, 7, 14933640, 11291160, 135732240, 90842400], [211604534, 212340360, 11749812, 7, 16, 143354287, 255191776, 90842400, 135732240]], 'aut_group': None, 'aut_hash': 6376613793978181277, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 48, 'aut_perms': [967280471687115451845503797890604964005660371247559744292901, 9207338922187193738776085689817781521611380610723070604678146, 12047228081690748459392254480251137155358223887920596437081437, 5854712021235692481712871864046775476562129480678941055767048, 12372005063013073454319669454203164563996738285551959060822170], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 3, 2, 1], [2, 4, 1, 1], [2, 6, 1, 1], [2, 6, 4, 1], [2, 12, 1, 1], [2, 12, 2, 1], [2, 24, 2, 1], [3, 128, 1, 1], [4, 12, 2, 1], [4, 24, 1, 1], [4, 24, 2, 1], [4, 24, 4, 1], [4, 48, 4, 1], [6, 128, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.C_6.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 6376613793978181277, 'autcentquo_nilpotent': False, 'autcentquo_order': 6144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^6.C_6.C_2^4', 'cc_stats': [[1, 1, 1], [2, 3, 3], [2, 4, 1], [2, 6, 5], [2, 12, 3], [2, 24, 2], [3, 128, 1], [4, 12, 2], [4, 24, 7], [4, 48, 4], [6, 128, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '768.1090070', 'commutator_count': 1, 'commutator_label': '192.1541', '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': 1090070, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 3], [2, 4, 1, 1], [2, 6, 1, 5], [2, 12, 1, 3], [2, 24, 1, 2], [3, 128, 1, 1], [4, 12, 1, 2], [4, 24, 1, 7], [4, 48, 1, 4], [6, 128, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 9, 'exponent': 12, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 2]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '192.1538', 'hash': 1090070, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 3, 2, 2, 2, 2, 2, 2], 'inner_gens': [[1508405, 40723320, 1467364, 23, 16, 22186943, 14933656, 262459440, 135732240], [1508405, 40723320, 495363, 7, 16, 83589127, 124836496, 90842400, 135732240], [367922, 40723320, 495363, 16, 23, 14933656, 22186943, 135732240, 262459440], [1508414, 40723320, 495380, 7, 16, 11291167, 14933656, 90842400, 135732240], [1508405, 40723320, 495371, 7, 16, 11291167, 14933656, 90842400, 135732240], [16057454, 167450520, 22669940, 7, 16, 11291167, 14933656, 90842400, 135732240], [1508405, 212340360, 11749811, 7, 16, 11291167, 14933656, 90842400, 135732240], [134996405, 40723320, 262009443, 7, 16, 11291167, 14933656, 90842400, 135732240], [1508405, 40723320, 92268723, 7, 16, 11291167, 14933656, 90842400, 135732240]], 'inner_hash': 1090070, 'inner_nilpotent': False, 'inner_order': 768, 'inner_split': False, 'inner_tex': 'C_2^5:S_4', 'inner_used': [1, 2, 3, 4, 6], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 2], [3, 12], [6, 10], [12, 2]], 'label': '768.1090070', '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': 'C2^5:S4', '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': 16, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 30, 'number_divisions': 30, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 409, 'number_subgroup_classes': 1080, 'number_subgroups': 10046, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 127], [3, 128], [4, 384], [6, 128]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [40723320, 0, 0], 'outer_gens': [[41868125, 40723320, 495363, 90842407, 135732256, 143354280, 255191760, 90842400, 135732240], [1508405, 40723320, 495363, 90842407, 135732256, 83589127, 124836496, 90842400, 135732240], [1508405, 40723320, 495363, 7, 16, 83589120, 124836480, 90842400, 135732240]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 12], [6, 10], [12, 2]], 'representations': {'PC': {'code': '3194480519859125246986069361012777056449421718566668868840409004377152', 'gens': [1, 2, 4, 5, 6, 7, 8, 9], 'pres': [9, -2, -2, -3, -2, 2, 2, 2, 2, 2, 181, 46, 218, 4116, 1965, 2983, 3532, 21389, 16538, 8933, 8322, 771, 2103, 14695, 4336, 1969, 4868, 17999, 1241]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [11041563, 32746561, 12189505, 30581825, 6204507, 6210649, 8375387, 19232857, 11106369]}, 'Perm': {'d': 12, 'gens': [1508405, 40723320, 495363, 7, 16, 11291167, 14933656, 90842400, 135732240]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5:S_4', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 110944099
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 1090070, 'group_order': 768, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 110944110
    {'aut_label': '2A', 'centralizer': '3.a1', 'counter': 2, 'group_counter': 1090070, 'group_order': 768, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 90842400, 'size': 3}
  • id: 110944121
    {'aut_label': '2B', 'centralizer': '3.a1', 'counter': 3, 'group_counter': 1090070, 'group_order': 768, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 7, 'size': 3}
  • id: 110944123
    {'aut_label': '2B', 'centralizer': '3.a1', 'counter': 4, 'group_counter': 1090070, 'group_order': 768, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 90842407, 'size': 3}
  • id: 110944124
    {'aut_label': '2D', 'centralizer': '4.b1', 'counter': 5, 'group_counter': 1090070, 'group_order': 768, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 40723320, 'size': 4}
  • id: 110944125
    {'aut_label': '2E', 'centralizer': '6.a1', 'counter': 6, 'group_counter': 1090070, 'group_order': 768, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 90842416, 'size': 6}
  • id: 110944126
    {'aut_label': '2F', 'centralizer': '6.h1', 'counter': 7, 'group_counter': 1090070, 'group_order': 768, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 14933656, 'size': 6}
  • id: 110944127
    {'aut_label': '2F', 'centralizer': '6.h1', 'counter': 8, 'group_counter': 1090070, 'group_order': 768, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 94484903, 'size': 6}
  • id: 110944128
    {'aut_label': '2F', 'centralizer': '6.h1', 'counter': 9, 'group_counter': 1090070, 'group_order': 768, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 124836480, 'size': 6}
  • id: 110944100
    {'aut_label': '2F', 'centralizer': '6.h1', 'counter': 10, 'group_counter': 1090070, 'group_order': 768, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 258829920, 'size': 6}
  • id: 110944101
    {'aut_label': '2J', 'centralizer': '12.a1', 'counter': 11, 'group_counter': 1090070, 'group_order': 768, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 11291176, 'size': 12}
  • id: 110944102
    {'aut_label': '2K', 'centralizer': '12.v1', 'counter': 12, 'group_counter': 1090070, 'group_order': 768, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 40723327, 'size': 12}
  • id: 110944103
    {'aut_label': '2J', 'centralizer': '12.a1', 'counter': 13, 'group_counter': 1090070, 'group_order': 768, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 94484887, 'size': 12}
  • id: 110944104
    {'aut_label': '2M', 'centralizer': '24.e1', 'counter': 14, 'group_counter': 1090070, 'group_order': 768, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 127441, 'size': 24}
  • id: 110944105
    {'aut_label': '2M', 'centralizer': '24.e1', 'counter': 15, 'group_counter': 1090070, 'group_order': 768, 'label': '2N', 'order': 2, 'powers': [1, 15], 'representative': 40805401, 'size': 24}
  • id: 110944106
    {'aut_label': '3A', 'centralizer': '128.a1', 'counter': 16, 'group_counter': 1090070, 'group_order': 768, 'label': '3A', 'order': 3, 'powers': [16, 1], 'representative': 135123859, 'size': 128}
  • id: 110944107
    {'aut_label': '4A', 'centralizer': '12.z1', 'counter': 17, 'group_counter': 1090070, 'group_order': 768, 'label': '4A', 'order': 4, 'powers': [2, 17], 'representative': 44352840, 'size': 12}
  • id: 110944108
    {'aut_label': '4A', 'centralizer': '12.z1', 'counter': 18, 'group_counter': 1090070, 'group_order': 768, 'label': '4B', 'order': 4, 'powers': [2, 18], 'representative': 44352847, 'size': 12}
  • id: 110944109
    {'aut_label': '4C', 'centralizer': '24.f1', 'counter': 19, 'group_counter': 1090070, 'group_order': 768, 'label': '4C', 'order': 4, 'powers': [3, 19], 'representative': 127457, 'size': 24}
  • id: 110944111
    {'aut_label': '4C', 'centralizer': '24.f1', 'counter': 20, 'group_counter': 1090070, 'group_order': 768, 'label': '4D', 'order': 4, 'powers': [3, 20], 'representative': 40805417, 'size': 24}
  • id: 110944112
    {'aut_label': '4E', 'centralizer': '24.cg1', 'counter': 21, 'group_counter': 1090070, 'group_order': 768, 'label': '4E', 'order': 4, 'powers': [2, 21], 'representative': 44352856, 'size': 24}
  • id: 110944113
    {'aut_label': '4F', 'centralizer': '24.d1', 'counter': 22, 'group_counter': 1090070, 'group_order': 768, 'label': '4F', 'order': 4, 'powers': [2, 22], 'representative': 44432641, 'size': 24}
  • id: 110944114
    {'aut_label': '4C', 'centralizer': '24.f1', 'counter': 23, 'group_counter': 1090070, 'group_order': 768, 'label': '4G', 'order': 4, 'powers': [4, 23], 'representative': 44432657, 'size': 24}
  • id: 110944115
    {'aut_label': '4F', 'centralizer': '24.d1', 'counter': 24, 'group_counter': 1090070, 'group_order': 768, 'label': '4H', 'order': 4, 'powers': [2, 24], 'representative': 91578245, 'size': 24}
  • id: 110944116
    {'aut_label': '4C', 'centralizer': '24.f1', 'counter': 25, 'group_counter': 1090070, 'group_order': 768, 'label': '4I', 'order': 4, 'powers': [4, 25], 'representative': 91578249, 'size': 24}
  • id: 110944117
    {'aut_label': '4J', 'centralizer': '48.v1', 'counter': 26, 'group_counter': 1090070, 'group_order': 768, 'label': '4J', 'order': 4, 'powers': [7, 26], 'representative': 142249098, 'size': 48}
  • id: 110944118
    {'aut_label': '4J', 'centralizer': '48.v1', 'counter': 27, 'group_counter': 1090070, 'group_order': 768, 'label': '4K', 'order': 4, 'powers': [8, 27], 'representative': 199750333, 'size': 48}
  • id: 110944119
    {'aut_label': '4J', 'centralizer': '48.v1', 'counter': 28, 'group_counter': 1090070, 'group_order': 768, 'label': '4L', 'order': 4, 'powers': [9, 28], 'representative': 95206334, 'size': 48}
  • id: 110944120
    {'aut_label': '4J', 'centralizer': '48.v1', 'counter': 29, 'group_counter': 1090070, 'group_order': 768, 'label': '4M', 'order': 4, 'powers': [10, 29], 'representative': 201525841, 'size': 48}
  • id: 110944122
    {'aut_label': '6A', 'centralizer': '128.a1', 'counter': 30, 'group_counter': 1090070, 'group_order': 768, 'label': '6A', 'order': 6, 'powers': [16, 5], 'representative': 302687411, 'size': 128}
• 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: 4799493
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.1a', '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], 'schur_index': 1}
  • id: 4799504
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.1b', '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], 'schur_index': 1}
  • id: 4799515
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.1c', '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], 'schur_index': 1}
  • id: 4799517
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.1d', '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], 'schur_index': 1}
  • id: 4799518
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1], 'schur_index': 1}
  • id: 4799519
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, -2, 2, 0, 0, -1, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'schur_index': 1}
  • id: 4799520
    {'cdim': 3, 'counter': 7, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, 1, 1, 0, 3, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 0], 'schur_index': 1}
  • id: 4799521
    {'cdim': 3, 'counter': 8, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3b', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, -1, 3, 3, -1, -1, -1, -1, -1, 1, 1, 0, -1, 3, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 0], 'schur_index': 1}
  • id: 4799522
    {'cdim': 3, 'counter': 9, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3c', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, 3, -1, 1, 1, 0, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0], 'schur_index': 1}
  • id: 4799494
    {'cdim': 3, 'counter': 10, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3d', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, 0, 3, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 0], 'schur_index': 1}
  • id: 4799495
    {'cdim': 3, 'counter': 11, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3e', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, 0, -1, 3, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 0], 'schur_index': 1}
  • id: 4799496
    {'cdim': 3, 'counter': 12, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3f', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, 3, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0], 'schur_index': 1}
  • id: 4799497
    {'cdim': 3, 'counter': 13, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -1, -1, -1, 3, 3, -1, 1, -1, -1, 1, 0, -3, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 0], 'schur_index': 1}
  • id: 4799498
    {'cdim': 3, 'counter': 14, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -1, -1, -1, 3, 3, -1, 1, -1, 1, -1, 0, -3, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 0], 'schur_index': 1}
  • id: 4799499
    {'cdim': 3, 'counter': 15, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3i', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -1, 3, 3, -1, -1, -1, 1, -1, -1, 1, 0, 1, -3, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 0], 'schur_index': 1}
  • id: 4799500
    {'cdim': 3, 'counter': 16, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3j', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -1, 3, 3, -1, -1, -1, 1, -1, 1, -1, 0, 1, -3, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 0], 'schur_index': 1}
  • id: 4799501
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3k', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, 3, -1, -1, -1, -1, -1, -3, -1, -1, 1, 0, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 0], 'schur_index': 1}
  • id: 4799502
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.3l', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -3, 3, -1, -1, -1, -1, -1, -3, -1, 1, -1, 0, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 0], 'schur_index': 1}
  • id: 4799503
    {'cdim': 6, 'counter': 19, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6a', 'multiplicity': 1, 'nt': [8, 34], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 6, -2, -2, -2, -2, -2, 2, -2, 2, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799505
    {'cdim': 6, 'counter': 20, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6b', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, -2, -2, 6, 0, -2, -2, 2, -2, 2, 2, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799506
    {'cdim': 6, 'counter': 21, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6c', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, -2, -2, 6, 0, -2, 2, -2, 2, -2, -2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799507
    {'cdim': 6, 'counter': 22, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6d', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, -2, 6, -2, 0, -2, -2, 2, -2, 2, -2, 0, 2, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799508
    {'cdim': 6, 'counter': 23, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6e', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, -2, 6, -2, 0, -2, 2, -2, 2, -2, 2, 0, -2, 2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799509
    {'cdim': 6, 'counter': 24, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6f', 'multiplicity': 1, 'nt': [12, 100], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -6, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799510
    {'cdim': 6, 'counter': 25, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6g', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, -2, -2, 6, 0, -2, -2, 2, -2, 2, 2, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799511
    {'cdim': 6, 'counter': 26, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6h', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, -2, -2, 6, 0, -2, 2, -2, 2, -2, -2, 0, 2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799512
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6i', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, -2, 6, -2, 0, -2, -2, 2, -2, 2, -2, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799513
    {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.6j', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, -2, 6, -2, 0, -2, 2, -2, 2, -2, 2, 0, -2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799514
    {'cdim': 12, 'counter': 29, 'faithful': True, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.12a', 'multiplicity': 1, 'nt': [16, 1068], 'qdim': 12, 'qvalues': [12, -4, -4, -4, 0, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4799516
    {'cdim': 12, 'counter': 30, 'faithful': True, 'group': '768.1090070', 'group_order': 768, 'image': None, 'label': '768.1090070.12b', 'multiplicity': 1, 'nt': [16, 1068], 'qdim': 12, 'qvalues': [12, -4, -4, -4, 0, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 7845937
    {'center': None, 'center_index': 1, 'center_order': 768, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 768, 'label': '768.1090070.1a', '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]]]}
  • id: 7845948
    {'center': None, 'center_index': 1, 'center_order': 768, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 384, 'label': '768.1090070.1b', '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]]]}
  • id: 7845959
    {'center': None, 'center_index': 1, 'center_order': 768, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 384, 'label': '768.1090070.1c', '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]]]}
  • id: 7845961
    {'center': None, 'center_index': 1, 'center_order': 768, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 384, 'label': '768.1090070.1d', '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]]]}
  • id: 7845962
    {'center': None, 'center_index': 6, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '768.1090070.2a', '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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 7845963
    {'center': None, 'center_index': 6, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 64, 'label': '768.1090070.2b', '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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 7845964
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 7, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '768.1090070.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 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]], [[1, 0]], [[0, 0]]]}
  • id: 7845965
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 8, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '768.1090070.3b', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 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]]]}
  • id: 7845966
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 9, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '768.1090070.3c', '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]], [[-1, 0]], [[-1, 0]], [[3, 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]], [[0, 0]]]}
  • id: 7845938
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 10, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '768.1090070.3d', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 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]], [[-1, 0]], [[0, 0]]]}
  • id: 7845939
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 11, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '768.1090070.3e', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 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]]]}
  • id: 7845940
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 12, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '768.1090070.3f', '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]], [[-1, 0]], [[-1, 0]], [[3, 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]], [[0, 0]]]}
  • id: 7845941
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 13, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '768.1090070.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 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]], [[1, 0]], [[0, 0]]]}
  • id: 7845942
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 14, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '768.1090070.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 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]], [[-1, 0]], [[0, 0]]]}
  • id: 7845943
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 15, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '768.1090070.3i', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 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]]]}
  • id: 7845944
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 16, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '768.1090070.3j', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 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]]]}
  • id: 7845945
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '768.1090070.3k', '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]], [[-1, 0]], [[-1, 0]], [[-3, 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]], [[0, 0]]]}
  • id: 7845946
    {'center': None, 'center_index': 24, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '768.1090070.3l', '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]], [[-1, 0]], [[-1, 0]], [[-3, 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]], [[0, 0]]]}
  • id: 7845947
    {'center': None, 'center_index': 96, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '96.227', 'image_order': 96, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '768.1090070.6a', 'nt': [8, 34], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845949
    {'center': None, 'center_index': 192, 'center_order': 4, 'counter': 20, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '768.1090070.6b', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845950
    {'center': None, 'center_index': 192, 'center_order': 4, 'counter': 21, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '768.1090070.6c', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845951
    {'center': None, 'center_index': 192, 'center_order': 4, 'counter': 22, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '768.1090070.6d', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845952
    {'center': None, 'center_index': 192, 'center_order': 4, 'counter': 23, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '768.1090070.6e', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845953
    {'center': None, 'center_index': 96, 'center_order': 8, 'counter': 24, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '768.1090070.6f', 'nt': [12, 100], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845954
    {'center': None, 'center_index': 192, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '768.1090070.6g', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845955
    {'center': None, 'center_index': 192, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '768.1090070.6h', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845956
    {'center': None, 'center_index': 192, 'center_order': 4, 'counter': 27, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '768.1090070.6i', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845957
    {'center': None, 'center_index': 192, 'center_order': 4, 'counter': 28, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '768.1090070.6j', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845958
    {'center': None, 'center_index': 768, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '768.1090070', 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '768.1090070.12a', 'nt': [16, 1068], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7845960
    {'center': None, 'center_index': 768, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '768.1090070', 'group_counter': 1090070, 'group_order': 768, 'image': None, 'image_isoclass': '768.1090070', 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '768.1090070.12b', 'nt': [16, 1068], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 68518359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 768, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '768.1090070.1.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': '768.1090070', 'subgroup_hash': 1090070, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 384, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18221', 'subgroup_hash': 18221, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 384, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '768.1090070.3.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': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 68518713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 192, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.4.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': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.4.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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: 68518735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.4.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.6.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': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.6.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': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.6.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': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.6.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': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.6.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': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.6.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': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.6.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': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.6.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: 68518426
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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: 68518437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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: 68518448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 32, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.8.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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 8, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.8.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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.8.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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.8.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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.12.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': ['D2', 'C3'], '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: 68518504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 68518570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.199', 'subgroup_hash': 199, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.23', 'subgroup_hash': 23, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 68518706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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: 68518707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.12.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': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518716
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518718
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.16.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': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.16.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': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518721
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.16.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': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518723
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.24.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: 68518725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.24.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': '24.12', '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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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: 68518727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518753
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 68518754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 68518758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.br1', '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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518363
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.bq1', '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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 68518364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518368
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.ca1', '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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.by1', '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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.bz1', '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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 68518378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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: 68518388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.cp1', '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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.cq1', '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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.co1', '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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.24.cz2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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: 68518402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.32.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: 68518408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518409
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 144, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.48.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': ['S', 'C4'], '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: 68518410
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 145, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.48.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: 68518411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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: 68518412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518413
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68518416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518420
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518421
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.l2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l2', 'outer_equivalence': True, 'perfect': False, '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: 68518423
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518424
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68518425
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 68518427
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.q1', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518429
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.p1', '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: 68518430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518431
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518432
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.t2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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: 68518434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518436
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.ba1', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.bb1', '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.y1', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.z1', '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518443
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.bf2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf2', 'outer_equivalence': True, 'perfect': False, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 68518449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 68518450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518451
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518452
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.bj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 68518454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.bt1', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.bs1', '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68518466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.cb1', '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.cc1', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.bz1', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.ca1', '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68518480
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68518483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.cj1', '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68518484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.ci1', '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68518485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.ct1', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.cu1', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.cs1', '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68518497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.dh1', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.dd1', '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.de1', '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.df1', '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518510
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.dg1', '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: 68518511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68518512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518516
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518517
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.dm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dm2', 'outer_equivalence': True, 'perfect': False, '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: 68518518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.dn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dn2', 'outer_equivalence': True, 'perfect': False, '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: 68518520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.do2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.do2', 'outer_equivalence': True, 'perfect': False, '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: 68518522
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68518523
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.dp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dp2', 'outer_equivalence': True, 'perfect': False, '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: 68518524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518528
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518529
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.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: 68518531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.48.du2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.du2', 'outer_equivalence': True, 'perfect': False, '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: 68518532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.64.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: 68518535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.64.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68518539
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 261, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.96.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': [], '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: 68518540
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 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: 68518541
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 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: 68518542
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c2', 'outer_equivalence': True, 'perfect': False, '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: 68518543
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518544
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.f1', '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: 68518545
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.e1', '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: 68518546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518547
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 68518550
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518551
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518552
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.m1', '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: 68518553
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.l1', '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: 68518554
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 68518555
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518556
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518557
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518558
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518561
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518566
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518567
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bc1', '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: 68518571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bb1', '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: 68518572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518577
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bg1', '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: 68518578
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 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: 68518579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518580
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518584
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518585
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518586
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 68518587
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518591
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bt1', '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: 68518592
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518594
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.br1', '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: 68518595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 68518598
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518599
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cb1', '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: 68518601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 68518602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518609
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518610
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.ci2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ci2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 68518611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518613
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.ck2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ck2', 'outer_equivalence': True, 'perfect': False, '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: 68518614
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.ck3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ck3', 'outer_equivalence': True, 'perfect': False, '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: 68518616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518617
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518619
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518620
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.co2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.co2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 68518621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.co3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.co3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 68518622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cs2', 'outer_equivalence': True, 'perfect': False, '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: 68518628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518633
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cx2', 'outer_equivalence': True, 'perfect': False, '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: 68518634
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cx3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cx3', 'outer_equivalence': True, 'perfect': False, '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: 68518635
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cy2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cy2', 'outer_equivalence': True, 'perfect': False, '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: 68518638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.cy3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.cy3', 'outer_equivalence': True, 'perfect': False, '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: 68518639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.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: 68518640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.96.db2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.db2', 'outer_equivalence': True, 'perfect': False, '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: 68518643
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 355, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.128.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: 68518644
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68518645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 357, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.192.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, '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': ['Phi'], '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: 68518646
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 358, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090070.192.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.955', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 955, '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': ['C5'], '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: 68518647
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 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: 68518649
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518650
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518651
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518652
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g2', 'outer_equivalence': True, 'perfect': False, '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: 68518654
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.i1', '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: 68518655
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.i2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.h2', 'outer_equivalence': True, 'perfect': False, '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: 68518656
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.h1', '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: 68518657
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.i2', 'outer_equivalence': True, 'perfect': False, '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: 68518658
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518660
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518661
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.192.m1', '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518662
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 372, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.192.l1', '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518663
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518664
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.s1', '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: 68518668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.r1', '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: 68518669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518671
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518673
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518675
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518677
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.bb1', '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: 68518678
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.ba1', '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: 68518679
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518682
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.bd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 68518683
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518684
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68518685
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.bg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 68518687
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518688
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.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: 68518689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.bj1', '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: 68518690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.bi1', '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: 68518691
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090070.192.bi2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 68518694
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 400, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '768.1090070.256.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: 68518695
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 401, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.384.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 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: 68518696
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 402, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.384.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 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: 68518697
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 403, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.384.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: 68518698
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.384.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: 68518699
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 405, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.384.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: 68518700
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.384.g1', '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: 68518701
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.384.f1', '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: 68518702
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090070.384.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: 68518703
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090070', 'ambient_counter': 1090070, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': True, 'core_order': 1, 'counter': 409, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '768.1090070.768.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': '768.1090070', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1090070, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D3', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 68518563
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.c1', '48.i1', '48.bo1', '48.cq1'], 'contains': ['192.e1', '192.h1', '192.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3259, -1, 5834, -1], 'generators': [40723320, 262459440, 22186927], 'label': '768.1090070.96.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '96.v1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518640
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '96.da1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.bz1', '48.dn1', '48.dn2'], 'contains': ['192.bd1', '192.be1', '192.bf1'], 'core': '768.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [9200, -1, 1145, -1], 'generators': [22186936, 11291176, 1508405], 'label': '768.1090070.96.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1', 'old_label': '96.da1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518641
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '96.db1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.f1', '48.cd1', '48.dn1'], 'contains': ['192.be1', '192.bf1', '192.bh1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9255, -1, 996, -1], 'generators': [22186920, 11291160, 1508405], 'label': '768.1090070.96.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1', 'old_label': '96.db1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518642
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '96.db2', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.cd1', '48.dn2'], 'contains': ['192.be1', '192.bf1', '192.bh2'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9090, -1, 1256, -1], 'generators': [94484880, 258829920, 1508405], 'label': '768.1090070.96.db2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1', 'old_label': '96.db2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.db2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 68518643
    {'ambient': '768.1090070', 'aut_centralizer_order': 48, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.c1', '32.e1', '64.c1'], 'contains': ['256.a1', '384.c1'], 'core': '768.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [9878, -1, 702, -1], 'generators': [40723320, 1467364], 'label': '768.1090070.128.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.c1', 'old_label': '128.a1', 'projective_image': '768.1090070', '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: 68518644
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.b1', '32.d1', '32.f1', '64.c1'], 'contains': ['256.a1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [9665, -1, 403, -1], 'generators': [1467364, 1508405], 'label': '768.1090070.128.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.c1', 'old_label': '128.b1', 'projective_image': '768.1090070', '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': '6.1'}
  • id: 68518702
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '384.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.b1', '192.j1', '192.t1', '192.x1', '192.be1', '192.bj1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5267, -1, 4345, -1], 'generators': [1508405], 'label': '768.1090070.384.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '384.h1', 'projective_image': '768.1090070', '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: 68518359
    {'ambient': '768.1090070', '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': '768.a1', 'complements': ['768.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '3.a1', '4.b1', '4.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9403, 2294, 948, 1939], 'generators': [11291167, 1467364, 23, 7, 40723320, 1508405, 135732240, 262459440, 22186943], 'label': '768.1090070.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '768.1090070', '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': '768.1090070'}
  • id: 68518360
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1'], 'contains': ['12.h1', '12.i1', '12.j1', '12.p1', '12.s1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4895, -1, 4483, -1], 'generators': [22186920, 22186936, 40723320, 14933656, 1508418, 135732240, 262459440], 'label': '768.1090070.6.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': '768.1090070', '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': '64.202'}
  • id: 68518361
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '12.l1', '12.x1'], 'contains': ['48.cg1', '48.cl1', '48.cm1', '48.cw1', '48.cx1', '48.dd1', '48.de1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5752, -1, 3515, -1], 'generators': [22186920, 262459440, 159828487, 135732240, 7], 'label': '768.1090070.24.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bp1', 'projective_image': '768.1090070', '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: 68518362
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.n1', '12.q1', '12.u1'], 'contains': ['48.q1', '48.bt1', '48.ch1', '48.cj1', '48.co1', '48.cu1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4454, -1, 5081, -1], 'generators': [40723327, 14933656, 262459440, 135732240, 16], 'label': '768.1090070.24.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bq1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518363
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.f1', '12.l1'], 'contains': ['48.e1', '48.p1', '48.bs1', '48.cg1', '48.ci1', '48.cs1', '48.da1', '48.dg1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7179, -1, 2021, -1], 'generators': [23, 11291167, 22186936, 262459440, 135732240], 'label': '768.1090070.24.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.br1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518364
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.g1', '12.m1', '12.o1', '12.r1', '12.w1'], 'contains': ['48.r1', '48.s1', '48.u1', '48.bu1', '48.ch1', '48.ck1', '48.cv1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3278, -1, 6643, -1], 'generators': [14933656, 262459440, 135732240, 1508405, 16], 'label': '768.1090070.24.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bs1', 'projective_image': '768.1090070', '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': '32.46'}
  • id: 68518365
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '12.o1', '12.p1', '12.q1', '12.x1'], 'contains': ['48.ch1', '48.cl1', '48.cw1', '48.cx1', '48.cy1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5244, -1, 4399, -1], 'generators': [280995863, 14933656, 262459440, 135732240, 16], 'label': '768.1090070.24.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bt1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518366
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '12.m1', '12.p1', '12.s1', '12.w1'], 'contains': ['48.t1', '48.t2', '48.ch1', '48.cn1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3727, -1, 6044, -1], 'generators': [14933656, 262459440, 135732240, 16, 1508409], 'label': '768.1090070.24.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bu1', 'projective_image': '768.1090070', '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': '32.46'}
  • id: 68518367
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.i1', '12.n1', '12.o1', '12.p1', '12.r1', '12.s1', '12.y1'], 'contains': ['48.v1', '48.bv1', '48.ch1', '48.cz1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5662, -1, 3650, -1], 'generators': [23668578, 14933656, 262459440, 135732240, 16], 'label': '768.1090070.24.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bv1', 'projective_image': '768.1090070', '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': '32.46'}
  • id: 68518368
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.j1', '12.q1', '12.r1', '12.s1'], 'contains': ['48.b1', '48.f1', '48.w1', '48.bw1', '48.cg1', '48.ch1', '48.cs1', '48.da1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6880, -1, 2080, -1], 'generators': [11291167, 22186920, 262459440, 135732240, 7], 'label': '768.1090070.24.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bw1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518369
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.t1', '12.u1'], 'contains': ['48.x1', '48.bx1', '48.cj1', '48.ci1', '48.cm1', '48.db1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4302, -1, 5367, -1], 'generators': [40723343, 262459440, 135732240, 11291176, 7], 'label': '768.1090070.24.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bx1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518370
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.m1', '12.t1', '12.v1'], 'contains': ['48.ba1', '48.bb1', '48.cj1', '48.ck1', '48.cn1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2716, -1, 7414, -1], 'generators': [40723343, 262459440, 135732240, 1508418, 16], 'label': '768.1090070.24.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.by1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518371
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.a1'], 'contains': ['12.m1', '12.n1', '12.o1', '12.p1', '12.q1', '12.r1', '12.s1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5143, -1, 4195, -1], 'generators': [22186920, 14933656, 40723343, 22186936, 262459440, 135732240, 1508405], 'label': '768.1090070.6.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': '768.1090070', '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': '64.202'}
  • id: 68518372
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.k1', '12.t1', '12.w1'], 'contains': ['48.y1', '48.z1', '48.ci1', '48.ck1', '48.cn1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2245, -1, 7799, -1], 'generators': [262459440, 135732240, 14933647, 14933663, 1508405], 'label': '768.1090070.24.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.bz1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518373
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.l1', '12.x1'], 'contains': ['48.ci1', '48.cl1', '48.dd1', '48.de1', '48.df1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6159, -1, 2995, -1], 'generators': [280995863, 262459440, 135732240, 11291176, 7], 'label': '768.1090070.24.bz1', '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': '768.1090070', '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: 68518374
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.k1', '12.m1', '12.z1'], 'contains': ['48.bd1', '48.bh1', '48.ck1', '48.cn1', '48.co1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1495, -1, 8015, -1], 'generators': [262459440, 135732240, 1508405, 16, 201398407], 'label': '768.1090070.24.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.cb1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518375
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.t1', '12.z1'], 'contains': ['48.bc1', '48.be1', '48.bg1', '48.by1', '48.ck1', '48.cm1', '48.di1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [363, -1, 9706, -1], 'generators': [262459440, 201398416, 135732240, 1508405, 16], 'label': '768.1090070.24.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.cc1', 'projective_image': '768.1090070', '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: 68518376
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.t1', '12.z1'], 'contains': ['48.bf1', '48.bf2', '48.cm1', '48.cn1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1977, -1, 8248, -1], 'generators': [262459440, 201398416, 135732240, 1508418, 16], 'label': '768.1090070.24.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.cd1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518377
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.u1', '12.w1', '12.x1', '12.y1'], 'contains': ['48.a1', '48.n1', '48.n2', '48.bj1', '48.bj2', '48.cg1', '48.ch1', '48.ci1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6076, -1, 2399, -1], 'generators': [23, 11291167, 262459440, 135732240, 7], 'label': '768.1090070.24.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ce1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518378
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '12.v1', '12.w1', '12.z1'], 'contains': ['48.a1', '48.bk1', '48.bm1', '48.ck1', '48.cn1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3814, -1, 7030, -1], 'generators': [23, 262459440, 135732240, 1508405, 7], 'label': '768.1090070.24.cf1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.cf1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518379
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '12.x1', '12.z1'], 'contains': ['48.a1', '48.o1', '48.bl1', '48.cl1', '48.cm1', '48.co1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4074, -1, 5676, -1], 'generators': [23, 262459440, 159828487, 135732240, 7], 'label': '768.1090070.24.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cg1', 'projective_image': '768.1090070', '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': '8.3'}
  • id: 68518380
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.j1', '12.ba1'], 'contains': ['48.cp1', '48.cq1', '48.cs1', '48.cy1', '48.dd1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4990, -1, 4030, -1], 'generators': [40723320, 262459440, 135732240, 14933647, 11291160], 'label': '768.1090070.24.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ch1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518381
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.g1', '12.ba1', '12.bb1'], 'contains': ['48.bq1', '48.br1', '48.cp1', '48.cr1', '48.cv1', '48.di1'], 'core': '96.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [451, -1, 9524, -1], 'generators': [40723320, 262459440, 135732240, 1508405, 14933640], 'label': '768.1090070.24.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.ci1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518382
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 12, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.b1', '12.c1', '12.g1', '12.h1', '12.k1', '12.m1', '12.t1', '12.u1', '12.v1', '12.w1', '12.z1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2403, -1, 7636, -1], 'generators': [23, 7, 40723320, 1508405, 14933656, 135732240, 262459440], 'label': '768.1090070.6.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': '768.1090070', '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': '64.202'}
  • id: 68518383
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.i1', '12.ba1', '12.bb1'], 'contains': ['48.cp1', '48.cz1'], 'core': '96.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4519, -1, 5854, -1], 'generators': [40723320, 262459440, 135732240, 12430214, 14933640], 'label': '768.1090070.24.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cj1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518384
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.j1'], 'contains': ['48.cp1', '48.cq1', '48.cw1', '48.da1', '48.de1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5492, -1, 3260, -1], 'generators': [22186920, 11291167, 40723320, 135732240, 262459440], 'label': '768.1090070.24.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ck1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518385
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '12.f1'], 'contains': ['48.cq1', '48.df1', '48.dg1'], 'core': '96.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6942, -1, 2307, -1], 'generators': [40723320, 22186936, 262459440, 135732240, 14933647], 'label': '768.1090070.24.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.cl1', 'projective_image': '768.1090070', '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': '24.13'}
  • id: 68518386
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.l1', '12.q1'], 'contains': ['48.cu1', '48.cs1', '48.cw1', '48.db1', '48.dc1', '48.dd1', '48.df1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6358, -1, 2865, -1], 'generators': [40723336, 262459440, 135732240, 14933647, 11291160], 'label': '768.1090070.24.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cm1', 'projective_image': '768.1090070', '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: 68518387
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '12.l1', '12.bc1'], 'contains': ['48.ct1', '48.cs1', '48.cx1', '48.db1', '48.de1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5408, -1, 4155, -1], 'generators': [40723327, 262459440, 135732240, 14933647, 11291160], 'label': '768.1090070.24.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cn1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518388
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.g1', '12.bc1', '12.bd1'], 'contains': ['48.cb1', '48.cc1', '48.ct1', '48.cv1', '48.dh1', '48.di1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [78, -1, 9605, -1], 'generators': [40723336, 262459440, 135732240, 1508405, 14933640], 'label': '768.1090070.24.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.co1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518389
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.i1', '12.bc1', '12.bd1'], 'contains': ['48.ct1', '48.cz1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3954, -1, 5935, -1], 'generators': [40723336, 262459440, 135732240, 12430214, 14933640], 'label': '768.1090070.24.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cp1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518390
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.r1', '12.ba1', '12.bc1'], 'contains': ['48.bz1', '48.ca1', '48.cs1', '48.cv1', '48.cz1'], 'core': '192.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5575, -1, 4653, -1], 'generators': [22186936, 262459440, 135732240, 11291176, 1508405], 'label': '768.1090070.24.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cq1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518391
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.o1', '12.bb1', '12.bc1'], 'contains': ['48.cv1', '48.cx1', '48.cz1'], 'core': '192.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4788, -1, 5773, -1], 'generators': [262459440, 135732240, 1508405, 159828480, 14933640], 'label': '768.1090070.24.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cr1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518392
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.o1', '12.ba1', '12.bd1'], 'contains': ['48.cv1', '48.cy1', '48.cz1'], 'core': '192.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4008, -1, 5465, -1], 'generators': [159828496, 262459440, 135732240, 12430214, 14933640], 'label': '768.1090070.24.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cs1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518393
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 12, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.i1', '12.n1', '12.u1', '12.y1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4960, -1, 4291, -1], 'generators': [23668578, 23, 7, 40723320, 14933656, 135732240, 262459440], 'label': '768.1090070.6.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '768.1090070', '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': '64.202'}
  • id: 68518394
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '12.l1', '12.q1'], 'contains': ['48.ct1', '48.cu1', '48.cw1', '48.cx1', '48.da1', '48.db1', '48.dd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5840, -1, 3385, -1], 'generators': [40723327, 11291167, 22186920, 262459440, 135732240], 'label': '768.1090070.24.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ct1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518395
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.q1'], 'contains': ['48.cu1', '48.cy1', '48.da1', '48.dc1', '48.df1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6246, -1, 2741, -1], 'generators': [11291167, 22186920, 40723336, 262459440, 135732240], 'label': '768.1090070.24.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cu1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518396
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '12.q1', '12.bd1'], 'contains': ['48.b1', '48.ct1', '48.cu1', '48.cw1', '48.cy1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [5074, -1, 3905, -1], 'generators': [40723327, 22186920, 262459440, 135732240, 11291160], 'label': '768.1090070.24.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cv1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518397
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.e1', '12.r1', '12.bb1', '12.bd1'], 'contains': ['48.b1', '48.cd1', '48.ce1', '48.cv1', '48.cz1'], 'core': '48.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [6014, -1, 3780, -1], 'generators': [22186920, 262459440, 135732240, 11291160, 1508405], 'label': '768.1090070.24.cw1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cw1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518398
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.l1'], 'contains': ['48.db1', '48.dc1', '48.dd1', '48.de1', '48.dg1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6698, -1, 2616, -1], 'generators': [22186936, 40723336, 14933647, 135732240, 262459440], 'label': '768.1090070.24.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cx1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518399
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.d1'], 'contains': ['48.dk1', '48.dl1', '48.dm2', '48.dn1', '48.dn2', '48.do1', '48.do2'], 'core': '768.a1', 'coset_action_label': '24T2407', 'count': 96, 'diagramx': [8963, -1, 1411, -1], 'generators': [243901463, 132089760, 22186936, 124836496, 1508405], 'label': '768.1090070.24.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '24.cy1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518400
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.f1', '12.d1'], 'contains': ['48.dn1', '48.do1', '48.dr1', '48.ds1', '48.dt1'], 'core': '192.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [9286, -1, 780, -1], 'generators': [243901463, 23, 124836496, 1508405, 7], 'label': '768.1090070.24.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '24.cz1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518401
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.cz2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1'], 'contains': ['48.dn2', '48.do2', '48.dr1', '48.ds1', '48.dt2'], 'core': '192.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [9054, -1, 1268, -1], 'generators': [23, 124836496, 94484903, 1508405, 7], 'label': '768.1090070.24.cz2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '24.cz2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68518402
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.c1', '8.d1', '16.b1'], 'contains': ['64.a1', '96.a1', '128.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9783, -1, 911, -1], 'generators': [40723320, 1467364, 262459440, 135732240], 'label': '768.1090070.32.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': '768.1090070', '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': '24.12'}
  • id: 68518403
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.e1', '16.b1'], 'contains': ['64.a1', '96.cc1', '128.b1'], 'core': '192.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [9477, -1, 403, -1], 'generators': [1467364, 262459440, 135732240, 1508405], 'label': '768.1090070.32.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': '768.1090070', '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': '24.12'}
  • id: 68518404
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1'], 'contains': ['12.o1', '12.p1', '12.w1', '12.x1', '12.y1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5042, -1, 4387, -1], 'generators': [280995863, 23, 7, 1508405, 14933656, 135732240, 262459440], 'label': '768.1090070.6.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.g1', 'projective_image': '768.1090070', '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': '64.202'}
  • id: 68518405
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '16.e1'], 'contains': ['64.b1', '96.ct1', '128.a1'], 'core': '192.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [9681, -1, 575, -1], 'generators': [23, 40723320, 1467364, 7], 'label': '768.1090070.32.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.e1', 'old_label': '32.c1', 'projective_image': '768.1090070', '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': '24.12'}
  • id: 68518406
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.f1', '16.e1'], 'contains': ['64.b1', '96.cv1', '128.b1'], 'core': '192.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [9516, -1, 215, -1], 'generators': [23, 1467364, 1508405, 7], 'label': '768.1090070.32.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.e1', 'old_label': '32.d1', 'projective_image': '768.1090070', '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': '24.12'}
  • id: 68518407
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1'], 'contains': ['64.d1', '96.cw1', '128.a1'], 'core': '768.a1', 'coset_action_label': '32T34628', 'count': 32, 'diagramx': [9921, -1, 478, -1], 'generators': [40723320, 135732263, 1467364, 262459447], 'label': '768.1090070.32.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.e1', 'old_label': '32.e1', 'projective_image': '768.1090070', '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': '12.3'}
  • id: 68518408
    {'ambient': '768.1090070', 'aut_centralizer_order': 2, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.e1', '8.f1'], 'contains': ['64.e1', '96.db1', '128.b1'], 'core': '768.a1', 'coset_action_label': '32T34622', 'count': 128, 'diagramx': [9442, -1, 109, -1], 'generators': [22186920, 1467364, 11291160, 1508405], 'label': '768.1090070.32.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1', 'old_label': '32.f1', 'projective_image': '768.1090070', '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': '24.12'}
  • id: 68518409
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.ce1', '24.cf1', '24.cg1'], 'contains': ['96.i1', '96.s1', '96.by1'], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5369, 4279, 4647, 6846], 'generators': [23, 262459440, 135732240, 7], 'label': '768.1090070.48.a1', 'mobius_quo': 2, 'mobius_sub': 24, 'normal_closure': '48.a1', 'normal_contained_in': ['12.a1', '24.a1'], 'normal_contains': ['192.a1', '192.b1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '768.1090070', '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: 68518410
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.8', 'aut_weyl_index': 256, 'centralizer': '12.a1', 'complements': ['16.e1'], 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '24.b1', '24.bw1', '24.cv1', '24.cw1'], 'contains': ['96.bo1', '96.bz1'], 'core': '48.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6405, 979, 3237, 4787], 'generators': [22186920, 262459440, 135732240, 11291160], 'label': '768.1090070.48.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.b1', 'normal_contained_in': ['12.a1', '24.b1'], 'normal_contains': ['192.a1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '768.1090070', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 68518411
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.c1', '24.t1', '24.bi1'], 'contains': ['96.b1', '96.c1', '96.g1', '96.u1', '96.v1', '96.bi1', '96.bp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3498, -1, 6019, -1], 'generators': [22186920, 40723320, 262459440, 7], 'label': '768.1090070.48.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '48.c1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 68518412
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.c1', '24.t1', '24.bn1'], 'contains': ['96.c1', '96.f1', '96.g1', '96.bh1', '96.bi1', '96.bp1', '96.bq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3638, -1, 5762, -1], 'generators': [22186920, 40723343, 262459440, 7], 'label': '768.1090070.48.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '48.d1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518413
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.j1', '24.bb1', '24.bq1'], 'contains': ['96.c1', '96.c2', '96.e1', '96.bg1', '96.bg2', '96.bn1', '96.br1', '96.ck1', '96.ck2', '96.ck3', '96.cx1', '96.cx2', '96.cx3'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7646, -1, 2114, -1], 'generators': [11291167, 22186920, 22186936, 262459440], 'label': '768.1090070.48.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.e1', 'projective_image': '768.1090070', '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: 68518414
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.j1', '24.bb1', '24.bw1'], 'contains': ['96.c1', '96.c2', '96.d1', '96.bg1', '96.bn1', '96.bn2', '96.bo1', '96.co1', '96.co2', '96.co3', '96.cy1', '96.cy2', '96.cy3'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7606, -1, 1997, -1], 'generators': [11291167, 22186920, 262459440, 7], 'label': '768.1090070.48.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.f1', 'projective_image': '768.1090070', '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': '1.1'}
  • id: 68518415
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.d1', '12.e1', '12.r1', '12.s1', '12.w1', '12.y1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6138, -1, 2817, -1], 'generators': [11291167, 23, 7, 1508405, 135732240, 262459440, 22186943], 'label': '768.1090070.6.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '768.1090070', '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': '32.46'}
  • id: 68518416
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.c1'], 'contains': ['96.b1', '96.f1', '96.i1', '96.t1', '96.bc1', '96.cf1', '96.cr1', '96.cw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4442, -1, 5156, -1], 'generators': [40723320, 135732263, 262459440, 7], 'label': '768.1090070.48.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '48.g1', 'projective_image': '768.1090070', '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: 68518417
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '24.cf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.e1', '24.f1', '24.t1', '24.bj1'], 'contains': ['96.h1', '96.k1', '96.o1', '96.u1', '96.bh1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1805, -1, 8201, -1], 'generators': [40723320, 14933656, 135732240, 16], 'label': '768.1090070.48.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.h1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518418
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.g1', '24.h1', '24.i1', '24.t1', '24.bk1'], 'contains': ['96.h1', '96.l1', '96.q1', '96.v1', '96.bq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2112, -1, 7222, -1], 'generators': [23, 40723320, 22186936, 262459440], 'label': '768.1090070.48.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.i1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518419
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.e1', '24.g1', '24.u1', '24.bl1'], 'contains': ['96.h1', '96.n1', '96.r1', '96.w1', '96.bs1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1102, -1, 8681, -1], 'generators': [261314645, 135732240, 303182760, 16], 'label': '768.1090070.48.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.j1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518420
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '48.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.h1', '24.v1', '24.bl1'], 'contains': ['96.h1', '96.n1', '96.x1', '96.bt1', '96.cg1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1174, -1, 8601, -1], 'generators': [40723320, 135732240, 1508405, 16], 'label': '768.1090070.48.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.k1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518421
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '24.g1', '24.v1', '24.w1', '24.bm1'], 'contains': ['96.h1', '96.p1', '96.ch1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2581, -1, 7117, -1], 'generators': [40723320, 135732240, 16, 1508409], 'label': '768.1090070.48.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.l1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518422
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.l2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.l2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '24.h1', '24.i1', '24.u1', '24.bm1'], 'contains': ['96.h1', '96.p1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2052, -1, 7573, -1], 'generators': [261314649, 135732240, 303182760, 16], 'label': '768.1090070.48.l2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.l2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68518423
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '48.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.i1', '24.w1', '24.bl1'], 'contains': ['96.h1', '96.r1', '96.y1', '96.bu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [750, -1, 8786, -1], 'generators': [40723320, 261314645, 135732240, 16], 'label': '768.1090070.48.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.m1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518424
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.j1', '24.ce1'], 'contains': ['96.c1', '96.i1', '96.ba1', '96.bb1', '96.ci1', '96.cs1', '96.cz1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6758, -1, 2739, -1], 'generators': [23, 11291167, 90842400, 135732247], 'label': '768.1090070.48.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.n1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518425
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.n2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.j1', '24.ce1'], 'contains': ['96.c2', '96.d1', '96.e1', '96.i1', '96.z1', '96.ci1', '96.ci2', '96.cs2', '96.cz1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6879, -1, 2350, -1], 'generators': [11291167, 135732263, 262459440, 7], 'label': '768.1090070.48.n2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.n2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518426
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '4.b1'], 'contains': ['16.a1', '24.a1', '32.a1', '32.c1', '32.e1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9746, -1, 644, -1], 'generators': [23, 40723320, 1467364, 262459440, 135732240, 7], 'label': '768.1090070.8.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '8.a1', 'projective_image': '768.1090070', '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: 68518427
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.cg1'], 'contains': ['96.g1', '96.i1', '96.be1', '96.bf1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3428, -1, 6124, -1], 'generators': [280995863, 135732263, 262459440, 7], 'label': '768.1090070.48.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '48.o1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518428
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.k1', '24.l1', '24.m1', '24.t1', '24.br1'], 'contains': ['96.k1', '96.m1', '96.q1', '96.bi1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2874, -1, 6441, -1], 'generators': [40723327, 14933656, 135732240, 16], 'label': '768.1090070.48.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.p1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518429
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bb1', '24.bq1'], 'contains': ['96.j1', '96.l1', '96.bg1', '96.bn2', '96.br1', '96.ck1', '96.ck2', '96.ck3'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7685, -1, 2055, -1], 'generators': [23, 11291167, 22186936, 262459440], 'label': '768.1090070.48.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.q1', 'projective_image': '768.1090070', '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: 68518430
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.e1', '24.k1', '24.x1', '24.bs1'], 'contains': ['96.k1', '96.n1', '96.r1', '96.bj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1541, -1, 8299, -1], 'generators': [255191776, 135732240, 1508405, 16], 'label': '768.1090070.48.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.r1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518431
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '48.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '24.l1', '24.n1', '24.y1', '24.bs1'], 'contains': ['96.k1', '96.n1', '96.bk1', '96.cl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3370, -1, 5097, -1], 'generators': [14933656, 135732240, 1508405, 16], 'label': '768.1090070.48.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.s1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518432
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.t1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.f1', '24.k1', '24.o1', '24.y1', '24.z1', '24.bu1'], 'contains': ['96.k1', '96.p1', '96.cm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3862, -1, 4913, -1], 'generators': [14933656, 135732240, 16, 1508409], 'label': '768.1090070.48.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.t1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518433
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.t2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.t2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '24.l1', '24.m1', '24.x1', '24.bu1'], 'contains': ['96.k1', '96.p1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3000, -1, 6840, -1], 'generators': [255191776, 135732240, 1508418, 16], 'label': '768.1090070.48.t2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.t2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68518434
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '48.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.m1', '24.p1', '24.z1', '24.bs1'], 'contains': ['96.k1', '96.r1', '96.bl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3197, -1, 6645, -1], 'generators': [14933656, 261314645, 135732240, 16], 'label': '768.1090070.48.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.u1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518435
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.n1', '24.o1', '24.p1', '24.ba1', '24.bv1'], 'contains': ['96.k1', '96.bm1', '96.cn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7466, -1, 2495, -1], 'generators': [14933656, 12430209, 135732240, 16], 'label': '768.1090070.48.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '48.v1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518436
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.n1', '24.o1', '24.p1', '24.bb1', '24.bw1'], 'contains': ['96.j1', '96.k1', '96.bg2', '96.bn1', '96.bo1', '96.co1', '96.co2', '96.co3'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7567, -1, 2291, -1], 'generators': [11291167, 22186920, 90842400, 7], 'label': '768.1090070.48.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '48.w1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518437
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '4.b1'], 'contains': ['16.a1', '24.cf1', '32.b1', '32.d1'], 'core': '48.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9411, -1, 400, -1], 'generators': [23, 1467364, 262459440, 135732240, 1508405, 7], 'label': '768.1090070.8.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '8.b1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 68518438
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.q1', '24.r1', '24.s1', '24.t1', '24.bx1'], 'contains': ['96.m1', '96.l1', '96.o1', '96.bp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2178, -1, 7841, -1], 'generators': [40723327, 23, 22186936, 262459440], 'label': '768.1090070.48.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.x1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518439
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.k1', '24.l1', '24.q1', '24.r1', '24.u1', '24.v1', '24.ca1'], 'contains': ['96.m1', '96.n1', '96.p1', '96.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2419, -1, 7402, -1], 'generators': [40723327, 135732240, 16, 1508409], 'label': '768.1090070.48.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.y1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518440
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.k1', '24.m1', '24.q1', '24.s1', '24.u1', '24.w1', '24.ca1'], 'contains': ['96.m1', '96.p1', '96.r1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2316, -1, 7491, -1], 'generators': [40723327, 261314645, 135732240, 16], 'label': '768.1090070.48.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.z1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518441
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.g1', '24.h1', '24.q1', '24.r1', '24.x1', '24.y1', '24.by1'], 'contains': ['96.l1', '96.n1', '96.p1', '96.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2244, -1, 7662, -1], 'generators': [135732240, 14933647, 14933663, 1508405], 'label': '768.1090070.48.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.ba1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518442
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.g1', '24.i1', '24.q1', '24.s1', '24.x1', '24.z1', '24.by1'], 'contains': ['96.l1', '96.p1', '96.r1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1998, -1, 7752, -1], 'generators': [261314645, 135732240, 14933647, 14933663], 'label': '768.1090070.48.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bb1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518443
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.e1', '24.q1', '24.bc1', '24.cc1'], 'contains': ['96.n1', '96.o1', '96.r1', '96.bv1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [903, -1, 8899, -1], 'generators': [261314645, 201398416, 135732240, 16], 'label': '768.1090070.48.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bc1', 'projective_image': '768.1090070', '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: 68518444
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.g1', '24.h1', '24.k1', '24.l1', '24.bc1', '24.bd1', '24.cb1'], 'contains': ['96.n1', '96.p1', '96.q1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1667, -1, 8044, -1], 'generators': [201398423, 135732240, 1508405, 16], 'label': '768.1090070.48.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bd1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518445
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '48.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.r1', '24.bd1', '24.cc1'], 'contains': ['96.n1', '96.o1', '96.bw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [974, -1, 9004, -1], 'generators': [135732240, 178346296, 1508405, 16], 'label': '768.1090070.48.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.be1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518446
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '24.q1', '24.bd1', '24.be1', '24.cd1'], 'contains': ['96.o1', '96.p1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1310, -1, 8539, -1], 'generators': [135732240, 178346296, 16, 1508409], 'label': '768.1090070.48.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bf1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518447
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bf2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.bf2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '24.r1', '24.s1', '24.bc1', '24.cd1'], 'contains': ['96.o1', '96.p1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1396, -1, 8476, -1], 'generators': [261314649, 201398416, 135732240, 16], 'label': '768.1090070.48.bf2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bf2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68518448
    {'ambient': '768.1090070', 'aut_centralizer_order': 2, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '4.c1'], 'contains': ['16.c1', '24.b1', '32.a1'], 'core': '24.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [9578, -1, 933, -1], 'generators': [22186920, 40723320, 1467364, 262459440, 135732240, 11291160], 'label': '768.1090070.8.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.c1', 'projective_image': '768.1090070', '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': '192.955'}
  • id: 68518449
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '48.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.s1', '24.be1', '24.cc1'], 'contains': ['96.o1', '96.r1', '96.bx1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [680, -1, 9201, -1], 'generators': [261314645, 135732240, 178346296, 16], 'label': '768.1090070.48.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bg1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518450
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.g1', '24.i1', '24.k1', '24.m1', '24.bc1', '24.be1', '24.cb1'], 'contains': ['96.p1', '96.r1', '96.q1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1354, -1, 8118, -1], 'generators': [201398423, 135732240, 16, 1508409], 'label': '768.1090070.48.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bh1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518451
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.t1', '24.u1', '24.v1', '24.w1'], 'contains': ['96.b1', '96.f1', '96.h1', '96.m1', '96.s1', '96.cf1', '96.cr1', '96.ct1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3698, -1, 5683, -1], 'generators': [23, 40723320, 262459440, 7], 'label': '768.1090070.48.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bi1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518452
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.t1', '24.x1', '24.y1', '24.z1', '24.ba1', '24.bb1', '24.ce1'], 'contains': ['96.c1', '96.k1', '96.l1', '96.s1', '96.ci2', '96.cs2', '96.cu1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5540, -1, 3097, -1], 'generators': [23, 11291167, 90842400, 7], 'label': '768.1090070.48.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bj1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518453
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.bj2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bb1', '24.ce1'], 'contains': ['96.c2', '96.d1', '96.e1', '96.j1', '96.s1', '96.ci1', '96.cs1', '96.cs2', '96.cu1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [7026, -1, 2232, -1], 'generators': [23, 11291167, 262459440, 7], 'label': '768.1090070.48.bj2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.bj2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518454
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.u1', '24.v1', '24.x1', '24.y1', '24.bc1', '24.bd1', '24.cf1'], 'contains': ['96.n1', '96.p1', '96.s1', '96.cj1', '96.cv1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2941, -1, 6929, -1], 'generators': [23, 135732240, 1508405, 7], 'label': '768.1090070.48.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bk1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518455
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '24.bc1', '24.bd1', '24.be1', '24.cg1'], 'contains': ['96.g1', '96.o1', '96.q1', '96.s1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1933, -1, 7947, -1], 'generators': [23, 280995863, 262459440, 7], 'label': '768.1090070.48.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bl1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518456
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.u1', '24.w1', '24.x1', '24.z1', '24.bc1', '24.be1', '24.cf1'], 'contains': ['96.p1', '96.r1', '96.s1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2488, -1, 7312, -1], 'generators': [23, 261314645, 135732240, 7], 'label': '768.1090070.48.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bm1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518457
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.bf1', '24.bj1'], 'contains': ['96.t1', '96.u1', '96.ba1', '96.be1', '96.bh1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2662, -1, 6539, -1], 'generators': [40723320, 14933656, 135732240, 262459456], 'label': '768.1090070.48.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.bn1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518458
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.bk1'], 'contains': ['96.t1', '96.v1', '96.bb1', '96.bf1', '96.bq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3565, -1, 5860, -1], 'generators': [40723320, 135732263, 22186936, 262459440], 'label': '768.1090070.48.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '48.bo1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518459
    {'ambient': '768.1090070', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['16.d1', '24.cl1', '32.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9840, -1, 786, -1], 'generators': [22186936, 1467364, 40723320, 14933647, 135732240, 262459440], 'label': '768.1090070.8.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': '768.1090070', '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': '96.70'}
  • id: 68518460
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1', '24.bl1'], 'contains': ['96.t1', '96.w1', '96.bd1', '96.bt1', '96.bu1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [614, -1, 9496, -1], 'generators': [135732240, 262459456, 1508405, 303182760], 'label': '768.1090070.48.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.bp1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518461
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.bp2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1', '24.bl1'], 'contains': ['96.t1', '96.x1', '96.y1', '96.bd1', '96.bs1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [547, -1, 9299, -1], 'generators': [40723320, 135732240, 262459456, 1508405], 'label': '768.1090070.48.bp2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.bp2', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518462
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '24.bf1', '24.ci1'], 'contains': ['96.u1', '96.w1', '96.y1', '96.bj1', '96.bl1', '96.bv1', '96.bx1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [342, -1, 9776, -1], 'generators': [40723320, 261314645, 135732240, 14933640], 'label': '768.1090070.48.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.bq1', 'projective_image': '768.1090070', '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: 68518463
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '24.bf1', '24.ci1'], 'contains': ['96.u1', '96.w1', '96.x1', '96.bj1', '96.bk1', '96.bv1', '96.bw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [416, -1, 9595, -1], 'generators': [40723320, 135732240, 1508405, 14933640], 'label': '768.1090070.48.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.br1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518464
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.bg1', '24.br1'], 'contains': ['96.ba1', '96.bc1', '96.bf1', '96.bi1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4283, -1, 5235, -1], 'generators': [40723327, 14933656, 135732240, 262459456], 'label': '768.1090070.48.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.bs1', 'projective_image': '768.1090070', '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': '8.2'}
  • id: 68518465
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.j1', '24.bq1'], 'contains': ['96.z1', '96.bb1', '96.bg1', '96.bn2', '96.br1', '96.cx1', '96.cx2', '96.cx3'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7525, -1, 2173, -1], 'generators': [11291167, 135732263, 22186936, 262459440], 'label': '768.1090070.48.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.bt1', 'projective_image': '768.1090070', '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': '1.1'}
  • id: 68518466
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bf1', '24.bh1', '24.bs1'], 'contains': ['96.ba1', '96.bd1', '96.bj1', '96.bk1', '96.bl1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3127, -1, 6750, -1], 'generators': [14933656, 135732240, 262459456, 1508405], 'label': '768.1090070.48.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bu1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518467
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bg1', '24.bh1', '24.bv1'], 'contains': ['96.ba1', '96.bm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5984, -1, 3790, -1], 'generators': [14933656, 12430209, 135732240, 262459456], 'label': '768.1090070.48.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.bv1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518468
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.j1', '24.bh1', '24.bw1'], 'contains': ['96.z1', '96.ba1', '96.bg2', '96.bn1', '96.bo1', '96.cy1', '96.cy2', '96.cy3'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7340, -1, 2409, -1], 'generators': [11291167, 22186920, 90842400, 135732247], 'label': '768.1090070.48.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '48.bw1', 'projective_image': '768.1090070', '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: 68518469
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.bx1'], 'contains': ['96.bc1', '96.bb1', '96.be1', '96.bp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4216, -1, 5604, -1], 'generators': [40723327, 135732263, 22186936, 262459440], 'label': '768.1090070.48.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '48.bx1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518470
    {'ambient': '768.1090070', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '768.a1', 'complements': ['384.h1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.a1', '8.a1', '8.c1', '8.d1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9623, 3737, 807, 2583], 'generators': [11291167, 1467364, 23, 7, 40723320, 135732240, 262459440, 22186943], 'label': '768.1090070.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '768.1090070', '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': '768.1090070'}
  • id: 68518471
    {'ambient': '768.1090070', 'aut_centralizer_order': 2, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '4.c1'], 'contains': ['16.c1', '24.cw1', '32.b1', '32.f1'], 'core': '48.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [9303, -1, 537, -1], 'generators': [22186920, 1467364, 262459440, 135732240, 11291160, 1508405], 'label': '768.1090070.8.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.e1', 'projective_image': '768.1090070', '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': '192.955'}
  • id: 68518472
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bf1', '24.cc1'], 'contains': ['96.bd1', '96.be1', '96.bv1', '96.bw1', '96.bx1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [77, -1, 9974, -1], 'generators': [201398416, 135732240, 262459456, 1508405], 'label': '768.1090070.48.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.by1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518473
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '24.bf1', '24.cp1'], 'contains': ['96.bh1', '96.bj1', '96.bl1', '96.bs1', '96.bu1', '96.bv1', '96.bx1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [144, -1, 9841, -1], 'generators': [261314645, 40723336, 135732240, 14933640], 'label': '768.1090070.48.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.bz1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518474
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '24.bf1', '24.cp1'], 'contains': ['96.bh1', '96.bj1', '96.bk1', '96.bs1', '96.bt1', '96.bv1', '96.bw1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [282, -1, 9693, -1], 'generators': [40723336, 135732240, 1508405, 14933640], 'label': '768.1090070.48.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.ca1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518475
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.n1', '24.bh1', '24.co1'], 'contains': ['96.bg2', '96.bk1', '96.bm1', '96.da1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6811, -1, 2818, -1], 'generators': [22186936, 135732240, 11291176, 1508405], 'label': '768.1090070.48.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1', 'old_label': '48.cb1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518476
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.p1', '24.bh1', '24.co1'], 'contains': ['96.bg2', '96.bl1', '96.bm1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6711, -1, 3367, -1], 'generators': [261314645, 22186936, 135732240, 11291176], 'label': '768.1090070.48.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1', 'old_label': '48.cc1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518477
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.n1', '24.bh1', '24.cw1'], 'contains': ['96.bk1', '96.bm1', '96.bo1', '96.db1', '96.db2'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7392, -1, 2660, -1], 'generators': [22186920, 135732240, 11291160, 1508405], 'label': '768.1090070.48.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1', 'old_label': '48.cd1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518478
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.p1', '24.bh1', '24.cw1'], 'contains': ['96.bl1', '96.bm1', '96.bo1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6656, -1, 3167, -1], 'generators': [22186920, 261314645, 135732240, 11291160], 'label': '768.1090070.48.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1', 'old_label': '48.ce1', 'projective_image': '768.1090070', '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: 68518479
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.bi1', '24.bj1', '24.bk1', '24.bl1', '24.bm1'], 'contains': ['96.a1', '96.b1', '96.h1', '96.t1', '96.by1', '96.cb1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3331, -1, 5939, -1], 'generators': [23, 40723320, 262459440, 135732240], 'label': '768.1090070.48.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cf1', 'projective_image': '768.1090070', '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': '8.3'}
  • id: 68518480
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bi1', '24.bn1', '24.bo1', '24.bp1', '24.bq1', '24.bw1', '24.ce1'], 'contains': ['96.c1', '96.c2', '96.j1', '96.z1', '96.by1', '96.bz1', '96.ca1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6204, -1, 3038, -1], 'generators': [22186920, 262459440, 135732240, 7], 'label': '768.1090070.48.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cg1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518481
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1', '24.br1', '24.bs1', '24.bt1', '24.bu1', '24.bv1', '24.bw1', '24.ce1'], 'contains': ['96.d1', '96.k1', '96.ba1', '96.by1', '96.bz1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4904, -1, 4588, -1], 'generators': [14933656, 262459440, 135732240, 16], 'label': '768.1090070.48.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ch1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518482
    {'ambient': '768.1090070', 'aut_centralizer_order': 1, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1'], 'contains': ['16.f1', '24.cz1', '32.d1', '32.f1'], 'core': '192.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [9357, -1, 237, -1], 'generators': [243901463, 23, 1467364, 124836496, 1508405, 7], 'label': '768.1090070.8.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '8.f1', 'projective_image': '768.1090070', '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': '96.227'}
  • id: 68518483
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.bn1', '24.br1', '24.bx1', '24.ca1'], 'contains': ['96.f1', '96.m1', '96.bc1', '96.by1', '96.cb1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4335, -1, 5525, -1], 'generators': [40723327, 23, 262459440, 135732240], 'label': '768.1090070.48.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ci1', 'projective_image': '768.1090070', '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': '8.3'}
  • id: 68518484
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '24.bq1', '24.bx1', '24.by1', '24.bz1', '24.ce1'], 'contains': ['96.e1', '96.l1', '96.bb1', '96.by1', '96.ca1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5329, -1, 3958, -1], 'generators': [262459440, 135732240, 11291176, 7], 'label': '768.1090070.48.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cj1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518485
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bl1', '24.bs1', '24.ca1', '24.by1', '24.cb1', '24.cc1', '24.cf1'], 'contains': ['96.n1', '96.r1', '96.bd1', '96.by1', '96.cc1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1608, -1, 8397, -1], 'generators': [262459440, 135732240, 1508405, 16], 'label': '768.1090070.48.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.ck1', 'projective_image': '768.1090070', '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: 68518486
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bi1', '24.bn1', '24.bo1', '24.bp1', '24.bt1', '24.bz1', '24.cg1'], 'contains': ['96.g1', '96.by1', '96.cd1', '96.ce1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5271, -1, 4421, -1], 'generators': [23, 262459440, 159828487, 135732240], 'label': '768.1090070.48.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cl1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518487
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1', '24.bp1', '24.bx1', '24.cc1', '24.cd1', '24.cg1'], 'contains': ['96.o1', '96.be1', '96.by1', '96.cd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3273, -1, 6237, -1], 'generators': [23, 280995863, 262459440, 135732240], 'label': '768.1090070.48.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cm1', 'projective_image': '768.1090070', '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': '8.3'}
  • id: 68518488
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bm1', '24.bu1', '24.ca1', '24.by1', '24.cb1', '24.cd1', '24.cf1'], 'contains': ['96.p1', '96.by1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2729, -1, 7019, -1], 'generators': [262459440, 135732240, 1508418, 16], 'label': '768.1090070.48.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.cn1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518489
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 192, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '24.bo1', '24.br1', '24.cb1', '24.cg1'], 'contains': ['96.q1', '96.bf1', '96.by1', '96.ce1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4146, -1, 5341, -1], 'generators': [23, 262459440, 135732240, 280995856], 'label': '768.1090070.48.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.co1', 'projective_image': '768.1090070', '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': '8.3'}
  • id: 68518490
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.bi1', '24.bj1', '24.ch1', '24.ci1', '24.cj1', '24.ck1'], 'contains': ['96.a1', '96.u1', '96.bz1', '96.cd1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4388, -1, 5446, -1], 'generators': [22186920, 40723320, 262459440, 135732240], 'label': '768.1090070.48.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cp1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518491
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1', '24.bk1', '24.ch1', '24.ck1', '24.cl1'], 'contains': ['96.a1', '96.v1', '96.ca1', '96.ce1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5061, -1, 4217, -1], 'generators': [40723320, 262459440, 135732240, 11291176], 'label': '768.1090070.48.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cq1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518492
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.bl1', '24.ci1'], 'contains': ['96.a1', '96.w1', '96.x1', '96.y1', '96.cc1'], 'core': '96.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [832, -1, 9102, -1], 'generators': [40723320, 262459440, 135732240, 1508405], 'label': '768.1090070.48.cr1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.cr1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518493
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.211', 'aut_weyl_index': 64, 'centralizer': '12.a1', 'complements': ['64.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1', '6.h1'], 'contains': ['24.j1', '24.bb1', '24.bq1', '24.bw1', '24.ce1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6997, 2759, 2050, 1665], 'generators': [23, 11291167, 262459440, 135732240, 22186943, 7], 'label': '768.1090070.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['48.a1', '48.b1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '768.1090070', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 68518494
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.ct1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bj1', '24.bn1', '24.cn1', '24.cp1', '24.cq1', '24.ct1', '24.cv1'], 'contains': ['96.bh1', '96.bz1', '96.cb1', '96.cd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4758, -1, 4807, -1], 'generators': [22186920, 40723343, 262459440, 135732240], 'label': '768.1090070.48.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cs1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518495
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.cu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bi1', '24.bn1', '24.br1', '24.cm1', '24.ct1', '24.cu1', '24.cv1'], 'contains': ['96.bi1', '96.bz1', '96.cb1', '96.ce1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5421, -1, 4118, -1], 'generators': [40723327, 22186920, 262459440, 135732240], 'label': '768.1090070.48.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ct1', 'projective_image': '768.1090070', '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: 68518496
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.cs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bq1', '24.bw1', '24.ch1', '24.cm1', '24.cn1', '24.co1'], 'contains': ['96.bg1', '96.bg2', '96.bz1', '96.ca1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6339, -1, 3296, -1], 'generators': [262459440, 135732240, 14933647, 11291160], 'label': '768.1090070.48.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cu1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518497
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.cv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bs1', '24.ci1', '24.cp1', '24.co1', '24.cr1', '24.cs1', '24.cw1'], 'contains': ['96.bj1', '96.bk1', '96.bl1', '96.bz1', '96.cc1'], 'core': '192.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3061, -1, 6342, -1], 'generators': [262459440, 135732240, 1508405, 14933640], 'label': '768.1090070.48.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cv1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518498
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.cw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bo1', '24.bp1', '24.bt1', '24.ck1', '24.cm1', '24.ct1', '24.cv1'], 'contains': ['96.bz1', '96.cd1', '96.ce1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5587, -1, 3708, -1], 'generators': [22186920, 262459440, 159828487, 135732240], 'label': '768.1090070.48.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cw1', 'projective_image': '768.1090070', '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: 68518499
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.cx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.bp1', '24.bt1', '24.cn1', '24.cr1', '24.ct1'], 'contains': ['96.bz1', '96.cd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5206, -1, 4518, -1], 'generators': [22186920, 262459440, 135732240, 159828480], 'label': '768.1090070.48.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cx1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518500
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.cy1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bo1', '24.bt1', '24.ch1', '24.cs1', '24.cu1', '24.cv1'], 'contains': ['96.bz1', '96.ce1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5136, -1, 4029, -1], 'generators': [22186920, 262459440, 135732240, 159828503], 'label': '768.1090070.48.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cy1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518501
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.cz1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bv1', '24.cj1', '24.cq1', '24.co1', '24.cr1', '24.cs1', '24.cw1'], 'contains': ['96.bm1', '96.bz1'], 'core': '192.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5001, -1, 4717, -1], 'generators': [262459440, 135732240, 12430214, 14933640], 'label': '768.1090070.48.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cz1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518502
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.da1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1', '24.bw1', '24.ck1', '24.ct1', '24.cu1'], 'contains': ['96.bn1', '96.bn2', '96.bz1', '96.ca1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6551, -1, 2897, -1], 'generators': [11291167, 22186920, 262459440, 135732240], 'label': '768.1090070.48.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.da1', 'projective_image': '768.1090070', '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: 68518503
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.db1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bi1', '24.bn1', '24.bx1', '24.cm1', '24.cn1', '24.ct1', '24.cx1'], 'contains': ['96.bp1', '96.cb1', '96.ca1', '96.cd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5487, -1, 4315, -1], 'generators': [262459440, 159828487, 135732240, 11291176], 'label': '768.1090070.48.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': '768.1090070', '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': '8.5'}
  • id: 68518504
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.e1'], 'contains': ['24.d1', '24.f1', '24.g1', '24.i1', '24.k1', '24.m1', '24.q1', '24.s1', '24.t1', '24.u1', '24.w1', '24.x1', '24.z1', '24.bc1', '24.be1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2075, -1, 8105, -1], 'generators': [23, 40723320, 14933656, 261314645, 135732240, 7], 'label': '768.1090070.12.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.b1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 68518505
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.dc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '24.bn1', '24.cm1', '24.cu1', '24.cx1'], 'contains': ['96.bq1', '96.cb1', '96.ca1', '96.ce1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5647, -1, 3619, -1], 'generators': [40723327, 262459440, 135732240, 11291176], 'label': '768.1090070.48.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dc1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518506
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.dh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '24.cp1'], 'contains': ['96.bs1', '96.bt1', '96.bu1', '96.cb1', '96.cc1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [482, -1, 9398, -1], 'generators': [40723336, 262459440, 135732240, 1508405], 'label': '768.1090070.48.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.dd1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518507
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.dd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bo1', '24.bp1', '24.bz1', '24.ch1', '24.cm1', '24.ct1', '24.cx1'], 'contains': ['96.ca1', '96.cd1', '96.ce1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6156, -1, 3448, -1], 'generators': [280995863, 262459440, 135732240, 11291176], 'label': '768.1090070.48.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.de1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518508
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.de1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1', '24.bz1', '24.ck1', '24.cn1', '24.cx1'], 'contains': ['96.ca1', '96.cd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5911, -1, 3529, -1], 'generators': [262459440, 201398416, 135732240, 11291176], 'label': '768.1090070.48.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.df1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518509
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '48.df1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1', '24.bz1', '24.cl1', '24.cm1', '24.cu1'], 'contains': ['96.ca1', '96.ce1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6602, -1, 2967, -1], 'generators': [201398423, 262459440, 135732240, 11291176], 'label': '768.1090070.48.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.dg1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518510
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '48.dg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.8', 'aut_weyl_index': 256, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '24.bq1', '24.cl1', '24.cx1'], 'contains': ['96.br1', '96.ca1'], 'core': '192.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7300, -1, 2581, -1], 'generators': [22186936, 262459440, 135732240, 14933647], 'label': '768.1090070.48.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '48.dh1', 'projective_image': '768.1090070', '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': '6.2'}
  • id: 68518511
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.di1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cc1', '24.ci1', '24.cp1'], 'contains': ['96.bv1', '96.bw1', '96.bx1', '96.cc1', '96.cd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [18, -1, 9907, -1], 'generators': [201398400, 262459440, 135732240, 1508405], 'label': '768.1090070.48.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '48.di1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518512
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.dj1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1'], 'contains': ['96.cf1', '96.cg1', '96.ch1', '96.cj1', '96.cq1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4630, -1, 5018, -1], 'generators': [40723320, 90842423, 262459447, 1508405], 'label': '768.1090070.48.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.v1', 'old_label': '48.dj1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518513
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.dk1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.y1', '24.cy1'], 'contains': ['96.ci2', '96.cj1', '96.cl1', '96.cm1', '96.cp1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7775, -1, 1918, -1], 'generators': [14933656, 90842423, 262459447, 1508405], 'label': '768.1090070.48.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '48.dk1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518514
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.dl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.ba1', '24.cy1'], 'contains': ['96.ci2', '96.cn1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8823, -1, 1474, -1], 'generators': [14933656, 90842423, 12430209, 262459447], 'label': '768.1090070.48.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '48.dl1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518515
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.e1'], 'contains': ['24.e1', '24.f1', '24.g1', '24.h1', '24.k1', '24.l1', '24.q1', '24.r1', '24.t1', '24.u1', '24.v1', '24.x1', '24.y1', '24.bc1', '24.bd1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2201, -1, 7905, -1], 'generators': [23, 40723320, 14933656, 135732240, 1508405, 7], 'label': '768.1090070.12.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.c1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518516
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.dm1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.j1', '24.bb1'], 'contains': ['96.ci1', '96.ci2', '96.ck1', '96.ck2', '96.co1', '96.cx1', '96.cx2', '96.cy1', '96.cy2'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8342, -1, 1662, -1], 'generators': [243901463, 11291167, 132089760, 7], 'label': '768.1090070.48.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.dm1', 'projective_image': '768.1090070', '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': '1.1'}
  • id: 68518517
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.dm2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.j1', '24.bb1', '24.cy1'], 'contains': ['96.ci1', '96.ci2', '96.ck3', '96.co2', '96.co3', '96.cx1', '96.cx3', '96.cy1', '96.cy3'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8654, -1, 1603, -1], 'generators': [243901463, 11291167, 132089760, 22186936], 'label': '768.1090070.48.dm2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '48.dm2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dm2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68518518
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.dn1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.n1', '24.cy1', '24.cz1'], 'contains': ['96.cl1', '96.cn1', '96.co2', '96.da1', '96.db1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9286, -1, 672, -1], 'generators': [22186920, 14933656, 22186936, 1508405], 'label': '768.1090070.48.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '48.dn1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518519
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.dn2', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.n1', '24.cy1', '24.cz2'], 'contains': ['96.cl1', '96.cn1', '96.co3', '96.da1', '96.db2'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9219, -1, 1145, -1], 'generators': [94484880, 14933656, 243901456, 1508405], 'label': '768.1090070.48.dn2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '48.dn2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dn2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68518520
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.do1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.o1', '24.cy1', '24.cz1'], 'contains': ['96.cm1', '96.cn1', '96.co2'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9160, -1, 762, -1], 'generators': [22186920, 14933656, 22186936, 12430209], 'label': '768.1090070.48.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '48.do1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518521
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.do2', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.o1', '24.cy1', '24.cz2'], 'contains': ['96.cm1', '96.cn1', '96.co3'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9105, -1, 1235, -1], 'generators': [94484880, 14933656, 243901456, 12430209], 'label': '768.1090070.48.do2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '48.do2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.do2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68518522
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.dp1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.j1', '24.bb1'], 'contains': ['96.ck1', '96.ck3', '96.co1', '96.co3', '96.cs1', '96.cs2', '96.cx2', '96.cx3', '96.cy1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8613, -1, 1544, -1], 'generators': [243901463, 11291167, 135732263, 7], 'label': '768.1090070.48.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.dp1', 'projective_image': '768.1090070', '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': '1.1'}
  • id: 68518523
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.dp2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.j1', '24.bb1'], 'contains': ['96.ck2', '96.ck3', '96.co1', '96.co2', '96.cs1', '96.cs2', '96.cx1', '96.cy2', '96.cy3'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8178, -1, 1721, -1], 'generators': [243901463, 11291167, 22186920, 7], 'label': '768.1090070.48.dp2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.dp2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dp2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518524
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '48.dq1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '24.v1'], 'contains': ['96.cg1', '96.ch1', '96.cq1', '96.ct1', '96.cv1'], 'core': '192.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [5713, -1, 3879, -1], 'generators': [23, 40723320, 1508405, 7], 'label': '768.1090070.48.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.v1', 'old_label': '48.dq1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518525
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.dr1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.y1', '24.cz1', '24.cz2'], 'contains': ['96.cl1', '96.cm1', '96.cp1', '96.cu1', '96.cv1'], 'core': '192.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [9045, -1, 1324, -1], 'generators': [23, 14933656, 1508405, 7], 'label': '768.1090070.48.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '48.dr1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518526
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.h1'], 'contains': ['24.n1', '24.o1', '24.y1', '24.ba1', '24.bb1', '24.cy1', '24.cz1', '24.cz2'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [8005, -1, 1617, -1], 'generators': [243901463, 23, 14933656, 135732240, 1508405, 7], 'label': '768.1090070.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '12.d1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518527
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '48.ds1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.ba1', '24.cz1', '24.cz2'], 'contains': ['96.cn1', '96.cu1'], 'core': '192.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [9346, -1, 1055, -1], 'generators': [23, 14933656, 12430209, 7], 'label': '768.1090070.48.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '48.ds1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518528
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.dt1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.f1', '24.bb1', '24.cz1'], 'contains': ['96.ck1', '96.co2', '96.cu1'], 'core': '192.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [9393, -1, 833, -1], 'generators': [243901463, 23, 124836496, 7], 'label': '768.1090070.48.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '48.dt1', 'projective_image': '768.1090070', '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': '6.1'}
  • id: 68518529
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.dt2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.bb1', '24.cz2'], 'contains': ['96.ck2', '96.ck3', '96.co1', '96.co3', '96.cu1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [8992, -1, 1403, -1], 'generators': [243901463, 23, 11291167, 7], 'label': '768.1090070.48.dt2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '48.dt2', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518530
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.du1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.g1', '24.j1'], 'contains': ['96.cx2', '96.cy3', '96.cz1'], 'core': '768.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8032, -1, 1839, -1], 'generators': [243901463, 135732263, 22186936, 124836496], 'label': '768.1090070.48.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '48.du1', 'projective_image': '768.1090070', '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': '3.1'}
  • id: 68518531
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '48.du2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.j1'], 'contains': ['96.cx1', '96.cx3', '96.cy1', '96.cy2', '96.cz1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7923, -1, 1780, -1], 'generators': [243901463, 11291167, 135732263, 22186936], 'label': '768.1090070.48.du2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.du2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.du2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518532
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.c1', '16.d1', '32.a1', '32.b1'], 'contains': ['192.a1', '256.a1'], 'core': '192.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9844, -1, 364, -1], 'generators': [1467364, 262459440, 135732240], 'label': '768.1090070.64.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': '768.1090070', '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': '24.12'}
  • id: 68518533
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.f1', '32.c1', '32.d1'], 'contains': ['192.b1', '256.a1'], 'core': '192.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [9791, -1, 260, -1], 'generators': [23, 1467364, 7], 'label': '768.1090070.64.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.e1', 'old_label': '64.b1', 'projective_image': '768.1090070', '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': '24.12'}
  • id: 68518534
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.e1'], 'contains': ['128.a1', '128.b1', '192.x1'], 'core': '768.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [9722, -1, 944, -1], 'generators': [40723320, 1467364, 1508405], 'label': '768.1090070.64.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.c1', 'old_label': '64.c1', 'projective_image': '768.1090070', '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': '6.1'}
  • id: 68518535
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.g1', '32.e1'], 'contains': ['192.bc1', '256.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [9944, -1, 312, -1], 'generators': [135732263, 1467364, 262459447], 'label': '768.1090070.64.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.e1', 'old_label': '64.d1', 'projective_image': '768.1090070', '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': '12.3'}
  • id: 68518536
    {'ambient': '768.1090070', 'aut_centralizer_order': 2, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '16.f1', '16.g1', '32.f1'], 'contains': ['192.bh1', '256.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [9757, -1, 72, -1], 'generators': [22186920, 1467364, 11291160], 'label': '768.1090070.64.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1', 'old_label': '64.e1', 'projective_image': '768.1090070', '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': '24.12'}
  • id: 68518537
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.h1'], 'contains': ['24.o1', '24.p1', '24.z1', '24.ba1', '24.bb1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [7574, -1, 2149, -1], 'generators': [243901463, 23, 23668578, 14933656, 135732240, 7], 'label': '768.1090070.12.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '12.e1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518538
    {'ambient': '768.1090070', 'aut_centralizer_order': 2, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.f1', '16.g1'], 'contains': ['192.bi1', '256.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [9982, -1, 154, -1], 'generators': [1467364, 22186936, 14933647], 'label': '768.1090070.64.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.f1', 'old_label': '64.f1', 'projective_image': '768.1090070', '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': '12.3'}
  • id: 68518539
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '96.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '24.a1', 'complements': ['8.f1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.cf1', '48.cp1', '48.cq1', '48.cr1'], 'contains': ['192.a1', '192.e1'], 'core': '96.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3626, 4433, 5727, 8166], 'generators': [40723320, 262459440, 135732240], 'label': '768.1090070.96.a1', 'mobius_quo': 0, 'mobius_sub': 96, 'normal_closure': '96.a1', 'normal_contained_in': ['24.a1', '24.b1'], 'normal_contains': ['192.a1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '768.1090070', 'quotient_action_image': '24.12', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 68518540
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.c1', '48.g1', '48.bi1', '48.cf1'], 'contains': ['192.c1', '192.e1', '192.i1', '192.n1', '192.w1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3586, -1, 5409, -1], 'generators': [40723320, 262459440, 16], 'label': '768.1090070.96.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '96.b1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68518541
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.c1', '48.d1', '48.e1', '48.f1', '48.n1', '48.bj1', '48.cg1'], 'contains': ['192.c1', '192.g1', '192.h1', '192.p1', '192.y1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5937, -1, 3219, -1], 'generators': [22186920, 262459440, 7], 'label': '768.1090070.96.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.c1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68518542
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.c2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.f1', '48.n2', '48.bj2', '48.cg1'], 'contains': ['192.c1', '192.g2', '192.h2', '192.p1', '192.y1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6712, -1, 2645, -1], 'generators': [262459440, 14933647, 7], 'label': '768.1090070.96.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.c2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518543
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.f1', '48.n2', '48.bj2', '48.ch1'], 'contains': ['192.c1', '192.g2', '192.q1', '192.z1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6557, -1, 2704, -1], 'generators': [14933656, 262459440, 16], 'label': '768.1090070.96.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.d1', 'projective_image': '768.1090070', '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: 68518544
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.d1', '48.g1', '48.bi1', '48.cj1'], 'contains': ['192.c1', '192.i1', '192.i2', '192.s1', '192.bb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4082, -1, 5350, -1], 'generators': [40723343, 262459440, 16], 'label': '768.1090070.96.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '96.e1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518545
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.e1', '48.n2', '48.bj2', '48.ci1'], 'contains': ['192.c1', '192.h2', '192.r1', '192.ba1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6603, -1, 2881, -1], 'generators': [262459440, 11291176, 7], 'label': '768.1090070.96.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.f1', 'projective_image': '768.1090070', '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: 68518546
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.c1', '48.d1', '48.o1', '48.bl1', '48.cl1'], 'contains': ['192.c1', '192.k1', '192.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3188, -1, 5909, -1], 'generators': [280995840, 262459440, 16], 'label': '768.1090070.96.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '96.g1', 'projective_image': '768.1090070', '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: 68518547
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1', '48.i1', '48.j1', '48.k1', '48.l1', '48.l2', '48.m1', '48.bi1', '48.cf1'], 'contains': ['192.d1', '192.e1', '192.i2', '192.n1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2416, -1, 7149, -1], 'generators': [23, 40723320, 262459440], 'label': '768.1090070.96.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.h1', 'projective_image': '768.1090070', '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: 68518548
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1'], 'contains': ['24.bi1', '24.bk1', '24.bo1', '24.bq1', '24.bz1', '24.ch1', '24.ck1', '24.cl1', '24.cm1', '24.cu1', '24.cx1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5978, -1, 3207, -1], 'generators': [22186936, 11291167, 23, 40723320, 135732240, 262459440], 'label': '768.1090070.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.f1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518549
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '48.g1', '48.n1', '48.n2', '48.o1'], 'contains': ['192.c1', '192.f1', '192.o1', '192.v1', '192.bc1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5579, -1, 4175, -1], 'generators': [135732263, 262459440, 7], 'label': '768.1090070.96.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.i1', 'projective_image': '768.1090070', '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': '1.1'}
  • id: 68518550
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.p1', '48.w1', '48.bj2', '48.cg1'], 'contains': ['192.d1', '192.g2', '192.h2', '192.p1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6751, -1, 2822, -1], 'generators': [23, 262459440, 11291160], 'label': '768.1090070.96.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.j1', 'projective_image': '768.1090070', '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': '1.1'}
  • id: 68518551
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '6.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.h1', '48.q1', '48.r1', '48.s1', '48.t1', '48.t2', '48.u1', '48.v1', '48.w1', '48.bj1', '48.ch1'], 'contains': ['192.d1', '192.g1', '192.q1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3874, -1, 4730, -1], 'generators': [14933656, 135732240, 16], 'label': '768.1090070.96.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.k1', 'projective_image': '768.1090070', '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: 68518552
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1', '48.x1', '48.ba1', '48.bb1', '48.bi1', '48.cj1'], 'contains': ['192.d1', '192.i1', '192.s1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2788, -1, 5987, -1], 'generators': [40723327, 23, 262459440], 'label': '768.1090070.96.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.l1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518553
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.i1', '48.p1', '48.x1', '48.y1', '48.z1', '48.bj1', '48.ci1'], 'contains': ['192.d1', '192.h1', '192.r1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3665, -1, 5669, -1], 'generators': [23, 22186936, 262459440], 'label': '768.1090070.96.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.m1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518554
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.j1', '48.k1', '48.r1', '48.s1', '48.ba1', '48.y1', '48.bc1', '48.bd1', '48.be1', '48.bk1', '48.ck1'], 'contains': ['192.d1', '192.j1', '192.t1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1658, -1, 8133, -1], 'generators': [135732240, 1508405, 16], 'label': '768.1090070.96.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.n1', 'projective_image': '768.1090070', '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: 68518555
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1', '48.x1', '48.bc1', '48.be1', '48.bf1', '48.bf2', '48.bg1', '48.bl1', '48.cm1'], 'contains': ['192.d1', '192.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1338, -1, 8352, -1], 'generators': [23, 280995863, 262459440], 'label': '768.1090070.96.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.o1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518556
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.l1', '48.l2', '48.t1', '48.t2', '48.ba1', '48.bb1', '48.y1', '48.z1', '48.bd1', '48.bf1', '48.bf2', '48.bh1', '48.bk1', '48.bm1', '48.cn1'], 'contains': ['192.d1', '192.u1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2534, -1, 7019, -1], 'generators': [135732240, 16, 1508409], 'label': '768.1090070.96.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.p1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518557
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.j1', '48.m1', '48.r1', '48.u1', '48.bb1', '48.z1', '48.bc1', '48.bg1', '48.bh1', '48.bm1', '48.ck1'], 'contains': ['192.d1', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1430, -1, 8255, -1], 'generators': [261314645, 135732240, 16], 'label': '768.1090070.96.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.q1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518558
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1', '48.q1', '48.bd1', '48.bh1', '48.bl1', '48.co1'], 'contains': ['192.d1', '192.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2468, -1, 6832, -1], 'generators': [23, 262459440, 280995856], 'label': '768.1090070.96.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.r1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518559
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 12, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.e1'], 'contains': ['24.d1', '24.e1', '24.bf1', '24.bj1', '24.bl1', '24.bs1', '24.cc1', '24.ci1', '24.cp1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [608, -1, 9307, -1], 'generators': [40723320, 14933656, 262459440, 135732240, 1508405, 16], 'label': '768.1090070.12.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': '768.1090070', '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': '64.202'}
  • id: 68518560
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.a1', '48.bi1', '48.bj1', '48.bj2', '48.bk1', '48.bl1', '48.bm1'], 'contains': ['192.b1', '192.c1', '192.d1', '192.o1', '192.v1'], 'core': '192.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4679, -1, 4648, -1], 'generators': [23, 262459440, 7], 'label': '768.1090070.96.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.s1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518561
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1', '48.bn1', '48.bo1', '48.bp1', '48.bp2', '48.cf1'], 'contains': ['192.e1', '192.f1', '192.i2', '192.w1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2914, -1, 6046, -1], 'generators': [40723320, 135732263, 262459440], 'label': '768.1090070.96.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.t1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518562
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.cf1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.c1', '48.h1', '48.bn1', '48.bq1', '48.br1', '48.cp1'], 'contains': ['192.e1', '192.g1', '192.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2378, -1, 7205, -1], 'generators': [22186920, 40723320, 262459440], 'label': '768.1090070.96.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.u1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518564
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.j1', '48.bp1', '48.bq1', '48.br1', '48.cr1'], 'contains': ['192.e1', '192.j1', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [778, -1, 9126, -1], 'generators': [261314645, 135732240, 303182760], 'label': '768.1090070.96.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.w1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518565
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1', '48.bp2', '48.br1', '48.cr1'], 'contains': ['192.e1', '192.j1', '192.x1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [983, -1, 8811, -1], 'generators': [40723320, 135732240, 1508405], 'label': '768.1090070.96.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.x1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518566
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1', '48.bp2', '48.bq1', '48.cr1'], 'contains': ['192.e1', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [708, -1, 9052, -1], 'generators': [40723320, 261314645, 135732240], 'label': '768.1090070.96.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.y1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518567
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.n2', '48.bs1', '48.bw1', '48.cg1'], 'contains': ['192.f1', '192.g2', '192.h2', '192.y1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6338, -1, 3161, -1], 'generators': [135732263, 262459440, 11291160], 'label': '768.1090070.96.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.z1', 'projective_image': '768.1090070', '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': '1.1'}
  • id: 68518568
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.n1', '48.bn1', '48.bt1', '48.bu1', '48.bv1', '48.bw1', '48.ch1'], 'contains': ['192.f1', '192.g1', '192.z1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4884, -1, 4492, -1], 'generators': [14933656, 135732240, 262459456], 'label': '768.1090070.96.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ba1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518569
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1', '48.bt1', '48.bx1', '48.cj1'], 'contains': ['192.f1', '192.i1', '192.bb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4356, -1, 5291, -1], 'generators': [40723327, 135732263, 262459440], 'label': '768.1090070.96.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '96.bb1', 'projective_image': '768.1090070', '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': '4.1'}
  • id: 68518570
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 12, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.e1'], 'contains': ['24.f1', '24.bj1', '24.bm1', '24.bu1', '24.cd1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2759, -1, 7160, -1], 'generators': [16, 40723320, 14933656, 1508409, 135732240, 262459440], 'label': '768.1090070.12.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.h1', 'projective_image': '768.1090070', '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': '64.202'}
  • id: 68518571
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1', '48.bo1', '48.bs1', '48.bx1', '48.ci1'], 'contains': ['192.f1', '192.h1', '192.ba1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5433, -1, 4116, -1], 'generators': [135732263, 22186936, 262459440], 'label': '768.1090070.96.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.bc1', 'projective_image': '768.1090070', '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: 68518572
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bp1', '48.bp2', '48.bu1', '48.by1', '48.ck1'], 'contains': ['192.f1', '192.j1', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [919, -1, 8866, -1], 'generators': [135732240, 262459456, 1508405], 'label': '768.1090070.96.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.bd1', 'projective_image': '768.1090070', '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: 68518573
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1', '48.bn1', '48.bx1', '48.by1', '48.cm1'], 'contains': ['192.f1', '192.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2840, -1, 6237, -1], 'generators': [280995863, 135732263, 262459440], 'label': '768.1090070.96.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.be1', 'projective_image': '768.1090070', '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: 68518574
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1', '48.bo1', '48.bt1', '48.co1'], 'contains': ['192.f1', '192.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3752, -1, 5539, -1], 'generators': [135732263, 262459440, 280995856], 'label': '768.1090070.96.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '96.bf1', 'projective_image': '768.1090070', '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': '4.1'}
  • id: 68518575
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.cf1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.d1', '48.h1', '48.bn1', '48.cb1', '48.cc1', '48.ct1'], 'contains': ['192.g1', '192.i2', '192.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2344, -1, 7094, -1], 'generators': [22186920, 40723343, 262459440], 'label': '768.1090070.96.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '96.bg1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518576
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.c1', '48.d1', '48.q1', '48.bt1', '48.cu1'], 'contains': ['192.g1', '192.i1', '192.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3802, -1, 5464, -1], 'generators': [40723327, 22186920, 262459440], 'label': '768.1090070.96.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '96.bh1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518577
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.f1', '48.p1', '48.bs1', '48.cs1'], 'contains': ['192.g2', '192.h1', '192.h2', '192.bd1', '192.bd2'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7001, -1, 2527, -1], 'generators': [262459440, 14933647, 11291160], 'label': '768.1090070.96.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.bi1', 'projective_image': '768.1090070', '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: 68518578
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bg2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.w1', '48.bw1', '48.bz1', '48.ca1', '48.cs1'], 'contains': ['192.g1', '192.h2', '192.bd1', '192.bd2'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6791, -1, 3102, -1], 'generators': [22186920, 262459440, 14933663], 'label': '768.1090070.96.bg2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '96.bi2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68518579
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.bj1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.r1', '48.bq1', '48.br1', '48.bu1', '48.cb1', '48.cc1', '48.cv1'], 'contains': ['192.g1', '192.j1', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [656, -1, 8977, -1], 'generators': [135732240, 1508405, 255191760], 'label': '768.1090070.96.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.bj1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518580
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.s1', '48.br1', '48.bu1', '48.cc1', '48.bz1', '48.cd1', '48.cv1'], 'contains': ['192.g1', '192.j1', '192.be1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3056, -1, 5056, -1], 'generators': [135732240, 1508405, 14933640], 'label': '768.1090070.96.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bk1', 'projective_image': '768.1090070', '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': '8.3'}
  • id: 68518581
    {'ambient': '768.1090070', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '3072.dv', 'aut_weyl_index': 2, 'centralizer': '768.a1', 'complements': ['384.c1', '384.g1', '384.h1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.h1', '8.b1', '8.e1', '8.f1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9340, 825, 509, 764], 'generators': [11291167, 1467364, 23, 7, 1508405, 135732240, 262459440, 22186943], 'label': '768.1090070.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '768.1090070', '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': '768.1090070'}
  • id: 68518582
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '6.c1', '6.f1'], 'contains': ['24.bj1', '24.bv1', '24.cj1', '24.cq1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4625, -1, 5372, -1], 'generators': [23668578, 16, 40723320, 14933656, 135732240, 262459440], 'label': '768.1090070.12.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.i1', 'projective_image': '768.1090070', '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': '64.202'}
  • id: 68518583
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.bl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.u1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.u1', '48.bq1', '48.bu1', '48.cb1', '48.ca1', '48.ce1', '48.cv1'], 'contains': ['192.g1', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2966, -1, 6645, -1], 'generators': [261314645, 135732240, 14933640], 'label': '768.1090070.96.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bl1', 'projective_image': '768.1090070', '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': '8.3'}
  • id: 68518584
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.bm1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.v1', '48.bv1', '48.bz1', '48.ca1', '48.cd1', '48.ce1', '48.cz1'], 'contains': ['192.g1', '192.bf1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6185, -1, 3298, -1], 'generators': [135732240, 12430214, 14933640], 'label': '768.1090070.96.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1', 'old_label': '96.bm1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518585
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.f1', '48.w1', '48.bw1', '48.da1'], 'contains': ['192.g1', '192.g2', '192.h2', '192.bg1', '192.bg2'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6961, -1, 2763, -1], 'generators': [11291167, 22186920, 262459440], 'label': '768.1090070.96.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.bn1', 'projective_image': '768.1090070', '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: 68518586
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bn2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.f1', '48.p1', '48.bs1', '48.da1'], 'contains': ['192.g2', '192.h1', '192.bg1', '192.bg2'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7040, -1, 2468, -1], 'generators': [11291167, 262459440, 22186927], 'label': '768.1090070.96.bn2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.bn2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bn2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518587
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.bo1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.b1', '48.f1', '48.w1', '48.bw1', '48.cd1', '48.ce1'], 'contains': ['192.g1', '192.g2', '192.bh1', '192.bh2'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6875, -1, 3043, -1], 'generators': [22186920, 262459440, 11291160], 'label': '768.1090070.96.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '96.bo1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518588
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.bp1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.c1', '48.d1', '48.x1', '48.bx1', '48.db1'], 'contains': ['192.i1', '192.h1', '192.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3837, -1, 5783, -1], 'generators': [40723327, 262459440, 22186927], 'label': '768.1090070.96.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '96.bp1', 'projective_image': '768.1090070', '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: 68518589
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bq1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.d1', '48.i1', '48.bo1', '48.dc1'], 'contains': ['192.i2', '192.h1', '192.l1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3702, -1, 5614, -1], 'generators': [40723343, 262459440, 22186927], 'label': '768.1090070.96.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '96.bq1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518590
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bs1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.j1', '48.bp2', '48.cb1', '48.cc1', '48.dh1'], 'contains': ['192.i2', '192.j1', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [462, -1, 9250, -1], 'generators': [303182776, 135732240, 1508405], 'label': '768.1090070.96.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.br1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518591
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1', '48.bp1', '48.cc1', '48.dh1'], 'contains': ['192.i2', '192.j1', '192.bj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [836, -1, 8922, -1], 'generators': [40723336, 135732240, 1508405], 'label': '768.1090070.96.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.bs1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518592
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.bu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1', '48.bp1', '48.cb1', '48.dh1'], 'contains': ['192.i2', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [535, -1, 9373, -1], 'generators': [261314645, 40723336, 135732240], 'label': '768.1090070.96.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.bt1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518593
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.b1', '6.c1'], 'contains': ['24.b1', '24.bi1', '24.bj1', '24.bp1', '24.bt1', '24.bw1', '24.ch1', '24.ck1', '24.cn1', '24.ct1', '24.cv1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [5224, -1, 4076, -1], 'generators': [22186920, 11291167, 7, 40723320, 135732240, 262459440], 'label': '768.1090070.12.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.j1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518594
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.br1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.e1', '48.p1', '48.bs1', '48.dg1'], 'contains': ['192.h1', '192.h2', '192.bi1', '192.bi2'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7497, -1, 2586, -1], 'generators': [22186936, 262459440, 14933647], 'label': '768.1090070.96.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.bu1', 'projective_image': '768.1090070', '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: 68518595
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.bv1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bc1', '48.bq1', '48.br1', '48.by1', '48.cb1', '48.cc1', '48.di1'], 'contains': ['192.j1', '192.k1', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [287, -1, 9682, -1], 'generators': [201398400, 135732240, 1508405], 'label': '768.1090070.96.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.bv1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518596
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.be1', '48.br1', '48.by1', '48.cc1', '48.di1'], 'contains': ['192.j1', '192.k1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [337, -1, 9595, -1], 'generators': [135732240, 178346296, 1508405], 'label': '768.1090070.96.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.bw1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518597
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bg1', '48.bq1', '48.by1', '48.cb1', '48.di1'], 'contains': ['192.k1', '192.m1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [236, -1, 9776, -1], 'generators': [261314645, 135732240, 178346296], 'label': '768.1090070.96.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.bx1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518598
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '96.by1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '48.cf1', '48.cg1', '48.ch1', '48.cj1', '48.ci1', '48.ck1', '48.cl1', '48.cm1', '48.cn1', '48.co1'], 'contains': ['192.a1', '192.c1', '192.d1', '192.f1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4612, -1, 5232, -1], 'generators': [23, 262459440, 135732240], 'label': '768.1090070.96.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.by1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518599
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.b1', '48.cg1', '48.ch1', '48.cp1', '48.ct1', '48.cu1', '48.cs1', '48.cv1', '48.cw1', '48.cx1', '48.cy1', '48.cz1', '48.da1'], 'contains': ['192.a1', '192.g1', '192.g2'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5251, -1, 4332, -1], 'generators': [22186920, 262459440, 135732240], 'label': '768.1090070.96.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.bz1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518600
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '96.cb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cf1', '48.cj1', '48.ct1', '48.cu1', '48.db1', '48.dc1', '48.dh1'], 'contains': ['192.a1', '192.i1', '192.i2'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4241, -1, 5173, -1], 'generators': [40723343, 262459440, 135732240], 'label': '768.1090070.96.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.ca1', 'projective_image': '768.1090070', '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': '8.3'}
  • id: 68518601
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1', '48.ci1', '48.cq1', '48.cs1', '48.da1', '48.db1', '48.dc1', '48.dd1', '48.de1', '48.df1', '48.dg1'], 'contains': ['192.a1', '192.h1', '192.h2'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5800, -1, 3489, -1], 'generators': [262459440, 135732240, 11291176], 'label': '768.1090070.96.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.cb1', 'projective_image': '768.1090070', '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: 68518602
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cc1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.b1', '48.ck1', '48.cr1', '48.cv1', '48.dh1', '48.di1'], 'contains': ['192.a1', '192.j1', '192.m1'], 'core': '192.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1055, -1, 8756, -1], 'generators': [262459440, 135732240, 1508405], 'label': '768.1090070.96.cc1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '96.cc1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518603
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cl1', '48.cm1', '48.cp1', '48.ct1', '48.cw1', '48.cx1', '48.db1', '48.dd1', '48.de1', '48.di1'], 'contains': ['192.a1', '192.k1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4831, -1, 4570, -1], 'generators': [262459440, 159828487, 135732240], 'label': '768.1090070.96.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.cd1', 'projective_image': '768.1090070', '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': '8.3'}
  • id: 68518604
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 24, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1'], 'contains': ['24.g1', '24.h1', '24.i1', '24.bk1', '24.bl1', '24.bm1', '24.by1', '24.cb1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1675, -1, 7985, -1], 'generators': [40723320, 262459440, 135732240, 14933647, 14933663, 1508405], 'label': '768.1090070.12.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.k1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518605
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.ce1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cl1', '48.co1', '48.cq1', '48.cu1', '48.cw1', '48.cy1', '48.dc1', '48.dd1', '48.df1'], 'contains': ['192.a1', '192.l1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5325, -1, 4253, -1], 'generators': [159828496, 262459440, 135732240], 'label': '768.1090070.96.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '96.ce1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518606
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.cf1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.g1', '48.bi1', '48.dj1'], 'contains': ['192.n1', '192.o1', '192.s1', '192.w1', '192.bb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4548, -1, 4997, -1], 'generators': [40723320, 90842423, 7], 'label': '768.1090070.96.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1', 'old_label': '96.cf1', 'projective_image': '768.1090070', '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: 68518607
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.cg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.k1', '48.dj1', '48.dq1'], 'contains': ['192.n1', '192.t1', '192.x1', '192.bj1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4484, -1, 4938, -1], 'generators': [40723320, 1508405, 16], 'label': '768.1090070.96.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.v1', 'old_label': '96.cg1', 'projective_image': '768.1090070', '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: 68518608
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.ch1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.l1', '48.dj1', '48.dq1'], 'contains': ['192.n1', '192.u1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4731, -1, 4808, -1], 'generators': [40723320, 1508418, 16], 'label': '768.1090070.96.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.v1', 'old_label': '96.ch1', 'projective_image': '768.1090070', '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: 68518609
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.ci1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.n1', '48.n2', '48.bj2', '48.dm1', '48.dm2'], 'contains': ['192.o1', '192.p1', '192.y1', '192.z1', '192.ba1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7153, -1, 2292, -1], 'generators': [23, 11291167, 262459447], 'label': '768.1090070.96.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.ci1', 'projective_image': '768.1090070', '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: 68518610
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.ci2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.n2', '48.bj1', '48.dk1', '48.dl1', '48.dm1', '48.dm2'], 'contains': ['192.o1', '192.q1', '192.r1', '192.y1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7587, -1, 2115, -1], 'generators': [11291167, 90842423, 7], 'label': '768.1090070.96.ci2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '96.ci2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ci2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68518611
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.cj1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bk1', '48.dj1', '48.dk1'], 'contains': ['192.o1', '192.t1', '192.u1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5215, -1, 4387, -1], 'generators': [90842423, 262459447, 1508405], 'label': '768.1090070.96.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '96.cj1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518612
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.ck1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.p1', '48.dm1', '48.dp1', '48.dt1'], 'contains': ['192.p1', '192.r1', '192.bd1', '192.bg1', '192.bi1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8636, -1, 1526, -1], 'generators': [23, 11291167, 22186936], 'label': '768.1090070.96.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.ck1', 'projective_image': '768.1090070', '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: 68518613
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.ck2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.p1', '48.dm1', '48.dp2', '48.dt2'], 'contains': ['192.p1', '192.r1', '192.bd2', '192.bg1', '192.bi2'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8177, -1, 1821, -1], 'generators': [11291167, 243901456, 262459463], 'label': '768.1090070.96.ck2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.ck2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ck2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518614
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.ck3', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.e1', '48.p1', '48.dm2', '48.dp1', '48.dp2', '48.dt2'], 'contains': ['192.p1', '192.r1', '192.bd1', '192.bd2', '192.bg2', '192.bi2'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8703, -1, 1703, -1], 'generators': [11291167, 22186936, 262459463], 'label': '768.1090070.96.ck3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.ck3', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ck3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518615
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1'], 'contains': ['24.bn1', '24.bp1', '24.bq1', '24.bx1', '24.bz1', '24.cm1', '24.cn1', '24.ct1', '24.cx1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5850, -1, 3385, -1], 'generators': [22186936, 11291167, 280995863, 23, 135732240, 262459440], 'label': '768.1090070.12.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.l1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518616
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '96.cl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.s1', '48.dk1', '48.dn1', '48.dn2', '48.dr1'], 'contains': ['192.q1', '192.t1', '192.be1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8969, -1, 1311, -1], 'generators': [14933656, 1508405, 16], 'label': '768.1090070.96.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '96.cl1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518617
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '96.cm1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.t1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.t1', '48.dk1', '48.do1', '48.do2', '48.dr1'], 'contains': ['192.q1', '192.u1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8909, -1, 1389, -1], 'generators': [14933656, 1508418, 16], 'label': '768.1090070.96.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '96.cm1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518618
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '96.cn1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.v1', '48.dl1', '48.dn1', '48.dn2', '48.do1', '48.do2', '48.ds1'], 'contains': ['192.q1', '192.bf1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9151, -1, 1070, -1], 'generators': [14933656, 12430214, 16], 'label': '768.1090070.96.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '96.cn1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518619
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.co1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.f1', '48.w1', '48.dm1', '48.dp1', '48.dp2', '48.dt2'], 'contains': ['192.p1', '192.q1', '192.bd2', '192.bg1', '192.bg2', '192.bh2'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8582, -1, 1644, -1], 'generators': [11291167, 243901440, 7], 'label': '768.1090070.96.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.co1', 'projective_image': '768.1090070', '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: 68518620
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.co2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.f1', '48.w1', '48.dm2', '48.dn1', '48.do1', '48.dp2', '48.dt1'], 'contains': ['192.p1', '192.q1', '192.bd1', '192.bg1', '192.bh1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [9051, -1, 1200, -1], 'generators': [11291167, 22186920, 7], 'label': '768.1090070.96.co2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '96.co2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.co2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68518621
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.co3', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.f1', '48.w1', '48.dm2', '48.dn2', '48.do2', '48.dp1', '48.dt2'], 'contains': ['192.p1', '192.q1', '192.bd1', '192.bg2', '192.bh2'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8855, -1, 1467, -1], 'generators': [11291167, 94484880, 7], 'label': '768.1090070.96.co3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '96.co3', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.co3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68518622
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '96.cq1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.ba1', '48.dj1', '48.dq1'], 'contains': ['192.s1', '192.t1', '192.u1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4781, -1, 4883, -1], 'generators': [40723343, 1508418, 16], 'label': '768.1090070.96.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.v1', 'old_label': '96.cp1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518623
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '96.cp1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.y1', '48.dk1', '48.dr1'], 'contains': ['192.r1', '192.t1', '192.u1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7076, -1, 2988, -1], 'generators': [14933647, 14933663, 1508405], 'label': '768.1090070.96.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.y1', 'old_label': '96.cq1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518624
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.cr1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1', '48.bi1'], 'contains': ['192.n1', '192.s1', '192.v1', '192.w1', '192.bb1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4316, -1, 5114, -1], 'generators': [40723320, 262459463, 7], 'label': '768.1090070.96.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1', 'old_label': '96.cr1', 'projective_image': '768.1090070', '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': '1.1'}
  • id: 68518625
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cs1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.n1', '48.bj2', '48.dp1', '48.dp2'], 'contains': ['192.p1', '192.v1', '192.z1', '192.ba1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7252, -1, 2351, -1], 'generators': [11291167, 262459447, 262459463], 'label': '768.1090070.96.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.cs1', 'projective_image': '768.1090070', '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: 68518626
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '6.e1'], 'contains': ['24.k1', '24.l1', '24.m1', '24.br1', '24.bs1', '24.bu1', '24.ca1', '24.cb1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2839, -1, 6829, -1], 'generators': [40723327, 14933656, 262459440, 135732240, 1508405, 16], 'label': '768.1090070.12.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': '768.1090070', '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': '64.202'}
  • id: 68518627
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cs2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.n2', '48.bj1', '48.bj2', '48.dp1', '48.dp2'], 'contains': ['192.p1', '192.q1', '192.r1', '192.v1', '192.y1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7317, -1, 2233, -1], 'generators': [11291167, 262459463, 7], 'label': '768.1090070.96.cs2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.cs2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cs2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518628
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.ct1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.c1', '48.bi1', '48.dq1'], 'contains': ['192.b1', '192.n1', '192.s1'], 'core': '192.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5533, -1, 3920, -1], 'generators': [23, 40723320, 7], 'label': '768.1090070.96.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '96.ct1', 'projective_image': '768.1090070', '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': '6.1'}
  • id: 68518629
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cu1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.bj1', '48.bj2', '48.dr1', '48.ds1', '48.dt1', '48.dt2'], 'contains': ['192.b1', '192.p1', '192.q1', '192.r1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [9008, -1, 1585, -1], 'generators': [23, 11291167, 7], 'label': '768.1090070.96.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '96.cu1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518630
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '96.cv1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.d1', '48.bk1', '48.dq1', '48.dr1'], 'contains': ['192.b1', '192.t1', '192.u1'], 'core': '192.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [7755, -1, 2936, -1], 'generators': [23, 1508405, 7], 'label': '768.1090070.96.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '96.cv1', 'projective_image': '768.1090070', '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': '4.2'}
  • id: 68518631
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '96.cw1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1', '48.g1'], 'contains': ['192.w1', '192.bb1', '192.bc1'], 'core': '768.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5617, -1, 4057, -1], 'generators': [40723320, 135732263, 262459447], 'label': '768.1090070.96.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '96.cw1', 'projective_image': '768.1090070', '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': '3.1'}
  • id: 68518632
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cx1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.e1', '48.bs1', '48.dm1', '48.dm2', '48.dp2', '48.du2'], 'contains': ['192.y1', '192.ba1', '192.bd1', '192.bd2', '192.bg1', '192.bi2'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7896, -1, 1938, -1], 'generators': [11291167, 243901440, 22186936], 'label': '768.1090070.96.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.cx1', 'projective_image': '768.1090070', '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: 68518633
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cx2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.bs1', '48.dm1', '48.dp1', '48.du1'], 'contains': ['192.y1', '192.ba1', '192.bd2', '192.bg2', '192.bi1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8138, -1, 1997, -1], 'generators': [11291167, 135732263, 243901456], 'label': '768.1090070.96.cx2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.cx2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cx2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518634
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cx3', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.e1', '48.bs1', '48.dm2', '48.dp1', '48.du2'], 'contains': ['192.y1', '192.ba1', '192.bd1', '192.bg2', '192.bi2'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7834, -1, 1880, -1], 'generators': [11291167, 22186936, 90842423], 'label': '768.1090070.96.cx3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.cx3', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cx3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518635
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cy1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.f1', '48.bw1', '48.dm1', '48.dm2', '48.dp1', '48.du2'], 'contains': ['192.y1', '192.z1', '192.bd1', '192.bg1', '192.bg2', '192.bh2'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [8423, -1, 1762, -1], 'generators': [11291167, 22186920, 262459447], 'label': '768.1090070.96.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.cy1', 'projective_image': '768.1090070', '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: 68518636
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cy2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.f1', '48.bw1', '48.dm1', '48.dp2', '48.du2'], 'contains': ['192.y1', '192.z1', '192.bd2', '192.bg1', '192.bh2'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7676, -1, 2174, -1], 'generators': [11291167, 243901440, 262459447], 'label': '768.1090070.96.cy2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.cy2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cy2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518637
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16883', 'aut_weyl_index': 24, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '6.f1'], 'contains': ['24.bg1', '24.br1', '24.bv1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5119, -1, 4279, -1], 'generators': [40723327, 23668578, 14933656, 262459440, 135732240, 16], 'label': '768.1090070.12.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': '768.1090070', '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': '64.202'}
  • id: 68518638
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cy3', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.f1', '48.bw1', '48.dm2', '48.dp2', '48.du1'], 'contains': ['192.y1', '192.z1', '192.bd2', '192.bg2', '192.bh1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7966, -1, 2056, -1], 'generators': [11291167, 132089760, 262459447], 'label': '768.1090070.96.cy3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.cy3', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cy3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518639
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '96.cz1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.n1', '48.n2', '48.du1', '48.du2'], 'contains': ['192.y1', '192.z1', '192.ba1', '192.bc1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7114, -1, 2409, -1], 'generators': [11291167, 135732263, 262459447], 'label': '768.1090070.96.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.cz1', 'projective_image': '768.1090070', '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: 68518645
    {'ambient': '768.1090070', 'aut_centralizer_order': 1024, 'aut_label': '192.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '96.a1', '96.by1', '96.bz1', '96.cb1', '96.ca1', '96.cc1', '96.cd1', '96.ce1'], 'contains': ['384.a1'], 'core': '192.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4794, 4433, 4684, 8166], 'generators': [262459440, 135732240], 'label': '768.1090070.192.a1', 'mobius_quo': -1, 'mobius_sub': -192, 'normal_closure': '192.a1', 'normal_contained_in': ['48.a1', '48.b1', '96.a1'], 'normal_contains': ['768.a1'], 'normalizer': '1.a1', 'old_label': '192.a1', 'projective_image': '768.1090070', 'quotient_action_image': '6.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '192.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68518646
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '192.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '6.a1', 'complements': ['4.c1'], 'conjugacy_class_count': 2, 'contained_in': ['64.b1', '96.s1', '96.ct1', '96.cu1', '96.cv1'], 'contains': ['384.b1'], 'core': '192.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8234, 9175, 3408, 9485], 'generators': [23, 7], 'label': '768.1090070.192.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.b1', 'normal_contained_in': ['48.a1'], 'normal_contains': ['768.a1'], 'normalizer': '1.a1', 'old_label': '192.b1', 'projective_image': '768.1090070', 'quotient_action_image': '6.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '192.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68518647
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.b1', '96.c1', '96.c2', '96.d1', '96.f1', '96.e1', '96.g1', '96.i1', '96.s1', '96.by1'], 'contains': ['384.a1', '384.b1', '384.d1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5158, -1, 4462, -1], 'generators': [262459440, 16], 'label': '768.1090070.192.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.c1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518648
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.b1', '6.d1', '6.g1'], 'contains': ['24.bs1', '24.bt1', '24.bv1', '24.cr1', '24.cs1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4959, -1, 5112, -1], 'generators': [280995863, 14933656, 262459440, 135732240, 1508405, 16], 'label': '768.1090070.12.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.o1', 'projective_image': '768.1090070', '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': '64.202'}
  • id: 68518649
    {'ambient': '768.1090070', 'aut_centralizer_order': 1024, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '96.j1', '96.k1', '96.m1', '96.l1', '96.n1', '96.o1', '96.p1', '96.r1', '96.q1', '96.s1', '96.by1'], 'contains': ['384.a1', '384.b1'], 'core': '768.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3707, -1, 5688, -1], 'generators': [23, 262459440], 'label': '768.1090070.192.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': '768.1090070', '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: 68518650
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '96.b1', '96.h1', '96.t1', '96.u1', '96.v1', '96.w1', '96.x1', '96.y1'], 'contains': ['384.a1', '384.c1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3042, -1, 6076, -1], 'generators': [40723320, 262459440], 'label': '768.1090070.192.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '192.e1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518651
    {'ambient': '768.1090070', 'aut_centralizer_order': 1024, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1', '96.t1', '96.z1', '96.ba1', '96.bc1', '96.bb1', '96.bd1', '96.be1', '96.bf1', '96.by1'], 'contains': ['384.a1', '384.d1'], 'core': '768.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4557, -1, 5203, -1], 'generators': [135732263, 262459440], 'label': '768.1090070.192.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.f1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518652
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.c1', '96.k1', '96.u1', '96.ba1', '96.bh1', '96.bi1', '96.bg2', '96.bj1', '96.bk1', '96.bl1', '96.bm1', '96.bn1', '96.bo1', '96.bz1'], 'contains': ['384.a1', '384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4596, -1, 4559, -1], 'generators': [22186920, 262459440], 'label': '768.1090070.192.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.g1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518653
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.g2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c2', '96.d1', '96.j1', '96.z1', '96.bg1', '96.bn1', '96.bn2', '96.bo1', '96.bz1'], 'contains': ['384.a1', '384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6485, -1, 2763, -1], 'generators': [262459440, 14933640], 'label': '768.1090070.192.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.g2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518654
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '96.f1', '96.m1', '96.bc1', '96.bi1', '96.bp1', '96.cb1'], 'contains': ['384.a1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4082, -1, 5350, -1], 'generators': [40723336, 262459440], 'label': '768.1090070.192.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '192.h1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518655
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '192.i2', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1', '96.h1', '96.t1', '96.bh1', '96.bq1', '96.bs1', '96.bt1', '96.bu1', '96.cb1'], 'contains': ['384.a1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2914, -1, 6017, -1], 'generators': [40723343, 262459440], 'label': '768.1090070.192.i2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '192.h2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68518656
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c1', '96.l1', '96.v1', '96.bb1', '96.bg1', '96.bn2', '96.bp1', '96.bq1', '96.br1', '96.ca1'], 'contains': ['384.a1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5267, -1, 4404, -1], 'generators': [262459440, 22186927], 'label': '768.1090070.192.h1', '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': '768.1090070', '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: 68518657
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.h2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c2', '96.e1', '96.j1', '96.z1', '96.bg1', '96.bg2', '96.bn1', '96.br1', '96.ca1'], 'contains': ['384.a1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6676, -1, 2822, -1], 'generators': [262459440, 11291176], 'label': '768.1090070.192.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.i2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518658
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.n1', '96.w1', '96.x1', '96.bd1', '96.bj1', '96.bk1', '96.bs1', '96.bt1', '96.bv1', '96.bw1', '96.cc1'], 'contains': ['384.a1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [928, -1, 8866, -1], 'generators': [135732240, 1508405], 'label': '768.1090070.192.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '192.j1', 'projective_image': '768.1090070', '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: 68518659
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '6.d1', '6.g1'], 'contains': ['24.bt1', '24.bu1', '24.bv1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5039, -1, 4399, -1], 'generators': [280995863, 16, 14933656, 1508409, 135732240, 262459440], 'label': '768.1090070.12.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.p1', 'projective_image': '768.1090070', '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': '64.202'}
  • id: 68518660
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.g1', '96.o1', '96.u1', '96.be1', '96.bh1', '96.bp1', '96.bv1', '96.bw1', '96.bx1', '96.cd1'], 'contains': ['384.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2380, -1, 7094, -1], 'generators': [280995840, 262459440], 'label': '768.1090070.192.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '192.k1', 'projective_image': '768.1090070', '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: 68518661
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.r1', '96.w1', '96.y1', '96.bd1', '96.bj1', '96.bl1', '96.bs1', '96.bu1', '96.bv1', '96.bx1', '96.cc1'], 'contains': ['384.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [727, -1, 9014, -1], 'generators': [261314645, 135732240], 'label': '768.1090070.192.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '192.l1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518662
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1', '96.q1', '96.v1', '96.bf1', '96.bi1', '96.bq1', '96.ce1'], 'contains': ['384.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3763, -1, 5595, -1], 'generators': [262459440, 280995856], 'label': '768.1090070.192.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '192.m1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518663
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.b1', '96.h1', '96.cf1', '96.cg1', '96.ch1', '96.cr1', '96.ct1'], 'contains': ['384.b1', '384.c1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4478, -1, 4938, -1], 'generators': [23, 40723320], 'label': '768.1090070.192.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1', 'old_label': '192.n1', 'projective_image': '768.1090070', '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: 68518664
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '192.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.i1', '96.s1', '96.cf1', '96.ci1', '96.ci2', '96.cj1'], 'contains': ['384.b1', '384.d1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5414, -1, 4175, -1], 'generators': [90842423, 7], 'label': '768.1090070.192.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '192.o1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518665
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['96.c1', '96.c2', '96.j1', '96.ci1', '96.ck1', '96.ck2', '96.ck3', '96.co1', '96.co2', '96.co3', '96.cs1', '96.cs2', '96.cu1'], 'contains': ['384.b1', '384.e1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7830, -1, 1880, -1], 'generators': [22186920, 7], 'label': '768.1090070.192.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.p1', 'projective_image': '768.1090070', '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: 68518666
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.d1', '96.k1', '96.ci2', '96.cl1', '96.cm1', '96.cn1', '96.co1', '96.co2', '96.co3', '96.cs2', '96.cu1'], 'contains': ['384.b1', '384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8725, -1, 1585, -1], 'generators': [14933656, 16], 'label': '768.1090070.192.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '192.q1', 'projective_image': '768.1090070', '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: 68518667
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.f1', '96.m1', '96.cf1', '96.cq1', '96.cr1', '96.ct1'], 'contains': ['384.b1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4517, -1, 4997, -1], 'generators': [40723327, 23], 'label': '768.1090070.192.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1', 'old_label': '192.r1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518668
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.r1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.e1', '96.l1', '96.ci2', '96.ck1', '96.ck2', '96.ck3', '96.cp1', '96.cs2', '96.cu1'], 'contains': ['384.b1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7705, -1, 2115, -1], 'generators': [11291176, 7], 'label': '768.1090070.192.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '192.s1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518669
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.t1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.n1', '96.cg1', '96.cj1', '96.cl1', '96.cq1', '96.cp1', '96.cv1'], 'contains': ['384.b1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5307, -1, 4345, -1], 'generators': [1508405, 16], 'label': '768.1090070.192.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '192.t1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518670
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.d1'], 'contains': ['24.bn1', '24.bo1', '24.br1', '24.bt1', '24.bw1', '24.cm1', '24.ct1', '24.cu1', '24.cv1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [5490, -1, 3564, -1], 'generators': [11291167, 22186920, 40723343, 262459440, 135732240, 7], 'label': '768.1090070.12.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.q1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518671
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.u1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.p1', '96.ch1', '96.cj1', '96.cm1', '96.cq1', '96.cp1', '96.cv1'], 'contains': ['384.b1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5532, -1, 4289, -1], 'generators': [1508418, 16], 'label': '768.1090070.192.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '192.u1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518672
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '192.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1', '96.s1', '96.cr1', '96.cs1', '96.cs2'], 'contains': ['384.b1', '384.d1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5469, -1, 4234, -1], 'generators': [262459463, 7], 'label': '768.1090070.192.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '192.v1', 'projective_image': '768.1090070', '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: 68518673
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '192.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '96.t1', '96.cf1', '96.cr1', '96.cw1'], 'contains': ['384.c1', '384.d1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4349, -1, 5114, -1], 'generators': [40723320, 262459456], 'label': '768.1090070.192.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1', 'old_label': '192.w1', 'projective_image': '768.1090070', '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: 68518674
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.x1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1', '96.x1', '96.cg1'], 'contains': ['384.c1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4688, -1, 4879, -1], 'generators': [40723320, 1508405], 'label': '768.1090070.192.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.k1', 'old_label': '192.x1', 'projective_image': '768.1090070', '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: 68518675
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.y1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['96.c1', '96.c2', '96.z1', '96.ci1', '96.ci2', '96.cs2', '96.cx1', '96.cx2', '96.cx3', '96.cy1', '96.cy2', '96.cy3', '96.cz1'], 'contains': ['384.d1', '384.e1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7499, -1, 2174, -1], 'generators': [258829936, 11291160], 'label': '768.1090070.192.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.y1', 'projective_image': '768.1090070', '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: 68518676
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.d1', '96.ba1', '96.ci1', '96.cs1', '96.cy1', '96.cy2', '96.cy3', '96.cz1'], 'contains': ['384.d1', '384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7170, -1, 2351, -1], 'generators': [14933656, 262459456], 'label': '768.1090070.192.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.z1', 'projective_image': '768.1090070', '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: 68518677
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1', '96.bc1', '96.cf1', '96.cr1', '96.cw1'], 'contains': ['384.d1', '384.g1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4635, -1, 5056, -1], 'generators': [40723327, 262459456], 'label': '768.1090070.192.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1', 'old_label': '192.ba1', 'projective_image': '768.1090070', '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: 68518678
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.e1', '96.bb1', '96.ci1', '96.cs1', '96.cx1', '96.cx2', '96.cx3', '96.cz1'], 'contains': ['384.d1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7236, -1, 2292, -1], 'generators': [262459447, 11291176], 'label': '768.1090070.192.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.bb1', 'projective_image': '768.1090070', '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: 68518679
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '192.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1', '96.i1', '96.cw1', '96.cz1'], 'contains': ['384.d1'], 'core': '768.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6524, -1, 4057, -1], 'generators': [135732263, 262459447], 'label': '768.1090070.192.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '192.bc1', 'projective_image': '768.1090070', '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': '3.1'}
  • id: 68518680
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.bd1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['96.bg1', '96.bg2', '96.ck1', '96.ck3', '96.co2', '96.co3', '96.cx1', '96.cx3', '96.cy1', '96.da1'], 'contains': ['384.e1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8633, -1, 1644, -1], 'generators': [14933647, 11291160], 'label': '768.1090070.192.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '192.bd1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518681
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.b1', '6.d1', '6.h1'], 'contains': ['24.n1', '24.p1', '24.bh1', '24.bs1', '24.bv1', '24.bw1', '24.co1', '24.cw1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [6138, -1, 3028, -1], 'generators': [22186920, 14933656, 22186936, 262459440, 135732240, 1508405], 'label': '768.1090070.12.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.r1', 'projective_image': '768.1090070', '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': '32.46'}
  • id: 68518682
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.bd2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bg1', '96.bg2', '96.ck2', '96.ck3', '96.co1', '96.cx1', '96.cx2', '96.cy2', '96.cy3'], 'contains': ['384.e1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7909, -1, 2056, -1], 'generators': [255191767, 11291160], 'label': '768.1090070.192.bd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.bd2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bd2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518683
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '192.be1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bk1', '96.cl1', '96.da1', '96.db1', '96.db2'], 'contains': ['384.e1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9036, -1, 1311, -1], 'generators': [1508405, 14933640], 'label': '768.1090070.192.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1', 'old_label': '192.be1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518684
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '192.bf1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bm1', '96.cn1', '96.da1', '96.db1', '96.db2'], 'contains': ['384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [9090, -1, 1256, -1], 'generators': [12430214, 14933640], 'label': '768.1090070.192.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1', 'old_label': '192.bf1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518685
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.bg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bn1', '96.bn2', '96.ck1', '96.ck2', '96.co1', '96.co2', '96.cx1', '96.cy1', '96.cy2'], 'contains': ['384.e1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8096, -1, 1821, -1], 'generators': [11291167, 22186920], 'label': '768.1090070.192.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.bg1', 'projective_image': '768.1090070', '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: 68518686
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.bg2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bn1', '96.bn2', '96.ck3', '96.co1', '96.co3', '96.cx2', '96.cx3', '96.cy1', '96.cy3'], 'contains': ['384.e1', '384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8323, -1, 1938, -1], 'generators': [11291167, 243901447], 'label': '768.1090070.192.bg2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.bg2', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.bg2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518687
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.bh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.e1', '96.bo1', '96.co2', '96.cy3', '96.db1'], 'contains': ['384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9126, -1, 1200, -1], 'generators': [22186920, 11291160], 'label': '768.1090070.192.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '192.bh1', 'projective_image': '768.1090070', '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': '6.1'}
  • id: 68518688
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.bh2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bo1', '96.co1', '96.co3', '96.cy1', '96.cy2', '96.db2'], 'contains': ['384.e1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8593, -1, 1762, -1], 'generators': [243901440, 11291160], 'label': '768.1090070.192.bh2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '192.bh2', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518689
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '192.bj1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bt1', '96.cg1'], 'contains': ['384.g1', '384.h1'], 'core': '768.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3668, -1, 5262, -1], 'generators': [40723336, 1508405], 'label': '768.1090070.192.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.k1', 'old_label': '192.bi1', 'projective_image': '768.1090070', '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: 68518690
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.bi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.f1', '96.br1', '96.ck1', '96.cx2'], 'contains': ['384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8835, -1, 1703, -1], 'generators': [22186936, 14933647], 'label': '768.1090070.192.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '192.bj1', 'projective_image': '768.1090070', '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': '3.1'}
  • id: 68518691
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '192.bi2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.br1', '96.ck2', '96.ck3', '96.cx1', '96.cx3'], 'contains': ['384.f1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7869, -1, 1997, -1], 'generators': [255191767, 22186936], 'label': '768.1090070.192.bi2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '192.bj2', 'projective_image': '768.1090070', '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: 68518692
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 12, 'centralizer': '192.d1', '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'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5042, -1, 4291, -1], 'generators': [11291167, 23, 7, 40723320, 1508405, 135732240, 262459440, 22186943], 'label': '768.1090070.3.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': '768.1090070', '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': '64.202'}
  • id: 68518693
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '6.d1', '6.h1'], 'contains': ['24.o1', '24.bu1', '24.bv1', '24.bw1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5631, -1, 2898, -1], 'generators': [22186920, 14933656, 22186936, 262459440, 135732240, 1508418], 'label': '768.1090070.12.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.s1', 'projective_image': '768.1090070', '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': '32.46'}
  • id: 68518694
    {'ambient': '768.1090070', 'aut_centralizer_order': 48, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.d1', '64.e1', '64.f1', '128.a1', '128.b1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [9828, -1, 339, -1], 'generators': [1467364], 'label': '768.1090070.256.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.c1', 'old_label': '256.a1', 'projective_image': '768.1090070', '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: 68518695
    {'ambient': '768.1090070', 'aut_centralizer_order': 2048, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '192.c1', '192.d1', '192.e1', '192.f1', '192.g1', '192.g2', '192.i1', '192.i2', '192.h1', '192.h2', '192.j1', '192.k1', '192.m1', '192.l1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4487, -1, 5291, -1], 'generators': [262459440], 'label': '768.1090070.384.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '384.a1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518696
    {'ambient': '768.1090070', 'aut_centralizer_order': 1024, 'aut_label': '384.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.b1', '192.c1', '192.d1', '192.n1', '192.o1', '192.p1', '192.q1', '192.s1', '192.r1', '192.t1', '192.u1', '192.v1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5414, -1, 4234, -1], 'generators': [23], 'label': '768.1090070.384.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '384.b1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68518697
    {'ambient': '768.1090070', 'aut_centralizer_order': 1536, 'aut_label': '384.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.a1', '192.e1', '192.n1', '192.w1', '192.x1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4604, -1, 4908, -1], 'generators': [40723320], 'label': '768.1090070.384.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '384.c1', 'projective_image': '768.1090070', '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: 68518698
    {'ambient': '768.1090070', 'aut_centralizer_order': 1024, 'aut_label': '384.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1', '192.f1', '192.o1', '192.v1', '192.w1', '192.y1', '192.z1', '192.bb1', '192.ba1', '192.bc1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5331, -1, 4286, -1], 'generators': [262459456], 'label': '768.1090070.384.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '384.d1', 'projective_image': '768.1090070', '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: 68518699
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '384.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '6.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.g1', '192.g2', '192.p1', '192.q1', '192.y1', '192.z1', '192.bd1', '192.bd2', '192.be1', '192.bf1', '192.bg1', '192.bg2', '192.bh1', '192.bh2'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8096, -1, 1880, -1], 'generators': [22186920], 'label': '768.1090070.384.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '384.e1', 'projective_image': '768.1090070', '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: 68518700
    {'ambient': '768.1090070', 'aut_centralizer_order': 512, 'aut_label': '384.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.i1', '192.i2', '192.n1', '192.s1', '192.w1', '192.bb1', '192.bj1'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4350, -1, 5085, -1], 'generators': [40723343], 'label': '768.1090070.384.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1', 'old_label': '384.f1', 'projective_image': '768.1090070', '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: 68518701
    {'ambient': '768.1090070', 'aut_centralizer_order': 256, 'aut_label': '384.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.h1', '192.h2', '192.p1', '192.r1', '192.y1', '192.ba1', '192.bd1', '192.bd2', '192.bg1', '192.bg2', '192.bi1', '192.bi2'], 'contains': ['768.a1'], 'core': '768.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7851, -1, 2056, -1], 'generators': [11291176], 'label': '768.1090070.384.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '384.g1', 'projective_image': '768.1090070', '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: 68518703
    {'ambient': '768.1090070', '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.g1', '384.f1', '384.h1'], 'contains': [], 'core': '768.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5331, 9047, 4286, 9405], 'generators': [], 'label': '768.1090070.768.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '768.a1', 'normal_contained_in': ['192.a1', '192.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '768.a1', 'projective_image': '768.1090070', '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: 68518704
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1'], 'contains': ['24.q1', '24.r1', '24.s1', '24.bx1', '24.ca1', '24.by1', '24.cc1', '24.cd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1977, -1, 8248, -1], 'generators': [40723343, 262459440, 135732240, 14933647, 14933663, 1508405], 'label': '768.1090070.12.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.t1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518705
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.e1', '6.f1'], 'contains': ['24.a1', '24.c1', '24.t1', '24.bi1', '24.bj1', '24.bk1', '24.bn1', '24.br1', '24.bx1', '24.ce1', '24.cg1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4709, -1, 4988, -1], 'generators': [11291167, 23, 7, 40723320, 135732240, 262459440], 'label': '768.1090070.12.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.u1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518706
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.e1'], 'contains': ['24.a1', '24.u1', '24.v1', '24.w1', '24.bl1', '24.bm1', '24.ca1', '24.cf1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2940, -1, 7367, -1], 'generators': [23, 40723320, 262459440, 135732240, 1508405, 7], 'label': '768.1090070.12.v1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.v1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518707
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.e1', '6.g1', '6.h1'], 'contains': ['24.x1', '24.y1', '24.z1', '24.bs1', '24.bu1', '24.by1', '24.ce1', '24.cf1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3727, -1, 6292, -1], 'generators': [23, 14933656, 262459440, 135732240, 1508405, 7], 'label': '768.1090070.12.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.w1', 'projective_image': '768.1090070', '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': '32.46'}
  • id: 68518708
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.g1'], 'contains': ['24.bo1', '24.bp1', '24.bt1', '24.bz1', '24.ce1', '24.cg1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5380, -1, 3729, -1], 'generators': [11291167, 280995863, 23, 7, 135732240, 262459440], 'label': '768.1090070.12.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.x1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518709
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.f1', '6.g1', '6.h1'], 'contains': ['24.ba1', '24.bv1', '24.ce1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5577, -1, 2817, -1], 'generators': [23668578, 23, 7, 14933656, 135732240, 262459440], 'label': '768.1090070.12.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.y1', 'projective_image': '768.1090070', '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': '32.46'}
  • id: 68518710
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1'], 'contains': ['24.bc1', '24.bd1', '24.be1', '24.cb1', '24.cc1', '24.cd1', '24.cf1', '24.cg1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1493, -1, 8368, -1], 'generators': [23, 262459440, 201398416, 135732240, 1508405, 7], 'label': '768.1090070.12.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.z1', 'projective_image': '768.1090070', '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: 68518711
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1'], 'contains': ['24.ch1', '24.ci1', '24.cj1', '24.co1', '24.cs1'], 'core': '96.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4405, -1, 5627, -1], 'generators': [40723320, 22186936, 262459440, 135732240, 11291176, 1508405], 'label': '768.1090070.12.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.ba1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518712
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.b1'], 'contains': ['24.b1', '24.ci1', '24.cj1', '24.cr1', '24.cw1'], 'core': '24.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [4789, -1, 5242, -1], 'generators': [22186920, 40723320, 262459440, 135732240, 11291160, 1508405], 'label': '768.1090070.12.bb1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.bb1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518713
    {'ambient': '768.1090070', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '768.a1', 'complements': ['192.x1', '192.bj1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['12.a1', '16.a1', '16.c1', '16.d1', '16.f1', '16.g1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9646, 1779, 482, 764], 'generators': [23, 11291167, 1467364, 262459440, 135732240, 22186943, 7], 'label': '768.1090070.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '768.1090070', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 68518714
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1'], 'contains': ['24.cn1', '24.cp1', '24.cq1', '24.co1', '24.cr1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4538, -1, 5762, -1], 'generators': [22186936, 40723336, 262459440, 135732240, 11291176, 1508405], 'label': '768.1090070.12.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.bc1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518715
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1'], 'contains': ['24.cp1', '24.cq1', '24.cs1', '24.cv1', '24.cw1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [4165, -1, 5502, -1], 'generators': [22186920, 40723336, 262459440, 135732240, 11291160, 1508405], 'label': '768.1090070.12.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.bd1', 'projective_image': '768.1090070', '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': '32.27'}
  • id: 68518716
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.a1', '8.b1'], 'contains': ['48.a1', '64.a1', '64.b1', '64.d1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9728, -1, 345, -1], 'generators': [23, 1467364, 262459440, 135732240, 7], 'label': '768.1090070.16.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.a1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 68518717
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.c1'], 'contains': ['32.a1', '32.b1', '48.cr1', '64.c1'], 'core': '96.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9475, -1, 1070, -1], 'generators': [40723320, 1467364, 262459440, 135732240, 1508405], 'label': '768.1090070.16.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': '768.1090070', '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': '24.12'}
  • id: 68518718
    {'ambient': '768.1090070', 'aut_centralizer_order': 2, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '8.c1', '8.e1'], 'contains': ['48.b1', '64.a1', '64.e1'], 'core': '48.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [9600, -1, 454, -1], 'generators': [22186920, 1467364, 262459440, 135732240, 11291160], 'label': '768.1090070.16.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.c1', 'projective_image': '768.1090070', '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': '192.955'}
  • id: 68518719
    {'ambient': '768.1090070', 'aut_centralizer_order': 2, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.d1'], 'contains': ['48.dg1', '64.a1', '64.f1'], 'core': '192.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9944, -1, 535, -1], 'generators': [22186936, 1467364, 14933647, 135732240, 262459440], 'label': '768.1090070.16.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': '768.1090070', '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': '96.70'}
  • id: 68518720
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1'], 'contains': ['32.c1', '32.d1', '48.dq1', '64.c1'], 'core': '192.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [9540, -1, 973, -1], 'generators': [23, 40723320, 1467364, 1508405, 7], 'label': '768.1090070.16.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.e1', 'old_label': '16.e1', 'projective_image': '768.1090070', '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: 68518721
    {'ambient': '768.1090070', 'aut_centralizer_order': 1, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '8.f1'], 'contains': ['48.dt1', '64.b1', '64.e1', '64.f1'], 'core': '192.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [9655, -1, 34, -1], 'generators': [243901463, 23, 1467364, 124836496, 7], 'label': '768.1090070.16.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '16.f1', 'projective_image': '768.1090070', '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': '96.227'}
  • id: 68518722
    {'ambient': '768.1090070', 'aut_centralizer_order': 1, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1'], 'contains': ['48.du1', '64.d1', '64.e1', '64.f1'], 'core': '768.a1', 'coset_action_label': '16T1068', 'count': 32, 'diagramx': [9890, -1, 155, -1], 'generators': [243901463, 135732263, 1467364, 22186936, 124836496], 'label': '768.1090070.16.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1', 'old_label': '16.g1', 'projective_image': '768.1090070', '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': '48.50'}
  • id: 68518723
    {'ambient': '768.1090070', 'aut_centralizer_order': 128, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.a1', 'complements': ['32.f1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.u1', '12.v1'], 'contains': ['48.a1', '48.g1', '48.bi1', '48.cf1', '48.cj1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4567, 4279, 5281, 6846], 'generators': [23, 40723320, 262459440, 135732240, 7], 'label': '768.1090070.24.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['48.a1', '96.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '768.1090070', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 68518724
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 16, 'centralizer': '384.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.a1', '8.b1', '12.v1', '16.b1', '16.e1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9483, -1, 948, -1], 'generators': [23, 40723320, 1467364, 262459440, 135732240, 1508405, 7], 'label': '768.1090070.4.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '4.b1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 68518725
    {'ambient': '768.1090070', 'aut_centralizer_order': 32, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '48.a1', 'complements': ['32.f1', '32.d1'], 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '12.j1', '12.bb1'], 'contains': ['48.b1', '48.cp1', '48.cx1'], 'core': '24.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5158, 979, 4528, 4787], 'generators': [22186920, 40723320, 262459440, 135732240, 11291160], 'label': '768.1090070.24.b1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.b1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['48.b1', '96.a1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '768.1090070', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 68518726
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.u1'], 'contains': ['48.c1', '48.d1', '48.g1', '48.n1', '48.o1', '48.bn1', '48.bo1', '48.bt1', '48.bx1'], 'core': '768.a1', 'coset_action_label': '24T1632', 'count': 24, 'diagramx': [4150, -1, 5563, -1], 'generators': [23, 11291167, 40723320, 90842400, 135732247], 'label': '768.1090070.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.u1', 'old_label': '24.c1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 68518727
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.g1'], 'contains': ['48.h1', '48.j1', '48.m1', '48.r1', '48.u1', '48.bc1', '48.bg1', '48.bq1', '48.cb1'], 'core': '768.a1', 'coset_action_label': '24T2429', 'count': 12, 'diagramx': [519, -1, 9424, -1], 'generators': [40723320, 14933656, 261314645, 135732240, 16], 'label': '768.1090070.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.d1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518728
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.g1'], 'contains': ['48.h1', '48.j1', '48.k1', '48.r1', '48.s1', '48.bc1', '48.be1', '48.br1', '48.cc1'], 'core': '768.a1', 'coset_action_label': '24T2419', 'count': 12, 'diagramx': [717, -1, 9193, -1], 'generators': [40723320, 14933656, 135732240, 1508405, 16], 'label': '768.1090070.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.e1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518729
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '12.h1'], 'contains': ['48.h1', '48.l1', '48.l2', '48.t1', '48.t2', '48.bf1', '48.bf2'], 'core': '768.a1', 'coset_action_label': '24T2417', 'count': 24, 'diagramx': [2169, -1, 8135, -1], 'generators': [40723320, 14933656, 135732240, 16, 1508409], 'label': '768.1090070.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.f1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518730
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '12.k1'], 'contains': ['48.i1', '48.j1', '48.l1', '48.y1', '48.z1', '48.bd1', '48.bh1'], 'core': '768.a1', 'coset_action_label': '24T2421', 'count': 24, 'diagramx': [1664, -1, 8478, -1], 'generators': [261314645, 135732240, 14933647, 14933663, 303182760], 'label': '768.1090070.24.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.g1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518731
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.k1'], 'contains': ['48.i1', '48.k1', '48.l2', '48.y1', '48.bd1'], 'core': '768.a1', 'coset_action_label': '24T2423', 'count': 12, 'diagramx': [1584, -1, 8375, -1], 'generators': [40723320, 135732240, 14933647, 14933663, 1508405], 'label': '768.1090070.24.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.h1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518732
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.k1'], 'contains': ['48.i1', '48.l2', '48.m1', '48.z1', '48.bh1'], 'core': '768.a1', 'coset_action_label': '24T2426', 'count': 12, 'diagramx': [1156, -1, 8590, -1], 'generators': [40723320, 261314645, 135732240, 14933647, 14933663], 'label': '768.1090070.24.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.i1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518733
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1'], 'contains': ['48.e1', '48.f1', '48.n1', '48.n2', '48.bs1', '48.bw1', '48.dm1', '48.dm2', '48.dp1', '48.dp2', '48.du1', '48.du2'], 'core': '768.a1', 'coset_action_label': '24T2199', 'count': 24, 'diagramx': [7694, -1, 1714, -1], 'generators': [11291167, 135732263, 262459440, 22186943, 7], 'label': '768.1090070.24.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '24.j1', 'projective_image': '768.1090070', '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: 68518734
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '12.m1'], 'contains': ['48.q1', '48.r1', '48.t1', '48.ba1', '48.bb1', '48.bd1', '48.bh1'], 'core': '768.a1', 'coset_action_label': '24T2373', 'count': 24, 'diagramx': [2110, -1, 7902, -1], 'generators': [40723327, 14933656, 261314649, 135732240, 16], 'label': '768.1090070.24.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.k1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518735
    {'ambient': '768.1090070', 'aut_centralizer_order': 2, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '768.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['8.c1', '8.e1', '12.bb1', '16.b1'], 'core': '24.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [9403, -1, 1067, -1], 'generators': [22186920, 40723320, 1467364, 262459440, 135732240, 11291160, 1508405], 'label': '768.1090070.4.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '4.c1', 'projective_image': '768.1090070', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 68518736
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.m1'], 'contains': ['48.q1', '48.s1', '48.t2', '48.ba1', '48.bd1'], 'core': '768.a1', 'coset_action_label': '24T2382', 'count': 12, 'diagramx': [2980, -1, 6762, -1], 'generators': [40723327, 14933656, 135732240, 1508405, 16], 'label': '768.1090070.24.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.l1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518737
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.m1'], 'contains': ['48.q1', '48.t2', '48.u1', '48.bb1', '48.bh1'], 'core': '768.a1', 'coset_action_label': '24T2378', 'count': 12, 'diagramx': [2626, -1, 6896, -1], 'generators': [40723327, 14933656, 261314645, 135732240, 16], 'label': '768.1090070.24.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.m1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518738
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.r1'], 'contains': ['48.s1', '48.v1', '48.w1', '48.bz1', '48.cd1', '48.dn1', '48.dn2'], 'core': '768.a1', 'coset_action_label': '24T2408', 'count': 24, 'diagramx': [7637, -1, 1935, -1], 'generators': [22186920, 14933656, 22186936, 135732240, 1508405], 'label': '768.1090070.24.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '24.n1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518739
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.d1', '12.e1', '12.s1'], 'contains': ['48.t1', '48.v1', '48.w1', '48.do1', '48.do2'], 'core': '768.a1', 'coset_action_label': '24T2405', 'count': 48, 'diagramx': [7850, -1, 1811, -1], 'generators': [22186920, 14933656, 22186936, 135732240, 1508409], 'label': '768.1090070.24.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '24.o1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518740
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.e1', '12.r1'], 'contains': ['48.u1', '48.v1', '48.w1', '48.ca1', '48.ce1'], 'core': '768.a1', 'coset_action_label': '24T2406', 'count': 24, 'diagramx': [7337, -1, 2177, -1], 'generators': [22186920, 14933656, 261314645, 22186936, 135732240], 'label': '768.1090070.24.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '24.p1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518741
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '12.t1'], 'contains': ['48.x1', '48.ba1', '48.bb1', '48.y1', '48.z1', '48.bc1', '48.bf1'], 'core': '768.a1', 'coset_action_label': '24T2357', 'count': 24, 'diagramx': [1907, -1, 8702, -1], 'generators': [261314645, 40723343, 135732240, 14933647, 14933663], 'label': '768.1090070.24.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.q1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518742
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.t1'], 'contains': ['48.x1', '48.ba1', '48.y1', '48.be1', '48.bf2'], 'core': '768.a1', 'coset_action_label': '24T2365', 'count': 12, 'diagramx': [1742, -1, 8874, -1], 'generators': [135732240, 14933647, 14933663, 1508405, 303182783], 'label': '768.1090070.24.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.r1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518743
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.t1'], 'contains': ['48.x1', '48.bb1', '48.z1', '48.bf2', '48.bg1'], 'core': '768.a1', 'coset_action_label': '24T2355', 'count': 12, 'diagramx': [1358, -1, 8940, -1], 'generators': [261314645, 135732240, 14933647, 14933663, 303182783], 'label': '768.1090070.24.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.s1', 'projective_image': '768.1090070', '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': '32.51'}
  • id: 68518744
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '12.u1'], 'contains': ['48.c1', '48.d1', '48.h1', '48.i1', '48.q1', '48.x1', '48.bi1', '48.bj1', '48.bl1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [3131, -1, 6530, -1], 'generators': [23, 11291167, 40723320, 90842400, 7], 'label': '768.1090070.24.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.t1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518745
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '12.v1'], 'contains': ['48.j1', '48.l2', '48.ba1', '48.bb1', '48.bi1', '48.bk1', '48.bm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2418, -1, 7674, -1], 'generators': [23, 261314645, 135732240, 303182760, 7], 'label': '768.1090070.24.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.u1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518746
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20053', 'aut_weyl_index': 16, 'centralizer': '48.a1', 'complements': ['128.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.f1', '12.j1', '12.l1', '12.q1', '12.u1', '12.x1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5490, 3737, 3564, 2583], 'generators': [11291167, 23, 7, 40723320, 135732240, 262459440, 22186943], 'label': '768.1090070.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '24.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '768.1090070', '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': '48.48'}
  • id: 68518747
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.v1'], 'contains': ['48.k1', '48.l1', '48.ba1', '48.bi1', '48.bk1', '48.dj1', '48.dq1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3354, -1, 6416, -1], 'generators': [23, 40723320, 135732240, 1508405, 7], 'label': '768.1090070.24.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.v1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518748
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.v1'], 'contains': ['48.l1', '48.m1', '48.bb1', '48.bi1', '48.bm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2802, -1, 7544, -1], 'generators': [23, 40723320, 261314645, 135732240, 7], 'label': '768.1090070.24.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.w1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518749
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '12.w1'], 'contains': ['48.r1', '48.t2', '48.y1', '48.z1', '48.bj1', '48.bk1', '48.bm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2532, -1, 7289, -1], 'generators': [23, 255191776, 135732240, 1508405, 7], 'label': '768.1090070.24.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.x1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518750
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '12.d1', '12.w1'], 'contains': ['48.s1', '48.t1', '48.y1', '48.bj1', '48.bk1', '48.dk1', '48.dr1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [4378, -1, 4773, -1], 'generators': [23, 14933656, 135732240, 1508405, 7], 'label': '768.1090070.24.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': '768.1090070', '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': '32.46'}
  • id: 68518751
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.e1', '12.w1'], 'contains': ['48.t1', '48.u1', '48.z1', '48.bj1', '48.bm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3547, -1, 6292, -1], 'generators': [23, 14933656, 261314645, 135732240, 7], 'label': '768.1090070.24.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': '768.1090070', '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': '32.46'}
  • id: 68518752
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.e1', '12.y1'], 'contains': ['48.v1', '48.bj1', '48.dl1', '48.ds1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [7759, -1, 1617, -1], 'generators': [23, 23668578, 14933656, 135732240, 7], 'label': '768.1090070.24.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '24.ba1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518753
    {'ambient': '768.1090070', 'aut_centralizer_order': 64, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.d1', '12.e1'], 'contains': ['48.e1', '48.f1', '48.p1', '48.w1', '48.bj1', '48.bj2', '48.dm1', '48.dm2', '48.dp1', '48.dp2', '48.dt1', '48.dt2'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [8005, -1, 1520, -1], 'generators': [23, 11291167, 262459440, 22186943, 7], 'label': '768.1090070.24.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '24.bb1', 'projective_image': '768.1090070', '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': '2.1'}
  • id: 68518754
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '12.z1'], 'contains': ['48.bc1', '48.bd1', '48.bf2', '48.bh1', '48.bk1', '48.bl1', '48.bm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1414, -1, 8792, -1], 'generators': [23, 261314645, 201398416, 135732240, 7], 'label': '768.1090070.24.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.bc1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518755
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.z1'], 'contains': ['48.bd1', '48.be1', '48.bf1', '48.bk1', '48.bl1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1074, -1, 9014, -1], 'generators': [23, 135732240, 178346296, 1508405, 7], 'label': '768.1090070.24.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.bd1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518756
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.z1'], 'contains': ['48.bf1', '48.bg1', '48.bh1', '48.bl1', '48.bm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1019, -1, 9095, -1], 'generators': [23, 261314645, 135732240, 178346296, 7], 'label': '768.1090070.24.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.be1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518757
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 24, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1'], 'contains': ['12.g1', '12.i1', '12.j1', '12.o1', '12.r1', '12.ba1', '12.bb1', '12.bc1', '12.bd1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4723, -1, 5307, -1], 'generators': [22186920, 22186936, 40723320, 1508405, 14933656, 135732240, 262459440], 'label': '768.1090070.6.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': '768.1090070', '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': '64.202'}
  • id: 68518758
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.g1'], 'contains': ['48.bn1', '48.bp1', '48.bp2', '48.bq1', '48.br1', '48.bu1', '48.by1', '48.cb1', '48.cc1'], 'core': '768.a1', 'coset_action_label': '24T2248', 'count': 24, 'diagramx': [132, -1, 9806, -1], 'generators': [40723320, 14933656, 135732240, 262459456, 1508405], 'label': '768.1090070.24.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '24.bf1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518759
    {'ambient': '768.1090070', 'aut_centralizer_order': 4, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.n1'], 'contains': ['48.bt1', '48.bv1'], 'core': '768.a1', 'coset_action_label': '24T2392', 'count': 24, 'diagramx': [4920, -1, 4870, -1], 'generators': [40723327, 14933656, 12430209, 135732240, 262459456], 'label': '768.1090070.24.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1', 'old_label': '24.bg1', 'projective_image': '768.1090070', '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': '16.3'}
  • id: 68518760
    {'ambient': '768.1090070', 'aut_centralizer_order': 8, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.r1'], 'contains': ['48.bu1', '48.bv1', '48.bw1', '48.bz1', '48.ca1', '48.cd1', '48.ce1'], 'core': '768.a1', 'coset_action_label': '24T1639', 'count': 48, 'diagramx': [7118, -1, 2491, -1], 'generators': [255191776, 243901440, 22186936, 135732240, 1508405], 'label': '768.1090070.24.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1', 'old_label': '24.bh1', 'projective_image': '768.1090070', '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: 68518761
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.j1', '12.u1'], 'contains': ['48.c1', '48.cf1', '48.cg1', '48.cl1', '48.cp1', '48.cq1', '48.cu1', '48.db1'], 'core': '96.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4856, -1, 4968, -1], 'generators': [22186920, 40723320, 262459440, 135732240, 7], 'label': '768.1090070.24.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bi1', 'projective_image': '768.1090070', '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: 68518762
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.h1', '12.i1', '12.j1', '12.u1'], 'contains': ['48.h1', '48.bn1', '48.cf1', '48.ch1', '48.cm1', '48.cp1', '48.ct1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3644, -1, 6168, -1], 'generators': [40723320, 14933656, 262459440, 135732240, 16], 'label': '768.1090070.24.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bj1', 'projective_image': '768.1090070', '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': '16.11'}
  • id: 68518763
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 48, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.k1', '12.u1'], 'contains': ['48.i1', '48.bo1', '48.cf1', '48.ci1', '48.co1', '48.cq1', '48.dc1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4225, -1, 5195, -1], 'generators': [40723320, 262459440, 135732240, 11291176, 7], 'label': '768.1090070.24.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': '768.1090070', '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': '16.11'}
  • id: 68518764
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.k1', '12.v1'], 'contains': ['48.j1', '48.k1', '48.m1', '48.bp1', '48.bp2', '48.cf1', '48.ck1', '48.cr1', '48.dh1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [608, -1, 9307, -1], 'generators': [40723320, 262459440, 135732240, 1508405, 16], 'label': '768.1090070.24.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.bl1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518765
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.264', 'aut_weyl_index': 96, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.k1', '12.v1'], 'contains': ['48.l1', '48.l2', '48.cf1', '48.cn1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2893, -1, 7160, -1], 'generators': [40723320, 262459440, 135732240, 1508418, 16], 'label': '768.1090070.24.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.bm1', 'projective_image': '768.1090070', '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': '16.14'}
  • id: 68518766
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.l1', '12.q1', '12.u1'], 'contains': ['48.d1', '48.cg1', '48.cj1', '48.cl1', '48.ct1', '48.cu1', '48.db1', '48.dc1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5328, -1, 4274, -1], 'generators': [280995863, 22186920, 262459440, 135732240, 7], 'label': '768.1090070.24.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bn1', 'projective_image': '768.1090070', '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': '8.5'}
  • id: 68518767
    {'ambient': '768.1090070', 'aut_centralizer_order': 16, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.q1', '12.x1'], 'contains': ['48.cg1', '48.cl1', '48.co1', '48.cw1', '48.cy1', '48.dd1', '48.df1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5927, -1, 3130, -1], 'generators': [22186920, 262459440, 201398416, 135732240, 7], 'label': '768.1090070.24.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.bo1', 'projective_image': '768.1090070', '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'}