Abstract group data - 3168.c

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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': '72.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [2, 10, 30, 20, 30, 10, 10], 'aut_gens': [[13702999292, 15767835078, 158006], [9886182226, 17644958238, 43033609], [8634766984, 500566333, 28893263], [9010191600, 125141745, 40463034], [20272930639, 24340030945, 1320025], [3816817200, 11450451587, 61979640], [5068232659, 8009059127, 57551899], [9635899419, 20961208987, 31363397]], 'aut_group': None, 'aut_hash': 663454934575270710, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 21120, 'aut_permdeg': 58, 'aut_perms': [1732732255107955792136087714523083155611527696282609392845413795515060656585530, 1715500695344529927630688436017572204067639240528097053880490743038690386126869, 410949957957637167701383941578475739672622923628152146625556499012530057811211, 23440870890990985064437392413157911354402545286639407489330654141706757358531, 1439559129500943182807148742255642695193111227337758557736047596152297216861084, 1752221241673055078784697114190557739888993379513555775212589631060461638953067, 1766464214964711651262414835527118663334041021630008231056518429352221596925084], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 44, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 2, 4, 1], [4, 44, 1, 1], [6, 1, 2, 1], [6, 2, 2, 1], [6, 44, 2, 1], [8, 44, 2, 1], [9, 1, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 8, 1], [12, 44, 2, 1], [18, 1, 6, 1], [18, 2, 6, 1], [18, 44, 6, 1], [22, 2, 5, 1], [22, 2, 10, 1], [24, 44, 4, 1], [33, 2, 10, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 2, 24, 1], [36, 44, 6, 1], [44, 2, 10, 2], [44, 2, 40, 1], [66, 2, 10, 1], [66, 2, 20, 1], [72, 44, 12, 1], [99, 2, 30, 1], [132, 2, 20, 2], [132, 2, 80, 1], [198, 2, 30, 1], [198, 2, 60, 1], [396, 2, 60, 2], [396, 2, 240, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{22}.C_{30}.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '48.52', 'autcent_hash': 52, 'autcent_nilpotent': True, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '440.42', 'autcentquo_hash': 42, 'autcentquo_nilpotent': False, 'autcentquo_order': 440, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 44, 1], [3, 1, 2], [4, 1, 2], [4, 2, 5], [4, 44, 1], [6, 1, 2], [6, 2, 2], [6, 44, 2], [8, 44, 2], [9, 1, 6], [11, 2, 5], [12, 1, 4], [12, 2, 10], [12, 44, 2], [18, 1, 6], [18, 2, 6], [18, 44, 6], [22, 2, 15], [24, 44, 4], [33, 2, 10], [36, 1, 12], [36, 2, 30], [36, 44, 6], [44, 2, 60], [66, 2, 30], [72, 44, 12], [99, 2, 30], [132, 2, 120], [198, 2, 90], [396, 2, 360]], 'center_label': '36.2', 'center_order': 36, 'central_product': True, 'central_quotient': '88.5', 'commutator_count': 1, 'commutator_label': '44.2', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['352.11', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 44, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 2, 2, 2], [4, 44, 1, 1], [6, 1, 2, 1], [6, 2, 2, 1], [6, 44, 2, 1], [8, 44, 2, 1], [9, 1, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 4, 2], [12, 44, 2, 1], [18, 1, 6, 1], [18, 2, 6, 1], [18, 44, 6, 1], [22, 2, 5, 1], [22, 2, 10, 1], [24, 44, 4, 1], [33, 2, 10, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 2, 12, 2], [36, 44, 6, 1], [44, 2, 10, 2], [44, 2, 20, 2], [66, 2, 10, 1], [66, 2, 20, 1], [72, 44, 12, 1], [99, 2, 30, 1], [132, 2, 20, 2], [132, 2, 40, 2], [198, 2, 30, 1], [198, 2, 60, 1], [396, 2, 60, 2], [396, 2, 120, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 144, 'exponent': 792, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 0, 240]], 'familial': False, 'frattini_label': '24.9', 'frattini_quotient': '132.7', 'hash': 8813592882577988912, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 44, 'inner_gen_orders': [44, 22, 2], 'inner_gens': [[13702999292, 15767835078, 39829422], [13702999292, 15767835078, 19694773], [312854084, 17644958238, 158006]], 'inner_hash': 5, 'inner_nilpotent': False, 'inner_order': 88, 'inner_split': True, 'inner_tex': 'D_{44}', 'inner_used': [1, 3], 'irrC_degree': 2, 'irrQ_degree': 240, 'irrQ_dim': 240, 'irrR_degree': None, 'irrep_stats': [[1, 72], [2, 774]], 'label': '3168.c', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D44:C36', 'ngens': 3, '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, 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': 45, 'number_characteristic_subgroups': 57, 'number_conjugacy_classes': 846, 'number_divisions': 51, 'number_normal_subgroups': 57, 'number_subgroup_autclasses': 126, 'number_subgroup_classes': 132, 'number_subgroups': 774, 'old_label': None, 'order': 3168, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 47], [3, 2], [4, 56], [6, 94], [8, 88], [9, 6], [11, 10], [12, 112], [18, 282], [22, 30], [24, 176], [33, 20], [36, 336], [44, 120], [66, 60], [72, 528], [99, 60], [132, 240], [198, 180], [396, 720]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 2, 2, 30], 'outer_gen_pows': [62570774, 62570774, 62570774, 62570774], 'outer_gens': [[19709793593, 7195639040, 158006], [5130803685, 7195639040, 158006], [19084086004, 15767835078, 158006], [10574460798, 500566333, 158006]], 'outer_group': '240.208', 'outer_hash': 208, 'outer_nilpotent': True, 'outer_order': 240, 'outer_permdeg': 16, 'outer_perms': [40279680, 1307674368000, 362880, 6227026593], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{30}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 28, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 6], [6, 4], [8, 2], [10, 2], [12, 4], [20, 5], [24, 2], [40, 5], [60, 2], [80, 2], [120, 3], [240, 2]], 'representations': {'PC': {'code': '3976166881536833915045964957510993751887459000011900', 'gens': [1, 2, 7], 'pres': [8, -2, -2, -2, -3, -3, -11, -2, -2, 47841, 41, 48482, 66, 2563, 123, 9604, 156, 34565, 166]}, 'GLFp': {'d': 2, 'p': 397, 'gens': [13702999292, 15767835078, 158006]}, 'Perm': {'d': 28, 'gens': [837608818963245301260293356, 12129846060497475056316969246, 22632721498791788066242577348]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 36], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{44}:C_{36}', 'transitive_degree': 792, '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: 107011515
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 3, 'group_order': 3168, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 62570774, 'size': 1}
  • id: 107011626
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 3, 'group_order': 3168, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 24778026504, 'size': 1}
  • id: 107011737
    {'aut_label': '2B', 'centralizer': '2.b1.a1', 'counter': 3, 'group_counter': 3, 'group_order': 3168, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 24778026109, 'size': 2}
  • id: 107011848
    {'aut_label': '2C', 'centralizer': '44.d1.a1', 'counter': 4, 'group_counter': 3, 'group_order': 3168, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 57710302, 'size': 44}
  • id: 107011959
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 3, 'group_order': 3168, 'label': '3A1', 'order': 3, 'powers': [6, 1, 6, 6], 'representative': 2127406316, 'size': 1}
  • id: 107012070
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 3, 'group_order': 3168, 'label': '3A-1', 'order': 3, 'powers': [5, 1, 5, 5], 'representative': 22650620188, 'size': 1}
  • id: 107012181
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 3, 'group_order': 3168, 'label': '4A1', 'order': 4, 'powers': [2, 8, 7, 8], 'representative': 20898638516, 'size': 1}
  • id: 107012292
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 3, 'group_order': 3168, 'label': '4A-1', 'order': 4, 'powers': [2, 7, 8, 7], 'representative': 3941958762, 'size': 1}
  • id: 107012350
    {'aut_label': '4B', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 3, 'group_order': 3168, 'label': '4B', 'order': 4, 'powers': [2, 9, 9, 9], 'representative': 3941959033, 'size': 2}
  • id: 107011516
    {'aut_label': '4C1', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 3, 'group_order': 3168, 'label': '4C1', 'order': 4, 'powers': [3, 11, 10, 11], 'representative': 20898638578, 'size': 2}
  • id: 107011527
    {'aut_label': '4C1', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 3, 'group_order': 3168, 'label': '4C-1', 'order': 4, 'powers': [3, 10, 11, 10], 'representative': 3941959095, 'size': 2}
  • id: 107011538
    {'aut_label': '4C1', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 3, 'group_order': 3168, 'label': '4D1', 'order': 4, 'powers': [3, 13, 12, 13], 'representative': 62571107, 'size': 2}
  • id: 107011549
    {'aut_label': '4C1', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 3, 'group_order': 3168, 'label': '4D-1', 'order': 4, 'powers': [3, 12, 13, 12], 'representative': 62570836, 'size': 2}
  • id: 107011560
    {'aut_label': '4E', 'centralizer': '44.d1.a1', 'counter': 14, 'group_counter': 3, 'group_order': 3168, 'label': '4E', 'order': 4, 'powers': [2, 14, 14, 14], 'representative': 4911287, 'size': 44}
  • id: 107011571
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 3, 'group_order': 3168, 'label': '6A1', 'order': 6, 'powers': [6, 2, 16, 16], 'representative': 22713190962, 'size': 1}
  • id: 107011582
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 3, 'group_order': 3168, 'label': '6A-1', 'order': 6, 'powers': [5, 2, 15, 15], 'representative': 2189977090, 'size': 1}
  • id: 107011593
    {'aut_label': '6B1', 'centralizer': '2.b1.a1', 'counter': 17, 'group_counter': 3, 'group_order': 3168, 'label': '6B1', 'order': 6, 'powers': [5, 3, 18, 18], 'representative': 2189977417, 'size': 2}
  • id: 107011604
    {'aut_label': '6B1', 'centralizer': '2.b1.a1', 'counter': 18, 'group_counter': 3, 'group_order': 3168, 'label': '6B-1', 'order': 6, 'powers': [6, 3, 17, 17], 'representative': 22713190633, 'size': 2}
  • id: 107011615
    {'aut_label': '6C1', 'centralizer': '44.d1.a1', 'counter': 19, 'group_counter': 3, 'group_order': 3168, 'label': '6C1', 'order': 6, 'powers': [5, 4, 20, 20], 'representative': 45920593, 'size': 44}
  • id: 107011627
    {'aut_label': '6C1', 'centralizer': '44.d1.a1', 'counter': 20, 'group_counter': 3, 'group_order': 3168, 'label': '6C-1', 'order': 6, 'powers': [6, 4, 19, 19], 'representative': 21668260, 'size': 44}
  • id: 107011638
    {'aut_label': '8A1', 'centralizer': '44.f1.a1', 'counter': 21, 'group_counter': 3, 'group_order': 3168, 'label': '8A1', 'order': 8, 'powers': [7, 22, 21, 22], 'representative': 57552693, 'size': 44}
  • id: 107011649
    {'aut_label': '8A1', 'centralizer': '44.f1.a1', 'counter': 22, 'group_counter': 3, 'group_order': 3168, 'label': '8A-1', 'order': 8, 'powers': [8, 21, 22, 21], 'representative': 57709508, 'size': 44}
  • id: 107011660
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 23, 'group_counter': 3, 'group_order': 3168, 'label': '9A1', 'order': 9, 'powers': [25, 5, 28, 25], 'representative': 19522081488, 'size': 1}
  • id: 107011671
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 24, 'group_counter': 3, 'group_order': 3168, 'label': '9A-1', 'order': 9, 'powers': [26, 6, 27, 26], 'representative': 875990836, 'size': 1}
  • id: 107011682
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 25, 'group_counter': 3, 'group_order': 3168, 'label': '9A2', 'order': 9, 'powers': [27, 6, 23, 27], 'representative': 4943091146, 'size': 1}
  • id: 107011693
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 26, 'group_counter': 3, 'group_order': 3168, 'label': '9A-2', 'order': 9, 'powers': [28, 5, 24, 28], 'representative': 12263871704, 'size': 1}
  • id: 107011704
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 27, 'group_counter': 3, 'group_order': 3168, 'label': '9A4', 'order': 9, 'powers': [24, 5, 25, 24], 'representative': 17895241364, 'size': 1}
  • id: 107011715
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 28, 'group_counter': 3, 'group_order': 3168, 'label': '9A-4', 'order': 9, 'powers': [23, 6, 26, 23], 'representative': 19021515296, 'size': 1}
  • id: 107011726
    {'aut_label': '11A1', 'centralizer': '2.b1.a1', 'counter': 29, 'group_counter': 3, 'group_order': 3168, 'label': '11A1', 'order': 11, 'powers': [30, 31, 33, 1], 'representative': 16018118178, 'size': 2}
  • id: 107011738
    {'aut_label': '11A1', 'centralizer': '2.b1.a1', 'counter': 30, 'group_counter': 3, 'group_order': 3168, 'label': '11A2', 'order': 11, 'powers': [32, 33, 29, 1], 'representative': 1939694296, 'size': 2}
  • id: 107011749
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  • id: 107011760
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  • id: 107011782
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  • id: 107011793
    {'aut_label': '12A1', 'centralizer': '1.a1.a1', 'counter': 35, 'group_counter': 3, 'group_order': 3168, 'label': '12A-1', 'order': 12, 'powers': [15, 8, 37, 34], 'representative': 13765570280, 'size': 1}
  • id: 107011804
    {'aut_label': '12A1', 'centralizer': '1.a1.a1', 'counter': 36, 'group_counter': 3, 'group_order': 3168, 'label': '12A5', 'order': 12, 'powers': [15, 7, 34, 37], 'representative': 11075026998, 'size': 1}
  • id: 107011815
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  • id: 107011837
    {'aut_label': '12B1', 'centralizer': '2.b1.a1', 'counter': 39, 'group_counter': 3, 'group_order': 3168, 'label': '12B-1', 'order': 12, 'powers': [16, 9, 38, 38], 'representative': 9823611601, 'size': 2}
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    {'aut_label': '12C1', 'centralizer': '2.b1.a1', 'counter': 40, 'group_counter': 3, 'group_order': 3168, 'label': '12C1', 'order': 12, 'powers': [17, 10, 42, 41], 'representative': 9823611724, 'size': 2}
  • id: 107011860
    {'aut_label': '12C1', 'centralizer': '2.b1.a1', 'counter': 41, 'group_counter': 3, 'group_order': 3168, 'label': '12C-1', 'order': 12, 'powers': [18, 11, 43, 40], 'representative': 13765570095, 'size': 2}
  • id: 107011871
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    {'aut_label': '12C1', 'centralizer': '2.b1.a1', 'counter': 43, 'group_counter': 3, 'group_order': 3168, 'label': '12C-5', 'order': 12, 'powers': [17, 11, 41, 42], 'representative': 15016985883, 'size': 2}
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    {'aut_label': '12C1', 'centralizer': '2.b1.a1', 'counter': 45, 'group_counter': 3, 'group_order': 3168, 'label': '12D-1', 'order': 12, 'powers': [17, 13, 47, 44], 'representative': 2127406522, 'size': 2}
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    {'aut_label': '12C1', 'centralizer': '2.b1.a1', 'counter': 47, 'group_counter': 3, 'group_order': 3168, 'label': '12D-5', 'order': 12, 'powers': [18, 13, 45, 46], 'representative': 22650620046, 'size': 2}
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    {'aut_label': '12E1', 'centralizer': '44.d1.a1', 'counter': 49, 'group_counter': 3, 'group_order': 3168, 'label': '12E-1', 'order': 12, 'powers': [16, 14, 48, 48], 'representative': 41054167, 'size': 44}
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    {'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 50, 'group_counter': 3, 'group_order': 3168, 'label': '18A1', 'order': 18, 'powers': [25, 15, 52, 55], 'representative': 5318515790, 'size': 1}
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    {'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 53, 'group_counter': 3, 'group_order': 3168, 'label': '18A-5', 'order': 18, 'powers': [24, 15, 55, 51], 'representative': 6945355914, 'size': 1}
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    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 56, 'group_counter': 3, 'group_order': 3168, 'label': '18B1', 'order': 18, 'powers': [27, 17, 58, 61], 'representative': 19897505893, 'size': 2}
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    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 57, 'group_counter': 3, 'group_order': 3168, 'label': '18B-1', 'order': 18, 'powers': [28, 18, 59, 60], 'representative': 12576725569, 'size': 2}
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    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 58, 'group_counter': 3, 'group_order': 3168, 'label': '18B5', 'order': 18, 'powers': [25, 18, 60, 56], 'representative': 5318516017, 'size': 2}
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    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 59, 'group_counter': 3, 'group_order': 3168, 'label': '18B-5', 'order': 18, 'powers': [26, 17, 61, 57], 'representative': 23964606073, 'size': 2}
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    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 61, 'group_counter': 3, 'group_order': 3168, 'label': '18B-7', 'order': 18, 'powers': [24, 18, 56, 59], 'representative': 6945356089, 'size': 2}
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  • id: 107012104
    {'aut_label': '18C1', 'centralizer': '44.d1.a1', 'counter': 63, 'group_counter': 3, 'group_order': 3168, 'label': '18C-1', 'order': 18, 'powers': [24, 20, 65, 66], 'representative': 20970334, 'size': 44}
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  • id: 107012126
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  • id: 107012148
    {'aut_label': '18C1', 'centralizer': '44.d1.a1', 'counter': 67, 'group_counter': 3, 'group_order': 3168, 'label': '18C-7', 'order': 18, 'powers': [25, 20, 62, 65], 'representative': 15291646, 'size': 44}
  • id: 107012159
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  • id: 107012182
    {'aut_label': '22A1', 'centralizer': '2.b1.a1', 'counter': 70, 'group_counter': 3, 'group_order': 3168, 'label': '22A5', 'order': 22, 'powers': [33, 71, 69, 2], 'representative': 18646090358, 'size': 2}
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    {'aut_label': '22A1', 'centralizer': '2.b1.a1', 'counter': 71, 'group_counter': 3, 'group_order': 3168, 'label': '22A7', 'order': 22, 'powers': [32, 68, 72, 2], 'representative': 4004529838, 'size': 2}
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    {'aut_label': '22A1', 'centralizer': '2.b1.a1', 'counter': 72, 'group_counter': 3, 'group_order': 3168, 'label': '22A9', 'order': 22, 'powers': [30, 70, 68, 2], 'representative': 6695072852, 'size': 2}
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    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 73, 'group_counter': 3, 'group_order': 3168, 'label': '22B1', 'order': 22, 'powers': [33, 75, 77, 3], 'representative': 250283191, 'size': 2}
  • id: 107012226
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  • id: 107012347
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  • id: 107012351
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  • id: 107011519
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  • id: 107011521
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  • id: 107011522
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  • id: 107011523
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  • id: 107011524
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  • id: 107011525
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  • id: 107011526
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  • id: 107011528
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  • id: 107011529
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  • id: 107011530
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  • id: 107011531
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  • id: 107011532
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  • id: 107011533
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  • id: 107011534
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  • id: 107011536
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  • id: 107011541
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  • id: 107011629
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  • id: 107011630
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  • id: 107011631
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  • id: 107011632
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  • id: 107011634
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    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 218, 'group_counter': 3, 'group_order': 3168, 'label': '66B-5', 'order': 66, 'powers': [95, 78, 230, 17], 'representative': 15642693401, 'size': 2}
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    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 234, 'group_counter': 3, 'group_order': 3168, 'label': '66B-31', 'order': 66, 'powers': [87, 82, 228, 18], 'representative': 18208095198, 'size': 2}
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    {'aut_label': '72A1', 'centralizer': '44.f1.a1', 'counter': 235, 'group_counter': 3, 'group_order': 3168, 'label': '72A1', 'order': 72, 'powers': [97, 83, 237, 241], 'representative': 31050164, 'size': 44}
  • id: 107011667
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    {'aut_label': '72A1', 'centralizer': '44.f1.a1', 'counter': 240, 'group_counter': 3, 'group_order': 3168, 'label': '72A-7', 'order': 72, 'powers': [102, 85, 235, 238], 'representative': 37987342, 'size': 44}
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  • id: 107011676
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  • id: 107011678
    {'aut_label': '72A1', 'centralizer': '44.f1.a1', 'counter': 246, 'group_counter': 3, 'group_order': 3168, 'label': '72A-17', 'order': 72, 'powers': [108, 86, 244, 240], 'representative': 31522991, 'size': 44}
  • id: 107011679
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  • id: 107011680
    {'aut_label': '99A1', 'centralizer': '2.b1.a1', 'counter': 248, 'group_counter': 3, 'group_order': 3168, 'label': '99A-1', 'order': 99, 'powers': [250, 88, 254, 26], 'representative': 14015853401, 'size': 2}
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    {'aut_label': '99A1', 'centralizer': '2.b1.a1', 'counter': 254, 'group_counter': 3, 'group_order': 3168, 'label': '99A-5', 'order': 99, 'powers': [248, 94, 270, 24], 'representative': 7946488218, 'size': 2}
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  • id: 107011712
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  • id: 107011713
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  • id: 107011714
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  • id: 107011716
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  • id: 107011717
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  • id: 107011718
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  • id: 107011719
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  • id: 107011720
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  • id: 107011721
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  • id: 107012002
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  • id: 107012003
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  • id: 107012005
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  • id: 107012006
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  • id: 107012007
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  • id: 107012008
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  • id: 107012009
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  • id: 107012011
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  • id: 107012013
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 552, 'group_counter': 3, 'group_order': 3168, 'label': '396B-7', 'order': 396, 'powers': [402, 302, 566, 114], 'representative': 24465172588, 'size': 2}
  • id: 107012019
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 554, 'group_counter': 3, 'group_order': 3168, 'label': '396B-13', 'order': 396, 'powers': [404, 304, 580, 111], 'representative': 2815684807, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 555, 'group_counter': 3, 'group_order': 3168, 'label': '396B17', 'order': 396, 'powers': [405, 305, 570, 110], 'representative': 16456113445, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 556, 'group_counter': 3, 'group_order': 3168, 'label': '396B-17', 'order': 396, 'powers': [406, 306, 569, 109], 'representative': 19834935196, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 557, 'group_counter': 3, 'group_order': 3168, 'label': '396B19', 'order': 396, 'powers': [407, 307, 589, 109], 'representative': 23589181644, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 558, 'group_counter': 3, 'group_order': 3168, 'label': '396B-19', 'order': 396, 'powers': [408, 308, 590, 110], 'representative': 16143259669, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 559, 'group_counter': 3, 'group_order': 3168, 'label': '396B23', 'order': 396, 'powers': [409, 309, 577, 111], 'representative': 1751981651, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 560, 'group_counter': 3, 'group_order': 3168, 'label': '396B-23', 'order': 396, 'powers': [410, 310, 578, 112], 'representative': 14203565627, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 561, 'group_counter': 3, 'group_order': 3168, 'label': '396B25', 'order': 396, 'powers': [411, 307, 568, 113], 'representative': 18958944354, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 562, 'group_counter': 3, 'group_order': 3168, 'label': '396B-25', 'order': 396, 'powers': [412, 308, 567, 114], 'representative': 3128538688, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 563, 'group_counter': 3, 'group_order': 3168, 'label': '396B29', 'order': 396, 'powers': [402, 311, 601, 114], 'representative': 3253680202, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 564, 'group_counter': 3, 'group_order': 3168, 'label': '396B-29', 'order': 396, 'powers': [401, 312, 602, 113], 'representative': 20710925947, 'size': 2}
  • id: 107012032
    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 565, 'group_counter': 3, 'group_order': 3168, 'label': '396B35', 'order': 396, 'powers': [413, 313, 600, 110], 'representative': 3629104880, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 566, 'group_counter': 3, 'group_order': 3168, 'label': '396B-35', 'order': 396, 'powers': [414, 314, 599, 109], 'representative': 10261606861, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 567, 'group_counter': 3, 'group_order': 3168, 'label': '396B37', 'order': 396, 'powers': [415, 301, 605, 109], 'representative': 20022647619, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 568, 'group_counter': 3, 'group_order': 3168, 'label': '396B-37', 'order': 396, 'powers': [416, 302, 606, 110], 'representative': 14516419546, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 569, 'group_counter': 3, 'group_order': 3168, 'label': '396B41', 'order': 396, 'powers': [417, 315, 564, 111], 'representative': 18520949093, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 570, 'group_counter': 3, 'group_order': 3168, 'label': '396B-41', 'order': 396, 'powers': [418, 316, 563, 112], 'representative': 22400337017, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 571, 'group_counter': 3, 'group_order': 3168, 'label': '396B43', 'order': 396, 'powers': [419, 297, 598, 113], 'representative': 15892976564, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 572, 'group_counter': 3, 'group_order': 3168, 'label': '396B-43', 'order': 396, 'powers': [420, 298, 597, 114], 'representative': 15329839571, 'size': 2}
  • id: 107012041
    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 573, 'group_counter': 3, 'group_order': 3168, 'label': '396B47', 'order': 396, 'powers': [412, 315, 581, 114], 'representative': 22462907854, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 574, 'group_counter': 3, 'group_order': 3168, 'label': '396B-47', 'order': 396, 'powers': [411, 316, 582, 113], 'representative': 16393542620, 'size': 2}
  • id: 107012043
    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 575, 'group_counter': 3, 'group_order': 3168, 'label': '396B59', 'order': 396, 'powers': [421, 311, 592, 111], 'representative': 12764437872, 'size': 2}
  • id: 107012044
    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 576, 'group_counter': 3, 'group_order': 3168, 'label': '396B-59', 'order': 396, 'powers': [422, 312, 591, 112], 'representative': 20335501461, 'size': 2}
  • id: 107012045
    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 577, 'group_counter': 3, 'group_order': 3168, 'label': '396B61', 'order': 396, 'powers': [423, 306, 588, 113], 'representative': 8321912830, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 578, 'group_counter': 3, 'group_order': 3168, 'label': '396B-61', 'order': 396, 'powers': [424, 305, 587, 114], 'representative': 13014720984, 'size': 2}
  • id: 107012047
    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 579, 'group_counter': 3, 'group_order': 3168, 'label': '396B65', 'order': 396, 'powers': [420, 309, 556, 114], 'representative': 13202433255, 'size': 2}
  • id: 107012049
    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 580, 'group_counter': 3, 'group_order': 3168, 'label': '396B-65', 'order': 396, 'powers': [419, 310, 555, 113], 'representative': 10949885418, 'size': 2}
  • id: 107012050
    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 581, 'group_counter': 3, 'group_order': 3168, 'label': '396B73', 'order': 396, 'powers': [415, 312, 554, 109], 'representative': 8634766751, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 582, 'group_counter': 3, 'group_order': 3168, 'label': '396B-73', 'order': 396, 'powers': [416, 311, 553, 110], 'representative': 11700734716, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 583, 'group_counter': 3, 'group_order': 3168, 'label': '396B79', 'order': 396, 'powers': [425, 314, 548, 113], 'representative': 13452716256, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 584, 'group_counter': 3, 'group_order': 3168, 'label': '396B-79', 'order': 396, 'powers': [426, 313, 547, 114], 'representative': 24027177205, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 585, 'group_counter': 3, 'group_order': 3168, 'label': '396B83', 'order': 396, 'powers': [424, 299, 557, 114], 'representative': 12326442470, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 586, 'group_counter': 3, 'group_order': 3168, 'label': '396B-83', 'order': 396, 'powers': [423, 300, 558, 113], 'representative': 23526610912, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 587, 'group_counter': 3, 'group_order': 3168, 'label': '396B91', 'order': 396, 'powers': [407, 316, 575, 109], 'representative': 10887314522, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 588, 'group_counter': 3, 'group_order': 3168, 'label': '396B-91', 'order': 396, 'powers': [408, 315, 576, 110], 'representative': 10136465365, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 589, 'group_counter': 3, 'group_order': 3168, 'label': '396B95', 'order': 396, 'powers': [421, 302, 583, 111], 'representative': 13577857934, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 590, 'group_counter': 3, 'group_order': 3168, 'label': '396B-95', 'order': 396, 'powers': [422, 301, 584, 112], 'representative': 10073894525, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 591, 'group_counter': 3, 'group_order': 3168, 'label': '396B101', 'order': 396, 'powers': [426, 304, 593, 114], 'representative': 1501698565, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 592, 'group_counter': 3, 'group_order': 3168, 'label': '396B-101', 'order': 396, 'powers': [425, 303, 594, 113], 'representative': 21023779910, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 593, 'group_counter': 3, 'group_order': 3168, 'label': '396B109', 'order': 396, 'powers': [397, 310, 603, 109], 'representative': 24527743114, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 594, 'group_counter': 3, 'group_order': 3168, 'label': '396B-109', 'order': 396, 'powers': [398, 309, 604, 110], 'representative': 14891844132, 'size': 2}
  • id: 107012065
    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 595, 'group_counter': 3, 'group_order': 3168, 'label': '396B113', 'order': 396, 'powers': [417, 308, 551, 111], 'representative': 7007926677, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 596, 'group_counter': 3, 'group_order': 3168, 'label': '396B-113', 'order': 396, 'powers': [418, 307, 552, 112], 'representative': 7133068161, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 597, 'group_counter': 3, 'group_order': 3168, 'label': '396B127', 'order': 396, 'powers': [406, 300, 595, 109], 'representative': 15142127146, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 598, 'group_counter': 3, 'group_order': 3168, 'label': '396B-127', 'order': 396, 'powers': [405, 299, 596, 110], 'representative': 15705264157, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 599, 'group_counter': 3, 'group_order': 3168, 'label': '396B131', 'order': 396, 'powers': [409, 298, 586, 111], 'representative': 24402601839, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 600, 'group_counter': 3, 'group_order': 3168, 'label': '396B-131', 'order': 396, 'powers': [410, 297, 585, 112], 'representative': 15079556463, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 601, 'group_counter': 3, 'group_order': 3168, 'label': '396B145', 'order': 396, 'powers': [414, 303, 559, 109], 'representative': 19271798317, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 602, 'group_counter': 3, 'group_order': 3168, 'label': '396B-145', 'order': 396, 'powers': [413, 304, 560, 110], 'representative': 21962341662, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 603, 'group_counter': 3, 'group_order': 3168, 'label': '396B149', 'order': 396, 'powers': [399, 305, 574, 111], 'representative': 20210359730, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 604, 'group_counter': 3, 'group_order': 3168, 'label': '396B-149', 'order': 396, 'powers': [400, 306, 573, 112], 'representative': 6820214316, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 605, 'group_counter': 3, 'group_order': 3168, 'label': '396B167', 'order': 396, 'powers': [404, 313, 571, 111], 'representative': 23464040227, 'size': 2}
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    {'aut_label': '396B1', 'centralizer': '2.b1.a1', 'counter': 606, 'group_counter': 3, 'group_order': 3168, 'label': '396B-167', 'order': 396, 'powers': [403, 314, 572, 112], 'representative': 15454980949, 'size': 2}
  • id: 107012079
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 607, 'group_counter': 3, 'group_order': 3168, 'label': '396C1', 'order': 396, 'powers': [427, 317, 609, 115], 'representative': 12326442284, 'size': 2}
  • id: 107012080
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 608, 'group_counter': 3, 'group_order': 3168, 'label': '396C-1', 'order': 396, 'powers': [428, 318, 610, 116], 'representative': 16581255109, 'size': 2}
  • id: 107012081
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 609, 'group_counter': 3, 'group_order': 3168, 'label': '396C5', 'order': 396, 'powers': [429, 319, 621, 117], 'representative': 23589181664, 'size': 2}
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    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 610, 'group_counter': 3, 'group_order': 3168, 'label': '396C-5', 'order': 396, 'powers': [430, 320, 622, 118], 'representative': 16143259550, 'size': 2}
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    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 611, 'group_counter': 3, 'group_order': 3168, 'label': '396C7', 'order': 396, 'powers': [431, 321, 627, 119], 'representative': 22024912298, 'size': 2}
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    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 612, 'group_counter': 3, 'group_order': 3168, 'label': '396C-7', 'order': 396, 'powers': [432, 322, 628, 120], 'representative': 15454980988, 'size': 2}
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  • id: 107012087
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 614, 'group_counter': 3, 'group_order': 3168, 'label': '396C-13', 'order': 396, 'powers': [434, 324, 646, 124], 'representative': 24527743235, 'size': 2}
  • id: 107012088
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 615, 'group_counter': 3, 'group_order': 3168, 'label': '396C17', 'order': 396, 'powers': [435, 325, 657, 125], 'representative': 16393542559, 'size': 2}
  • id: 107012089
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 616, 'group_counter': 3, 'group_order': 3168, 'label': '396C-17', 'order': 396, 'powers': [436, 326, 658, 126], 'representative': 24089747952, 'size': 2}
  • id: 107012090
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 617, 'group_counter': 3, 'group_order': 3168, 'label': '396C19', 'order': 396, 'powers': [437, 327, 663, 126], 'representative': 24465172540, 'size': 2}
  • id: 107012091
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 618, 'group_counter': 3, 'group_order': 3168, 'label': '396C-19', 'order': 396, 'powers': [438, 328, 664, 125], 'representative': 8196771329, 'size': 2}
  • id: 107012092
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 619, 'group_counter': 3, 'group_order': 3168, 'label': '396C23', 'order': 396, 'powers': [439, 329, 677, 124], 'representative': 19834935278, 'size': 2}
  • id: 107012094
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    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 786, 'group_counter': 3, 'group_order': 3168, 'label': '396D-97', 'order': 396, 'powers': [471, 377, 780, 133], 'representative': 24027177153, 'size': 2}
  • id: 107012278
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 787, 'group_counter': 3, 'group_order': 3168, 'label': '396D101', 'order': 396, 'powers': [471, 376, 793, 132], 'representative': 20085218146, 'size': 2}
  • id: 107012279
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 788, 'group_counter': 3, 'group_order': 3168, 'label': '396D-101', 'order': 396, 'powers': [472, 375, 794, 131], 'representative': 21023779775, 'size': 2}
  • id: 107012280
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 789, 'group_counter': 3, 'group_order': 3168, 'label': '396D103', 'order': 396, 'powers': [455, 374, 799, 130], 'representative': 20335501443, 'size': 2}
  • id: 107012282
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 790, 'group_counter': 3, 'group_order': 3168, 'label': '396D-103', 'order': 396, 'powers': [456, 373, 800, 129], 'representative': 14015853356, 'size': 2}
  • id: 107012283
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 791, 'group_counter': 3, 'group_order': 3168, 'label': '396D107', 'order': 396, 'powers': [430, 372, 811, 128], 'representative': 17582387471, 'size': 2}
  • id: 107012284
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 792, 'group_counter': 3, 'group_order': 3168, 'label': '396D-107', 'order': 396, 'powers': [429, 371, 812, 127], 'representative': 23589181575, 'size': 2}
  • id: 107012285
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 793, 'group_counter': 3, 'group_order': 3168, 'label': '396D109', 'order': 396, 'powers': [446, 370, 815, 127], 'representative': 6131935836, 'size': 2}
  • id: 107012286
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 794, 'group_counter': 3, 'group_order': 3168, 'label': '396D-109', 'order': 396, 'powers': [445, 369, 816, 128], 'representative': 9886182226, 'size': 2}
  • id: 107012287
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 795, 'group_counter': 3, 'group_order': 3168, 'label': '396D113', 'order': 396, 'powers': [476, 368, 829, 129], 'representative': 7007926587, 'size': 2}
  • id: 107012288
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 796, 'group_counter': 3, 'group_order': 3168, 'label': '396D-113', 'order': 396, 'powers': [475, 367, 830, 130], 'representative': 22588049092, 'size': 2}
  • id: 107012289
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 797, 'group_counter': 3, 'group_order': 3168, 'label': '396D115', 'order': 396, 'powers': [479, 366, 835, 131], 'representative': 22212624436, 'size': 2}
  • id: 107012290
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 798, 'group_counter': 3, 'group_order': 3168, 'label': '396D-115', 'order': 396, 'powers': [480, 365, 836, 132], 'representative': 18333236697, 'size': 2}
  • id: 107012291
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 799, 'group_counter': 3, 'group_order': 3168, 'label': '396D119', 'order': 396, 'powers': [449, 364, 846, 133], 'representative': 23276327580, 'size': 2}
  • id: 107012294
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 800, 'group_counter': 3, 'group_order': 3168, 'label': '396D-119', 'order': 396, 'powers': [450, 363, 845, 134], 'representative': 11387880813, 'size': 2}
  • id: 107012295
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 801, 'group_counter': 3, 'group_order': 3168, 'label': '396D125', 'order': 396, 'powers': [452, 362, 828, 137], 'representative': 14516419465, 'size': 2}
  • id: 107012296
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 802, 'group_counter': 3, 'group_order': 3168, 'label': '396D-125', 'order': 396, 'powers': [451, 361, 827, 138], 'representative': 22337766281, 'size': 2}
  • id: 107012297
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 803, 'group_counter': 3, 'group_order': 3168, 'label': '396D127', 'order': 396, 'powers': [468, 360, 822, 138], 'representative': 15142127187, 'size': 2}
  • id: 107012298
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 804, 'group_counter': 3, 'group_order': 3168, 'label': '396D-127', 'order': 396, 'powers': [467, 359, 821, 137], 'representative': 15705264128, 'size': 2}
  • id: 107012299
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 805, 'group_counter': 3, 'group_order': 3168, 'label': '396D131', 'order': 396, 'powers': [473, 358, 810, 136], 'representative': 24402601646, 'size': 2}
  • id: 107012300
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 806, 'group_counter': 3, 'group_order': 3168, 'label': '396D-131', 'order': 396, 'powers': [474, 357, 809, 135], 'representative': 10637031507, 'size': 2}
  • id: 107012301
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 807, 'group_counter': 3, 'group_order': 3168, 'label': '396D133', 'order': 396, 'powers': [459, 357, 804, 134], 'representative': 13890711728, 'size': 2}
  • id: 107012302
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 808, 'group_counter': 3, 'group_order': 3168, 'label': '396D-133', 'order': 396, 'powers': [460, 358, 803, 133], 'representative': 15329839577, 'size': 2}
  • id: 107012303
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 809, 'group_counter': 3, 'group_order': 3168, 'label': '396D137', 'order': 396, 'powers': [427, 359, 792, 132], 'representative': 24652884759, 'size': 2}
  • id: 107012305
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 810, 'group_counter': 3, 'group_order': 3168, 'label': '396D-137', 'order': 396, 'powers': [428, 360, 791, 131], 'representative': 16518684204, 'size': 2}
  • id: 107012306
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 811, 'group_counter': 3, 'group_order': 3168, 'label': '396D139', 'order': 396, 'powers': [442, 361, 786, 130], 'representative': 14266136405, 'size': 2}
  • id: 107012307
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 812, 'group_counter': 3, 'group_order': 3168, 'label': '396D-139', 'order': 396, 'powers': [441, 362, 785, 129], 'representative': 15580122694, 'size': 2}
  • id: 107012308
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 813, 'group_counter': 3, 'group_order': 3168, 'label': '396D145', 'order': 396, 'powers': [483, 363, 768, 127], 'representative': 21774629237, 'size': 2}
  • id: 107012309
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 814, 'group_counter': 3, 'group_order': 3168, 'label': '396D-145', 'order': 396, 'powers': [484, 364, 767, 128], 'representative': 21962341404, 'size': 2}
  • id: 107012310
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 815, 'group_counter': 3, 'group_order': 3168, 'label': '396D149', 'order': 396, 'powers': [453, 365, 756, 129], 'representative': 20210359716, 'size': 2}
  • id: 107012311
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 816, 'group_counter': 3, 'group_order': 3168, 'label': '396D-149', 'order': 396, 'powers': [454, 366, 755, 130], 'representative': 17457245726, 'size': 2}
  • id: 107012312
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 817, 'group_counter': 3, 'group_order': 3168, 'label': '396D151', 'order': 396, 'powers': [435, 367, 750, 131], 'representative': 22775761507, 'size': 2}
  • id: 107012313
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 818, 'group_counter': 3, 'group_order': 3168, 'label': '396D-151', 'order': 396, 'powers': [436, 368, 749, 132], 'representative': 3128538662, 'size': 2}
  • id: 107012314
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 819, 'group_counter': 3, 'group_order': 3168, 'label': '396D155', 'order': 396, 'powers': [448, 369, 736, 133], 'representative': 21837199988, 'size': 2}
  • id: 107012316
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 820, 'group_counter': 3, 'group_order': 3168, 'label': '396D-155', 'order': 396, 'powers': [447, 370, 735, 134], 'representative': 19146656681, 'size': 2}
  • id: 107012317
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 821, 'group_counter': 3, 'group_order': 3168, 'label': '396D157', 'order': 396, 'powers': [464, 371, 732, 135], 'representative': 7133068197, 'size': 2}
  • id: 107012318
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 822, 'group_counter': 3, 'group_order': 3168, 'label': '396D-157', 'order': 396, 'powers': [463, 372, 731, 136], 'representative': 6319648163, 'size': 2}
  • id: 107012319
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 823, 'group_counter': 3, 'group_order': 3168, 'label': '396D161', 'order': 396, 'powers': [477, 373, 733, 137], 'representative': 11700734624, 'size': 2}
  • id: 107012320
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 824, 'group_counter': 3, 'group_order': 3168, 'label': '396D-161', 'order': 396, 'powers': [478, 374, 734, 138], 'representative': 19396939768, 'size': 2}
  • id: 107012321
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 825, 'group_counter': 3, 'group_order': 3168, 'label': '396D163', 'order': 396, 'powers': [461, 375, 739, 138], 'representative': 19271798094, 'size': 2}
  • id: 107012322
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 826, 'group_counter': 3, 'group_order': 3168, 'label': '396D-163', 'order': 396, 'powers': [462, 376, 740, 137], 'representative': 21211492325, 'size': 2}
  • id: 107012323
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 827, 'group_counter': 3, 'group_order': 3168, 'label': '396D167', 'order': 396, 'powers': [431, 377, 753, 136], 'representative': 22024912291, 'size': 2}
  • id: 107012324
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 828, 'group_counter': 3, 'group_order': 3168, 'label': '396D-167', 'order': 396, 'powers': [432, 378, 754, 135], 'representative': 21274063067, 'size': 2}
  • id: 107012325
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 829, 'group_counter': 3, 'group_order': 3168, 'label': '396D169', 'order': 396, 'powers': [438, 379, 759, 134], 'representative': 16643825684, 'size': 2}
  • id: 107012327
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 830, 'group_counter': 3, 'group_order': 3168, 'label': '396D-169', 'order': 396, 'powers': [437, 380, 760, 133], 'representative': 24465172343, 'size': 2}
  • id: 107012328
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 831, 'group_counter': 3, 'group_order': 3168, 'label': '396D173', 'order': 396, 'powers': [470, 381, 771, 132], 'representative': 22462907533, 'size': 2}
  • id: 107012329
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 832, 'group_counter': 3, 'group_order': 3168, 'label': '396D-173', 'order': 396, 'powers': [469, 382, 772, 131], 'representative': 10511889958, 'size': 2}
  • id: 107012330
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 833, 'group_counter': 3, 'group_order': 3168, 'label': '396D175', 'order': 396, 'powers': [486, 383, 775, 130], 'representative': 15079556302, 'size': 2}
  • id: 107012331
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 834, 'group_counter': 3, 'group_order': 3168, 'label': '396D-175', 'order': 396, 'powers': [485, 384, 776, 129], 'representative': 23088615590, 'size': 2}
  • id: 107012332
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 835, 'group_counter': 3, 'group_order': 3168, 'label': '396D179', 'order': 396, 'powers': [457, 385, 789, 128], 'representative': 23401469264, 'size': 2}
  • id: 107012333
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 836, 'group_counter': 3, 'group_order': 3168, 'label': '396D-179', 'order': 396, 'powers': [458, 386, 790, 127], 'representative': 10887314571, 'size': 2}
  • id: 107012334
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 837, 'group_counter': 3, 'group_order': 3168, 'label': '396D181', 'order': 396, 'powers': [439, 387, 795, 127], 'representative': 10011323760, 'size': 2}
  • id: 107012335
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 838, 'group_counter': 3, 'group_order': 3168, 'label': '396D-181', 'order': 396, 'powers': [440, 388, 796, 128], 'representative': 8384483649, 'size': 2}
  • id: 107012336
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 839, 'group_counter': 3, 'group_order': 3168, 'label': '396D185', 'order': 396, 'powers': [444, 389, 807, 129], 'representative': 23464040216, 'size': 2}
  • id: 107012338
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 840, 'group_counter': 3, 'group_order': 3168, 'label': '396D-185', 'order': 396, 'powers': [443, 390, 808, 130], 'representative': 19960076605, 'size': 2}
  • id: 107012339
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 841, 'group_counter': 3, 'group_order': 3168, 'label': '396D191', 'order': 396, 'powers': [481, 391, 825, 133], 'representative': 3253680215, 'size': 2}
  • id: 107012340
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 842, 'group_counter': 3, 'group_order': 3168, 'label': '396D-191', 'order': 396, 'powers': [482, 392, 826, 134], 'representative': 13077291641, 'size': 2}
  • id: 107012341
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 843, 'group_counter': 3, 'group_order': 3168, 'label': '396D193', 'order': 396, 'powers': [465, 393, 831, 135], 'representative': 9010191421, 'size': 2}
  • id: 107012342
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 844, 'group_counter': 3, 'group_order': 3168, 'label': '396D-193', 'order': 396, 'powers': [466, 394, 832, 136], 'representative': 18458378086, 'size': 2}
  • id: 107012343
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 845, 'group_counter': 3, 'group_order': 3168, 'label': '396D197', 'order': 396, 'powers': [433, 395, 843, 137], 'representative': 14891844003, 'size': 2}
  • id: 107012344
    {'aut_label': '396C1', 'centralizer': '2.b1.a1', 'counter': 846, 'group_counter': 3, 'group_order': 3168, 'label': '396D-197', 'order': 396, 'powers': [434, 396, 844, 138], 'representative': 24527743194, 'size': 2}
• 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: 3732213
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 3732224
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  • id: 3732235
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  • id: 3732246
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  • id: 3732257
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  • id: 3732260
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  • id: 3732261
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  • id: 3732262
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  • id: 3732263
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  • id: 3732223
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 2, 2, 2, 2, 0, 0, 0, -2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, 2, -2, 0, 0, 0, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, -2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, -2, 2, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 2, -2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 2, 0, 0, -2, 2, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, -2, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 2, -2, 0, 0, 2, 0, -2, 0, -2, -2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 2, 0, 2, 2, 0, -2, 2, 0, 2, -2, -2, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 2, -2, 0, -2, -2, 0, -2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, -2, 2, 0, -2, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0], 'schur_index': 1}
  • id: 3732225
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 2, 2, -2, -2, 0, 0, 0, -2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, -2, -2, 0, -2, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, -2, 0, -2, -2, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -2, 0, -2, -2, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, -2, -2, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, -2, 0, 0, -2, 0, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, 0, -2, 0, 0, -2, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, -2, 0, -2, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -2, 0, -2, -2, 0, -2, -2, 0, -2, -2, -2, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, -2, -2, 0, -2, -2, 0, -2, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, -2, -2, 0, -2, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0], 'schur_index': 1}
  • id: 3732215
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.1k', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, -4, -4, 0, 0, 0, 4, 0, 4, 4, 4, -4, -4, -4, -4, 0, 0, -2, -2, -2, -2, -2, -2, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, 4, -4, 4, -4, -4, -4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -4, -4, -4, -4, -4, -4, 4, -4, 4, 0, 0, 0, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, -4, -4, 4, -4, -4, -4, -4, 4, 4, -4, -4, 4, 4, -4, -4, 4, 4, -4, -4, -4, -4, 4, 4, -4, -4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, -4, 4, -4, 0, 0, 0, 0, -4, 4, -4, 0, 0, 0, 0, 0, 4, -4, -4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 4, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, -4, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -4, -4, -4, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 2, 0, 0, -2, 2, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, -2, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 2, -2, 0, 0, 2, 0, -2, 0, -2, -2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 2, 0, 2, 2, 0, -2, 2, 0, 2, -2, -2, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 2, -2, 0, -2, -2, 0, -2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, -2, 2, 0, -2, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0], 'schur_index': 1}
  • id: 3732216
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.1l', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, 4, -4, 4, 4, 4, -4, -4, 0, 0, 0, 4, 0, -4, 4, 4, -4, -4, 4, 4, 0, 0, -2, -2, -2, -2, -2, -2, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -4, -4, 4, -4, 4, -4, -4, -4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, 4, -4, 4, 0, 0, 0, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, -4, -4, 4, -4, -4, -4, -4, 4, 4, -4, -4, 4, 4, -4, -4, 4, 4, -4, -4, -4, -4, 4, 4, -4, -4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, -4, 4, -4, 0, 0, 0, 0, -4, 4, -4, 0, 0, 0, 0, 0, 4, -4, -4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 4, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, -4, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -4, -4, -4, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 2, 0, 0, -2, 2, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, -2, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 2, -2, 0, 0, 2, 0, -2, 0, -2, -2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 2, 0, 2, 2, 0, -2, 2, 0, 2, -2, -2, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 2, -2, 0, -2, -2, 0, -2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, -2, 2, 0, -2, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0], 'schur_index': 1}
  • id: 3732226
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2c', 'multiplicity': 2, 'nt': [8, 17], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 0, 0, -2, 2, -2, 0, 2, 0, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 2, -2, 2, -2, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, -4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, 0, 0, 2, -2, 2, 0, -2, 2, 2, -2, -2, -2, 0, 2, 2, -2, 2, -2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 0, 2, 2, 2, -2, 2, 2, 2, 0, -2, -2, 2, -2, 2, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, -2, 2, -2, -2, 0, 2, 2, 2, -2, -2, 0, 0, 0, -4, 0, 0, 0, 0, -4, -4, 0, 0, -4, -4, 0, 0, -4, -4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, 0, 0, 0, -2, 2, -2, -2, 0, 0, 0, -2, -2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 2, 0, 2, 2, -2, 2, -2, 2, 2, 0, 0, 2, -2, 2, -2, 2, 2, 0, 0, 0, 2, -2, 0, -2, 0, -2, 2, 0, 2, -2, -2, 2, -2, -2, -2, -2, 0, 2, -2, -2, 0, 0, 0, 2, 2, -2, 2, 2, 0, 0, 2, 0, 2, -2, 0, -2, 0, -2, 2, -2, -2, 2, 0, 2, 0, 0, 0, 2, -2, -2, 0, 2, 2, -2, 2, -2, 2, 2, 0, -2, 2, 0, -2, 2, -2, -2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, -4, 0, -4, -4, -4, -4, 0, -4, 0, -4, 0, 0, -4, 0, -4, -4, -4, 0, -4, 0, 0, 0, 0, 0, -4, -4, -4, 0, -4, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, -4, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 2, -2, -2, -2, -2, 2, -2, 2, -2, 0, 0, -2, 2, 2, 2, 2, 0, 2, -2, 2, 2, 2, 2, 2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 2, 0, -2, 0, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, -2, -2, 0, -2, 0, -2, -2, 0, -2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, -2, -2, 0, 0, -2, -2, -2, -2, 2, 2, 2, 0, 2, 2, 0, -2, 0, -2, 2, 0, -2, 0, 0, -2, 0, -2, -2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, -2, 0, -2, 2, 0, 2, 0, 0, 2, 0, 2, -2, 0, 2, -2, 0, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, -2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, -2, 2, 0, 2, 0, -2, -2, 2, -2, -2, 2, -2, 2, -2, -2, 2, 0, 2, 0, -2, 0, 2, -2, 0, 0, -2, 0, 0, 2, 2, 0, -2, 2, -2, 2, -2, 0, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 2, -2, 2, -2, 2, 2, -2, -2, -2, -2, 0, -2, 0, 0, -2, 0, -2, -2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, -2, -2, 0, 2, 0, 2, 0, 0, -2, 0, -2, -2, -2, -2, -2, 0, -2, -2, -2, 0, 0, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, 2, 2, 2, 0, 2, -2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, -2, 2, 0, 0, 2, 2, 2, 0, -2, 0, 0, 2, 0, 2, -2, 0, 2, 0, 0, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, -2, -2], 'schur_index': 1}
  • id: 3732227
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2d', 'multiplicity': 2, 'nt': [8, 17], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 0, 0, 2, -2, 2, 0, -2, 0, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, -2, 2, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, -4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, 0, 0, -2, 2, -2, 0, 2, -2, -2, 2, 2, 2, 0, -2, -2, 2, -2, 2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, 0, -2, -2, -2, 2, -2, -2, -2, 0, 2, 2, -2, 2, -2, 0, -2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 2, -2, 2, 2, 0, -2, -2, -2, 2, 2, 0, 0, 0, -4, 0, 0, 0, 0, -4, -4, 0, 0, -4, -4, 0, 0, -4, -4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 0, 0, 0, 2, -2, 2, 2, 0, 0, 0, 2, 2, 2, 2, -2, 0, 0, 0, 0, -2, 2, -2, 0, -2, -2, 2, -2, 2, -2, -2, 0, 0, -2, 2, -2, 2, -2, -2, 0, 0, 0, -2, 2, 0, 2, 0, 2, -2, 0, -2, 2, 2, -2, 2, 2, 2, 2, 0, -2, 2, 2, 0, 0, 0, -2, -2, 2, -2, -2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 2, -2, 2, 2, -2, 0, -2, 0, 0, 0, -2, 2, 2, 0, -2, -2, 2, -2, 2, -2, -2, 0, 2, -2, 0, 2, -2, 2, 2, -2, -2, -2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, -4, 0, -4, -4, -4, -4, 0, -4, 0, -4, 0, 0, -4, 0, -4, -4, -4, 0, -4, 0, 0, 0, 0, 0, -4, -4, -4, 0, -4, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, -4, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, -2, 2, 2, 2, 2, -2, 2, -2, 2, 0, 0, 2, -2, -2, -2, -2, 0, -2, 2, -2, -2, -2, -2, -2, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, -2, 0, 0, 2, 2, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, -2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, -2, 0, -2, -2, -2, 0, -2, -2, -2, -2, -2, 0, 0, -2, 0, -2, 0, 2, 2, 0, 0, 2, 2, 2, 2, -2, -2, -2, 0, -2, -2, 0, 2, 0, 2, -2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, -2, 0, -2, 0, 0, -2, 0, -2, 2, 0, -2, 2, 0, -2, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, 2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 2, -2, 0, -2, 0, 2, 2, -2, 2, 2, -2, 2, -2, 2, 2, -2, 0, -2, 0, 2, 0, -2, 2, 0, 0, 2, 0, 0, -2, -2, 0, 2, -2, 2, -2, 2, 0, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 2, 0, -2, 2, -2, 2, -2, -2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, -2, -2, 0, -2, -2, 0, -2, -2, -2, -2, 0, 0, 0, 2, 2, 0, -2, 0, -2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, -2, -2, -2, 0, -2, 2, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, -2, 0, -2, -2, -2, -2, 2, -2, 0, 0, -2, -2, -2, 0, 2, 0, 0, -2, 0, -2, 2, 0, -2, 0, 0, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 2, 2], 'schur_index': 1}
  • id: 3732228
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2e', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 4, 4, 4, 4, 0, 0, 0, -4, 0, 0, 4, 4, -4, -4, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, 4, -4, -4, -4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, -4, 4, -4, 0, 0, 0, -4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, -4, -4, 4, -4, -4, -4, -4, 4, 4, -4, -4, 4, 4, -4, -4, 4, 4, -4, -4, -4, -4, 4, 4, -4, -4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 4, -4, 4, 0, 0, 0, 0, 4, -4, 4, 0, 0, 0, 0, 0, -4, 4, 4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -4, 4, 4, 0, 0, -4, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, -4, -4, 0, -4, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -4, 0, 4, -4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 4, 4, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, -2, 2, 0, 2, 0, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 2, -2, 0, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 2, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, -2, 2, 0, 0, -2, 0, 2, 0, 2, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, -2, -2, 0, 2, -2, 0, -2, 2, 2, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, -2, 2, 0, 2, 2, 0, 2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, -2, 0, 2, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0], 'schur_index': 1}
  • id: 3732229
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2f', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 4, 4, -4, -4, 0, 0, 0, -4, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, -4, -4, -4, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, -4, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, -4, -4, 0, -4, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -4, 0, -4, -4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0], 'schur_index': 1}
  • id: 3732217
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  • id: 3732218
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  • id: 3732219
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  • id: 3732220
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  • id: 3732230
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  • id: 3732231
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  • id: 3732232
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  • id: 3732233
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  • id: 3732221
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  • id: 3732222
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  • id: 3732234
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  • id: 3732236
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  • id: 3732237
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  • id: 3732238
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  • id: 3732239
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2o', 'multiplicity': 10, 'nt': [44, 7], 'qdim': 20, 'qvalues': [20, 20, -20, 0, 20, 20, -20, -20, 0, 0, 0, 20, 0, 0, 20, 20, -20, -20, 0, 0, 0, 0, 20, 20, 20, 20, 20, 20, -2, -2, -2, -2, -2, -20, -20, -20, -20, 20, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 20, 20, 20, 20, 20, -20, -20, -20, -20, -20, -20, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -20, -20, -20, -20, -20, -20, -20, -20, -20, -20, -20, -20, 20, 0, 0, 0, 0, 20, 20, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, 2, -2, 0, 0, 0, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 2, -2, 2, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 2, 0, 0, -2, 2, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, -2, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 2, -2, 0, 0, 2, 0, -2, 0, -2, -2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 2, 0, 2, 2, 0, -2, 2, 0, 2, -2, -2, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 2, -2, 0, -2, -2, 0, -2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, -2, 2, 0, -2, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0], 'schur_index': 1}
  • id: 3732240
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2p', 'multiplicity': 10, 'nt': [44, 9], 'qdim': 20, 'qvalues': [20, 20, -20, 0, 20, 20, 20, 20, 0, 0, 0, -20, 0, 0, 20, 20, -20, -20, 0, 0, 0, 0, 20, 20, 20, 20, 20, 20, -2, -2, -2, -2, -2, 20, 20, 20, 20, -20, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 20, 20, 20, 20, 20, -20, -20, -20, -20, -20, -20, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -20, 0, 0, 0, 0, -20, -20, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, -2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, -2, 2, -2, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, -2, 2, 0, 2, 0, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 2, -2, 0, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 2, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, -2, 2, 0, 0, -2, 0, 2, 0, 2, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, -2, -2, 0, 2, -2, 0, -2, 2, 2, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, -2, 2, 0, 2, 2, 0, 2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, -2, 0, 2, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0], 'schur_index': 1}
  • id: 3732241
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  • id: 3732242
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  • id: 3732243
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  • id: 3732244
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  • id: 3732245
    {'cdim': 2, 'counter': 39, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2u', 'multiplicity': 20, 'nt': [88, 0], 'qdim': 40, 'qvalues': [40, -40, 0, 0, 40, 40, 0, 0, 20, -20, 20, 0, -20, 0, -40, -40, 0, 0, 0, 0, 0, 0, 40, 40, 40, 40, 40, 40, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 20, -20, 20, -20, -20, 20, -20, 20, 0, 0, -40, -40, -40, -40, -40, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -20, 20, 20, 0, 0, -20, 20, -20, 0, 20, -20, -20, 20, 20, 20, 0, -20, -20, 20, -20, 20, -20, 20, 20, -20, -20, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 0, 2, 2, 2, -2, 2, 2, 2, 0, -2, -2, 2, -2, 2, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, -2, 2, -2, -2, 0, 2, 2, 2, -2, -2, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -2, 0, 0, 0, -2, 2, -2, -2, 0, 0, 0, -2, -2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 2, 0, 2, 2, -2, 2, -2, 2, 2, 0, 0, 2, -2, 2, -2, 2, 2, 0, 0, 0, 2, -2, 0, -2, 0, -2, 2, 0, 2, -2, -2, 2, -2, -2, -2, -2, 0, 2, -2, -2, 0, 0, 0, 2, 2, -2, 2, 2, 0, 0, 2, 0, 2, -2, 0, -2, 0, -2, 2, -2, -2, 2, 0, 2, 0, 0, 0, 2, -2, -2, 0, 2, 2, -2, 2, -2, 2, 2, 0, -2, 2, 0, -2, 2, -2, -2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 4, 4, 4, 0, 4, 0, 4, 0, 0, 4, 0, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 2, -2, -2, -2, -2, 2, -2, 2, -2, 0, 0, -2, 2, 2, 2, 2, 0, 2, -2, 2, 2, 2, 2, 2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 2, 0, -2, 0, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, -2, -2, 0, -2, 0, -2, -2, 0, -2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, -2, -2, 0, 0, -2, -2, -2, -2, 2, 2, 2, 0, 2, 2, 0, -2, 0, -2, 2, 0, -2, 0, 0, -2, 0, -2, -2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, -2, 0, -2, 2, 0, 2, 0, 0, 2, 0, 2, -2, 0, 2, -2, 0, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, -2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, -2, 2, 0, 2, 0, -2, -2, 2, -2, -2, 2, -2, 2, -2, -2, 2, 0, 2, 0, -2, 0, 2, -2, 0, 0, -2, 0, 0, 2, 2, 0, -2, 2, -2, 2, -2, 0, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, -2, 0, 2, -2, 2, -2, 2, 2, -2, -2, -2, -2, 0, -2, 0, 0, -2, 0, -2, -2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, -2, -2, 0, 2, 0, 2, 0, 0, -2, 0, -2, -2, -2, -2, -2, 0, -2, -2, -2, 0, 0, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, 2, 2, 2, 0, 2, -2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, -2, 2, 0, 0, 2, 2, 2, 0, -2, 0, 0, 2, 0, 2, -2, 0, 2, 0, 0, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, -2, -2], 'schur_index': 1}
  • id: 3732247
    {'cdim': 2, 'counter': 40, 'faithful': False, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2v', 'multiplicity': 20, 'nt': [132, 0], 'qdim': 40, 'qvalues': [40, 40, -40, 0, 40, 40, -40, -40, 0, 0, 0, 40, 0, 0, 40, 40, -40, -40, 0, 0, 0, 0, -20, -20, -20, -20, -20, -20, -4, -4, -4, -4, -4, -40, -40, -40, -40, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, -20, -20, -20, -20, -20, 20, 20, 20, 20, 20, 20, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, -4, 4, 4, 4, -4, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -20, 0, 0, 0, 0, -20, -20, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, -4, 4, -4, 0, 0, 0, -4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 4, 4, -4, 4, 4, 4, 4, -4, -4, 4, 4, -4, -4, 4, 4, -4, -4, 4, 4, 4, 4, -4, -4, 4, 4, 4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 4, -4, 4, 0, 0, 0, 0, 4, -4, 4, 0, 0, 0, 0, 0, -4, 4, 4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -4, 4, 4, 0, 0, -4, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, -4, -4, 0, -4, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -4, 0, 4, -4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 2, -2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, -2, 2, 0, 2, 0, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 2, -2, 0, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, 0, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 2, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, -2, 2, 0, 0, -2, 0, 2, 0, 2, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, -2, -2, 0, 2, -2, 0, -2, 2, 2, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, -2, 2, 0, 2, 2, 0, 2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, -2, 0, 2, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0], 'schur_index': 1}
  • id: 3732248
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  • id: 3732249
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  • id: 3732250
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  • id: 3732251
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  • id: 3732252
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  • id: 3732253
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  • id: 3732254
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  • id: 3732255
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  • id: 3732256
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  • id: 3732258
    {'cdim': 2, 'counter': 50, 'faithful': True, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2af', 'multiplicity': 120, 'nt': [792, 0], 'qdim': 240, 'qvalues': [240, -240, 0, 0, -120, -120, 0, 0, -120, 120, -120, 0, 120, 0, 120, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -24, -24, -24, -24, 0, 0, 0, 0, 0, 0, 60, -60, 60, -60, -60, 60, -60, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 24, 0, 0, 0, 24, 0, 0, 0, 24, 24, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, 0, 0, 0, 0, 0, 12, 12, 12, 12, -12, -12, -12, 0, -12, -12, -12, 12, -12, -12, -12, 0, 12, 12, -12, 12, -12, 0, -12, -12, -12, -12, -12, 12, 12, 12, 12, 0, 12, -12, 12, 12, 0, -12, -12, -12, 12, 12, 0, 0, 0, -12, 0, 0, 0, 0, -12, -12, 0, 0, -12, -12, 0, 0, -12, -12, 0, 0, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -6, 6, -6, -6, 0, 0, 0, -6, -6, -6, -6, 6, 0, 0, 0, 0, 6, -6, 6, 0, 6, 6, -6, 6, -6, 6, 6, 0, 0, 6, -6, 6, -6, 6, 6, 0, 0, 0, 6, -6, 0, -6, 0, -6, 6, 0, 6, -6, -6, 6, -6, -6, -6, -6, 0, 6, -6, -6, 0, 0, 0, 6, 6, -6, 6, 6, 0, 0, 6, 0, 6, -6, 0, -6, 0, -6, 6, -6, -6, 6, 0, 6, 0, 0, 0, 6, -6, -6, 0, 6, 6, -6, 6, -6, 6, 6, 0, -6, 6, 0, -6, 6, -6, -6, 6, 6, 6, 6, 6, 0, 0, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3732259
    {'cdim': 2, 'counter': 51, 'faithful': True, 'group': '3168.c', 'group_order': 3168, 'image': None, 'label': '3168.c.2ag', 'multiplicity': 120, 'nt': [792, 0], 'qdim': 240, 'qvalues': [240, -240, 0, 0, -120, -120, 0, 0, 120, -120, 120, 0, -120, 0, 120, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -24, -24, -24, -24, 0, 0, 0, 0, 0, 0, -60, 60, -60, 60, 60, -60, 60, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 24, 0, 0, 0, 24, 0, 0, 0, 24, 24, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, 0, 0, 0, 0, 0, -12, -12, -12, -12, 12, 12, 12, 0, 12, 12, 12, -12, 12, 12, 12, 0, -12, -12, 12, -12, 12, 0, 12, 12, 12, 12, 12, -12, -12, -12, -12, 0, -12, 12, -12, -12, 0, 12, 12, 12, -12, -12, 0, 0, 0, -12, 0, 0, 0, 0, -12, -12, 0, 0, -12, -12, 0, 0, -12, -12, 0, 0, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, -6, 6, 6, 0, 0, 0, 6, 6, 6, 6, -6, 0, 0, 0, 0, -6, 6, -6, 0, -6, -6, 6, -6, 6, -6, -6, 0, 0, -6, 6, -6, 6, -6, -6, 0, 0, 0, -6, 6, 0, 6, 0, 6, -6, 0, -6, 6, 6, -6, 6, 6, 6, 6, 0, -6, 6, 6, 0, 0, 0, -6, -6, 6, -6, -6, 0, 0, -6, 0, -6, 6, 0, 6, 0, 6, -6, 6, 6, -6, 0, -6, 0, 0, 0, -6, 6, 6, 0, -6, -6, 6, -6, 6, -6, -6, 0, 6, -6, 0, 6, -6, 6, 6, -6, -6, -6, -6, -6, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• group 3168.c does not appear in gps_char
• 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: 60219941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 3168, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 66, 'label': '3168.c.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3168.c', 'subgroup_hash': 8813592882577988912, 'subgroup_order': 3168, 'subgroup_tex': 'D_{44}:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60219985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 1584, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1584.135', 'subgroup_hash': 135, 'subgroup_order': 1584, 'subgroup_tex': 'D_{44}:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60219996
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 1584, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1584.79', 'subgroup_hash': 79, 'subgroup_order': 1584, 'subgroup_tex': 'C_4\\times C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60220007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 1584, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1584.37', 'subgroup_hash': 37, 'subgroup_order': 1584, 'subgroup_tex': 'C_{132}.C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60220018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 1056, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1056.81', 'subgroup_hash': 81, 'subgroup_order': 1056, 'subgroup_tex': 'D_{44}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60220029
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 792, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '792.28', 'subgroup_hash': 28, 'subgroup_order': 792, 'subgroup_tex': 'C_2\\times C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60220040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 792, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '792.15', 'subgroup_hash': 15, 'subgroup_order': 792, 'subgroup_tex': 'C_9\\times D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60220051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 792, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '792.13', 'subgroup_hash': 13, 'subgroup_order': 792, 'subgroup_tex': 'C_{99}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60220062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '792.17', 'subgroup_hash': 17, 'subgroup_order': 792, 'subgroup_tex': 'C_{99}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60219942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 396, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '792.28', 'subgroup_hash': 28, 'subgroup_order': 792, 'subgroup_tex': 'C_2\\times C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60219953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '792.14', 'subgroup_hash': 14, 'subgroup_order': 792, 'subgroup_tex': 'D_{11}\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60219964
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '792.2', 'subgroup_hash': 2, 'subgroup_order': 792, 'subgroup_tex': 'C_{11}:C_{72}', 'supersolvable': True, 'sylow': 0}
  • id: 60219975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 528, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '528.129', 'subgroup_hash': 129, 'subgroup_order': 528, 'subgroup_tex': 'D_{44}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60219979
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 528, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '528.79', 'subgroup_hash': 79, 'subgroup_order': 528, 'subgroup_tex': 'C_4\\times C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60219980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 528, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '528.37', 'subgroup_hash': 37, 'subgroup_order': 528, 'subgroup_tex': 'C_{132}.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60219981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 396, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.10', 'subgroup_hash': 10, 'subgroup_order': 396, 'subgroup_tex': 'C_2\\times C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60219982
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 396, 'counter': 17, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.4', 'subgroup_hash': 4, 'subgroup_order': 396, 'subgroup_tex': 'C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60219983
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 396, 'counter': 18, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.4', 'subgroup_hash': 4, 'subgroup_order': 396, 'subgroup_tex': 'C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60219984
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 198, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '396.7', 'subgroup_hash': 7, 'subgroup_order': 396, 'subgroup_tex': 'C_9\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60219986
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 198, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '396.2', 'subgroup_hash': 2, 'subgroup_order': 396, 'subgroup_tex': 'C_{11}:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60219987
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 99, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '396.4', 'subgroup_hash': 4, 'subgroup_order': 396, 'subgroup_tex': 'C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60219988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 99, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '396.4', 'subgroup_hash': 4, 'subgroup_order': 396, 'subgroup_tex': 'C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60219989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 352, 'counter': 23, 'cyclic': False, 'direct': True, 'hall': 22, 'label': '3168.c.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '352.11', 'subgroup_hash': 11, 'subgroup_order': 352, 'subgroup_tex': 'D_{44}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60219990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '3168.c.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.54', 'subgroup_hash': 54, 'subgroup_order': 288, 'subgroup_tex': 'D_4:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60219991
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 264, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '264.28', 'subgroup_hash': 28, 'subgroup_order': 264, 'subgroup_tex': 'C_2\\times C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60219992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 264, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '264.15', 'subgroup_hash': 15, 'subgroup_order': 264, 'subgroup_tex': 'C_3\\times D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60219993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 264, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '264.13', 'subgroup_hash': 13, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60219994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '264.17', 'subgroup_hash': 17, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60219995
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 132, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '264.28', 'subgroup_hash': 28, 'subgroup_order': 264, 'subgroup_tex': 'C_2\\times C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60219997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '264.14', 'subgroup_hash': 14, 'subgroup_order': 264, 'subgroup_tex': 'C_{12}\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60219998
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '264.2', 'subgroup_hash': 2, 'subgroup_order': 264, 'subgroup_tex': 'C_{11}:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60219999
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 198, 'counter': 32, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '198.4', 'subgroup_hash': 4, 'subgroup_order': 198, 'subgroup_tex': 'C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60220000
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 99, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '198.4', 'subgroup_hash': 4, 'subgroup_order': 198, 'subgroup_tex': 'C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60220001
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 99, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '198.2', 'subgroup_hash': 2, 'subgroup_order': 198, 'subgroup_tex': 'C_9\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60220002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 176, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '176.30', 'subgroup_hash': 30, 'subgroup_order': 176, 'subgroup_tex': 'D_{44}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60220003
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 176, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.19', 'subgroup_hash': 19, 'subgroup_order': 176, 'subgroup_tex': 'C_4\\times C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60220004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 176, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.9', 'subgroup_hash': 9, 'subgroup_order': 176, 'subgroup_tex': 'C_{11}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60220005
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 144, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '22.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '22.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 22, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{11}', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.20', 'subgroup_hash': 20, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60220006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.22.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.50', 'subgroup_hash': 50, 'subgroup_order': 144, 'subgroup_tex': 'D_4:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60220008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.22.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.24', 'subgroup_hash': 24, 'subgroup_order': 144, 'subgroup_tex': 'C_9\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60220009
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 132, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.10', 'subgroup_hash': 10, 'subgroup_order': 132, 'subgroup_tex': 'C_2\\times C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60220010
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 132, 'counter': 42, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60220011
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 132, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60220012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 66, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60220013
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 66, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '132.2', 'subgroup_hash': 2, 'subgroup_order': 132, 'subgroup_tex': 'C_{11}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60220014
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 33, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60220015
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 33, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60220016
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 99, 'counter': 48, 'cyclic': True, 'direct': False, 'hall': 33, 'label': '3168.c.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '99.1', 'subgroup_hash': 1, 'subgroup_order': 99, 'subgroup_tex': 'C_{99}', 'supersolvable': True, 'sylow': 0}
  • id: 60220017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.33.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '33.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.54', 'subgroup_hash': 54, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60220019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 88, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.8', 'subgroup_hash': 8, 'subgroup_order': 88, 'subgroup_tex': 'C_2\\times C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60220020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 88, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{36}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.5', 'subgroup_hash': 5, 'subgroup_order': 88, 'subgroup_tex': 'D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60220021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 88, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{36}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.3', 'subgroup_hash': 3, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60220022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 44, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60220023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 44, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.8', 'subgroup_hash': 8, 'subgroup_order': 88, 'subgroup_tex': 'C_2\\times C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60220024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 44, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60220025
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 44, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.1', 'subgroup_hash': 1, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60220026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 72, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.44.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60220027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.44.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60220028
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 36, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.44.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60220030
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.44.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60220031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.44.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60220032
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.44.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.2', 'subgroup_hash': 2, 'subgroup_order': 72, 'subgroup_tex': 'C_{72}', 'supersolvable': True, 'sylow': 0}
  • id: 60220033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.44.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.11', 'subgroup_hash': 11, 'subgroup_order': 72, 'subgroup_tex': 'Q_8\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60220034
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 66, 'counter': 64, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.21', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 21, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60220035
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 33, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60220036
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 33, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60220037
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 48, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.66.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '66.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '66.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 66, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60220038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.66.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60220039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.66.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.24', 'subgroup_hash': 24, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60220041
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 44, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.4', 'subgroup_hash': 4, 'subgroup_order': 44, 'subgroup_tex': 'C_2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60220042
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 44, 'counter': 71, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60220043
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 44, 'counter': 72, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{36}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60220044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 22, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60220045
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 22, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60220046
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 11, 'counter': 75, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60220047
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 11, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.72.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60220048
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 36, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.88.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '88.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '88.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 88, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60220049
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 3168, 'characteristic': True, 'core_order': 36, 'counter': 78, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.88.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '88.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '88.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 88, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{44}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60220050
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 36, 'counter': 79, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.88.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '88.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '88.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 88, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60220052
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.88.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60220053
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.88.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60220054
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.88.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60220055
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 9, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.88.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60220056
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 33, 'counter': 84, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.54', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 54, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60220057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '3168.c.99.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '99.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 99, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 2}
  • id: 60220058
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 24, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.132.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60220059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.132.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60220060
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 12, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.132.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60220061
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.132.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60220063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.132.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60220064
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 91, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.132.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60220065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.132.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60220066
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 22, 'counter': 93, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.21', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 21, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_{36}', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60220067
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 11, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60220068
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 11, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60220069
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 3168, 'characteristic': True, 'core_order': 18, 'counter': 96, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.176.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '176.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '176.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 176, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60220070
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 9, 'counter': 97, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.176.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 176, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60220071
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 98, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.176.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 176, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60220072
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 16, 'counter': 99, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.198.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '198.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '198.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 198, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 60219943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.198.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 198, 'quotient_simple': None, '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: 60219944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.198.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 198, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60219945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 12, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.264.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '264.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '264.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 264, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{33}:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60219946
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 3168, 'characteristic': True, 'core_order': 12, 'counter': 103, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.264.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '264.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '264.15', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 264, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{44}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60219947
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 12, 'counter': 104, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.264.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '264.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '264.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 264, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60219948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.264.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60219949
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 106, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.264.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60219950
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 3, 'counter': 107, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.264.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60219951
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 3, 'counter': 108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.264.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60219952
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 11, 'counter': 109, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '3168.c.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.54', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 54, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_{36}', 'simple': True, 'solvable': True, 'special_labels': ['L3', 'C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
  • id: 60219954
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 3168, 'characteristic': True, 'core_order': 9, 'counter': 110, 'cyclic': True, 'direct': True, 'hall': 3, 'label': '3168.c.352.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '352.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '352.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 352, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{44}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 3}
  • id: 60219955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 8, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.396.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '396.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '396.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 396, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60219956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.396.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 396, 'quotient_simple': None, '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: 60219957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.396.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 396, 'quotient_simple': None, '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: 60219958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.396.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 396, 'quotient_simple': None, '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: 60219959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.396.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 396, 'quotient_simple': None, '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: 60219960
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 116, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.396.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 396, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60219961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.396.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 396, 'quotient_simple': None, '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: 60219962
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 3168, 'characteristic': True, 'core_order': 6, 'counter': 118, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.528.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '528.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '528.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 528, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}:C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60219963
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 3, 'counter': 119, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.528.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 528, 'quotient_simple': 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: 60219965
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.528.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 528, 'quotient_simple': 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: 60219966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3168.c.792.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '792.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '792.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 792, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{99}:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60219967
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 3168, 'characteristic': True, 'core_order': 4, 'counter': 122, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.792.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '792.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '792.15', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 792, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{44}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60219968
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 4, 'counter': 123, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.792.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '792.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '792.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 792, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{11}\\times C_{36}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60219969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3168.c.792.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 792, 'quotient_simple': 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: 60219970
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.792.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 792, 'quotient_simple': 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: 60219971
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.792.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 792, 'quotient_simple': 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: 60219972
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.792.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 792, 'quotient_simple': 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: 60219973
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 3168, 'characteristic': True, 'core_order': 3, 'counter': 128, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.1056.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1056.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1056.81', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 81, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1056, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{44}:C_{12}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 60219974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 3168, 'characteristic': True, 'core_order': 2, 'counter': 129, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3168.c.1584.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1584.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1584.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1584, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}:C_{36}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60219976
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': False, 'core_order': 1, 'counter': 130, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.1584.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1584.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1584, '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: 60219977
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 131, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3168.c.1584.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1584.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1584, '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: 60219978
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3168.c', 'ambient_counter': 3, 'ambient_order': 3168, 'ambient_tex': 'D_{44}:C_{36}', 'central': True, 'central_factor': False, 'centralizer_order': 3168, 'characteristic': True, 'core_order': 1, 'counter': 132, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '3168.c.3168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3168.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '3168.c', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8813592882577988912, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 3168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{44}:C_{36}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 60219954
    {'ambient': '3168.c', 'aut_centralizer_order': 3520, 'aut_label': '352.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3520, 'centralizer': '1.a1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '176.a1.a1', '176.b1.a1', '176.c1.a1'], 'contains': ['1056.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [167, 1564, 267, 9050, 2053, 1641, 2866, 2172], 'generators': [2127406316, 19522081488], 'label': '3168.c.352.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '352.a1.a1', 'normal_contained_in': ['32.a1.a1', '176.a1.a1'], 'normal_contains': ['1056.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '352.a1.a1', 'projective_image': '352.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '352.11', 'quotient_action_kernel_order': 352, 'quotient_fusion': None, 'short_label': '352.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219973
    {'ambient': '3168.c', 'aut_centralizer_order': 10560, 'aut_label': '1056.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '352.a1.a1', '528.a1.a1', '528.b1.a1', '528.c1.a1'], 'contains': ['3168.a1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1176, 1591, 1250, 9011, 4998, 2539, 3512, 3251], 'generators': [2127406316], 'label': '3168.c.1056.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1056.a1.a1', 'normal_contained_in': ['96.a1.a1', '352.a1.a1', '528.a1.a1'], 'normal_contains': ['3168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1056.a1.a1', 'projective_image': '1056.81', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1056.81', 'quotient_action_kernel_order': 1056, 'quotient_fusion': None, 'short_label': '1056.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219941
    {'ambient': '3168.c', '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': '88.b1.a1', 'complements': ['3168.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6126, 7861, 5959, 3490, 5768, 3460, 6624, 3641], 'generators': [7508493074, 15767835078, 16018118178, 158006, 3941958700, 24778026109, 23839464637, 13640428742], 'label': '3168.c.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '88.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60219942
    {'ambient': '3168.c', 'aut_centralizer_order': 44, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '240.208', 'aut_weyl_index': 88, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.f1.b1', '12.e1.a1', '44.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7525, -1, 1260, -1, 6364, -1, 9151, -1], 'generators': [7508493074, 16018118178, 3941958700, 24778026109, 23839464637, 13640428742], 'label': '3168.c.4.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.e1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219943
    {'ambient': '3168.c', 'aut_centralizer_order': 120, 'aut_label': '198.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '66.b1.a1', '99.a1.a1'], 'contains': ['396.a1.a1', '396.b1.a1', '396.d1.a1', '396.e1.a1', '396.g1.a1'], 'core': '396.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [7432, -1, 7973, -1, 7384, -1, 5357, -1], 'generators': [20898638245, 24778026504, 24778026109, 158006], 'label': '3168.c.198.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '198.b1.a1', 'projective_image': '792.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60219944
    {'ambient': '3168.c', 'aut_centralizer_order': 120, 'aut_label': '198.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '66.c1.a1', '99.a1.a1'], 'contains': ['396.a1.a1', '396.f1.a1'], 'core': '396.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9107, -1, 9199, -1, 9339, -1, 7796, -1], 'generators': [20898638245, 24778026504, 24778026109, 9929764], 'label': '3168.c.198.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '198.c1.a1', 'projective_image': '792.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60219945
    {'ambient': '3168.c', 'aut_centralizer_order': 5280, 'aut_label': '264.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '88.a1.a1', '132.a1.a1', '132.b1.a1', '132.c1.a1'], 'contains': ['528.a1.a1', '528.b1.a1', '792.a1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6711, 3722, 2939, 6807, 5552, 3448, 6286, 4674], 'generators': [24778026504, 2127406316, 24778026109], 'label': '3168.c.264.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '264.a1.a1', 'normal_contained_in': ['24.a1.a1', '88.a1.a1', '132.a1.a1'], 'normal_contains': ['528.a1.a1', '792.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '264.a1.a1', 'projective_image': '528.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '132.10', 'quotient_action_kernel_order': 132, 'quotient_fusion': None, 'short_label': '264.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219946
    {'ambient': '3168.c', 'aut_centralizer_order': 5280, 'aut_label': '264.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '88.b1.a1', '132.a1.a1', '132.d1.a1', '132.f1.a1'], 'contains': ['528.a1.a1', '792.b1.a1'], 'core': '264.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4724, 2481, 5776, 5087, 5293, 2795, 5176, 4020], 'generators': [24778026504, 2127406316, 3941958762], 'label': '3168.c.264.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '264.b1.a1', 'normal_contained_in': ['24.b1.a1', '88.b1.a1', '132.a1.a1'], 'normal_contains': ['528.a1.a1', '792.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '264.b1.a1', 'projective_image': '264.15', 'quotient_action_image': '1.1', 'quotient_action_kernel': '264.15', 'quotient_action_kernel_order': 264, 'quotient_fusion': None, 'short_label': '264.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219947
    {'ambient': '3168.c', 'aut_centralizer_order': 5280, 'aut_label': '264.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '88.c1.a1', '132.a1.a1', '132.e1.a1', '132.g1.a1'], 'contains': ['528.a1.a1', '792.c1.a1'], 'core': '264.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4138, 5874, 7303, 4266, 4887, 4101, 3204, 3507], 'generators': [20898638245, 24778026504, 2127406316], 'label': '3168.c.264.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '264.c1.a1', 'normal_contained_in': ['24.c1.a1', '88.c1.a1', '132.a1.a1'], 'normal_contains': ['528.a1.a1', '792.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '264.c1.a1', 'projective_image': '528.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '132.4', 'quotient_action_kernel_order': 132, 'quotient_fusion': None, 'short_label': '264.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219948
    {'ambient': '3168.c', 'aut_centralizer_order': 240, 'aut_label': '264.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '88.d1.a1', '132.b1.a1', '132.d1.a1', '132.e1.a1'], 'contains': ['528.a1.a1', '528.c1.a1', '792.d1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [1179, -1, 3560, -1, 3712, -1, 2950, -1], 'generators': [24778026504, 2127406316, 158006], 'label': '3168.c.264.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '264.d1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219949
    {'ambient': '3168.c', 'aut_centralizer_order': 240, 'aut_label': '264.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '88.e1.a1', '132.b1.a1', '132.d1.a1', '132.g1.a1'], 'contains': ['528.a1.a1', '792.e1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [1764, -1, 4332, -1, 4472, -1, 3603, -1], 'generators': [24778026504, 2127406316, 314821], 'label': '3168.c.264.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '264.e1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219950
    {'ambient': '3168.c', 'aut_centralizer_order': 1320, 'aut_label': '264.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '88.f1.a1', '132.c1.a1'], 'contains': ['528.b1.a1', '792.f1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8280, -1, 1042, -1, 7513, -1, 8940, -1], 'generators': [2127406316, 20898638578, 24778026109], 'label': '3168.c.264.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '66.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '264.f1.a1', 'projective_image': '1056.81', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219951
    {'ambient': '3168.c', 'aut_centralizer_order': 1320, 'aut_label': '264.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '88.f1.b1', '132.c1.a1'], 'contains': ['528.b1.a1', '792.f1.b1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8280, -1, 1350, -1, 7513, -1, 8433, -1], 'generators': [2127406316, 3941958700, 24778026109], 'label': '3168.c.264.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '66.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '264.f1.b1', 'projective_image': '1056.81', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219952
    {'ambient': '3168.c', 'aut_centralizer_order': 2112, 'aut_label': '288.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2112, 'centralizer': '2.b1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '144.a1.a1', '144.b1.a1', '144.c1.a1'], 'contains': ['3168.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3423, 1980, 3526, 8643, 6352, 3215, 3977, 3927], 'generators': [16018118178], 'label': '3168.c.288.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['96.a1.a1', '144.a1.a1'], 'normal_contains': ['3168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '3168.c', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.20', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219953
    {'ambient': '3168.c', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.e1.a1', '12.f1.a1', '44.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1592, -1, 4058, -1, 1840, -1, 1862, -1], 'generators': [13640428742, 44545782, 7508493074, 23839464637, 16018118178, 9072762367], 'label': '3168.c.4.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '88.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60219955
    {'ambient': '3168.c', 'aut_centralizer_order': 5280, 'aut_label': '396.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '132.a1.a1', '198.a1.a1', '198.b1.a1', '198.c1.a1'], 'contains': ['792.a1.a1', '792.b1.a1', '792.c1.a1'], 'core': '396.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7735, 6626, 8110, 3277, 7975, 6223, 5946, 7449], 'generators': [20898638245, 24778026504, 24778026109], 'label': '3168.c.396.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '396.a1.a1', 'normal_contained_in': ['36.a1.a1', '132.a1.a1', '198.a1.a1'], 'normal_contains': ['792.a1.a1', '792.b1.a1', '792.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '396.a1.a1', 'projective_image': '792.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '198.4', 'quotient_action_kernel_order': 198, 'quotient_fusion': None, 'short_label': '396.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219956
    {'ambient': '3168.c', 'aut_centralizer_order': 240, 'aut_label': '396.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '132.b1.a1', '198.b1.a1'], 'contains': ['792.a1.a1', '792.d1.a1', '792.e1.a1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4968, -1, 5393, -1, 6368, -1, 5357, -1], 'generators': [24778026504, 24778026109, 158006], 'label': '3168.c.396.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '396.b1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60219957
    {'ambient': '3168.c', 'aut_centralizer_order': 2640, 'aut_label': '396.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '132.c1.a1', '198.a1.a1'], 'contains': ['792.a1.a1', '792.f1.a1', '792.f1.b1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9320, -1, 2691, -1, 8833, -1, 8686, -1], 'generators': [24778026504, 3941958700, 24778026109], 'label': '3168.c.396.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '198.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '396.c1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219958
    {'ambient': '3168.c', 'aut_centralizer_order': 240, 'aut_label': '396.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '132.d1.a1', '198.b1.a1'], 'contains': ['792.b1.a1', '792.d1.a1', '792.e1.a1'], 'core': '792.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4500, -1, 6698, -1, 6609, -1, 4922, -1], 'generators': [24778026504, 3941958762, 158006], 'label': '3168.c.396.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '396.d1.a1', 'projective_image': '792.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219959
    {'ambient': '3168.c', 'aut_centralizer_order': 240, 'aut_label': '396.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2640, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '132.e1.a1', '198.b1.a1'], 'contains': ['792.c1.a1', '792.d1.a1'], 'core': '792.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5984, -1, 7364, -1, 6202, -1, 3847, -1], 'generators': [20898638245, 24778026504, 158006], 'label': '3168.c.396.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '396.e1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60219960
    {'ambient': '3168.c', 'aut_centralizer_order': 240, 'aut_label': '396.f1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5280, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '132.f1.a1', '198.c1.a1'], 'contains': ['792.b1.a1'], 'core': '792.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7469, -1, 9152, -1, 8593, -1, 7429, -1], 'generators': [24778026504, 3941958762, 9929764], 'label': '3168.c.396.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '396.f1.a1', 'projective_image': '792.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219961
    {'ambient': '3168.c', 'aut_centralizer_order': 240, 'aut_label': '396.g1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2640, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '132.g1.a1', '198.b1.a1'], 'contains': ['792.c1.a1', '792.e1.a1'], 'core': '792.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5355, -1, 7737, -1, 7126, -1, 4414, -1], 'generators': [20898638245, 24778026504, 314821], 'label': '3168.c.396.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '396.g1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60219962
    {'ambient': '3168.c', 'aut_centralizer_order': 10560, 'aut_label': '528.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '176.a1.a1', '264.a1.a1', '264.b1.a1', '264.c1.a1', '264.d1.a1', '264.e1.a1'], 'contains': ['1056.a1.a1', '1584.a1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2545, 3148, 3339, 6807, 5090, 2795, 3603, 3507], 'generators': [24778026504, 2127406316], 'label': '3168.c.528.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '528.a1.a1', 'normal_contained_in': ['48.a1.a1', '176.a1.a1', '264.a1.a1', '264.b1.a1', '264.c1.a1'], 'normal_contains': ['1056.a1.a1', '1584.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '528.a1.a1', 'projective_image': '528.41', 'quotient_action_image': '1.1', 'quotient_action_kernel': '528.41', 'quotient_action_kernel_order': 528, 'quotient_fusion': None, 'short_label': '528.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219963
    {'ambient': '3168.c', 'aut_centralizer_order': 5280, 'aut_label': '528.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '176.b1.a1', '264.a1.a1', '264.f1.a1', '264.f1.b1'], 'contains': ['1056.a1.a1', '1584.b1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6696, -1, 1184, -1, 5918, -1, 8029, -1], 'generators': [2127406316, 24778026109], 'label': '3168.c.528.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '264.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '528.b1.a1', 'projective_image': '1056.81', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219964
    {'ambient': '3168.c', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.b1.a1', '12.g1.a1', '44.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4986, -1, 6153, -1, 5136, -1, 5760, -1], 'generators': [13640428742, 7508493074, 23839464637, 16018118178, 9929764, 9072762367], 'label': '3168.c.4.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.g1.a1', 'projective_image': '88.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60219965
    {'ambient': '3168.c', 'aut_centralizer_order': 240, 'aut_label': '528.c1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '176.c1.a1', '264.d1.a1'], 'contains': ['1056.a1.a1', '1584.c1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [493, -1, 1593, -1, 3712, -1, 2703, -1], 'generators': [2127406316, 158006], 'label': '3168.c.528.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.d1.a1', 'old_label': '528.c1.a1', 'projective_image': '1056.81', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219966
    {'ambient': '3168.c', 'aut_centralizer_order': 10560, 'aut_label': '792.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '264.a1.a1', '396.a1.a1', '396.b1.a1', '396.c1.a1'], 'contains': ['1584.a1.a1', '1584.b1.a1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7310, 5234, 4146, 5546, 7266, 5284, 6286, 6428], 'generators': [24778026504, 24778026109], 'label': '3168.c.792.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '792.a1.a1', 'normal_contained_in': ['72.a1.a1', '264.a1.a1', '396.a1.a1'], 'normal_contains': ['1584.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '792.a1.a1', 'projective_image': '1584.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '396.10', 'quotient_action_kernel_order': 396, 'quotient_fusion': None, 'short_label': '792.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219967
    {'ambient': '3168.c', 'aut_centralizer_order': 10560, 'aut_label': '792.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '264.b1.a1', '396.a1.a1', '396.d1.a1', '396.f1.a1'], 'contains': ['1584.a1.a1'], 'core': '792.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6129, 4693, 7288, 4545, 7089, 4206, 5357, 5816], 'generators': [24778026504, 3941958762], 'label': '3168.c.792.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '792.b1.a1', 'normal_contained_in': ['72.b1.a1', '264.b1.a1', '396.a1.a1'], 'normal_contains': ['1584.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '792.b1.a1', 'projective_image': '792.15', 'quotient_action_image': '1.1', 'quotient_action_kernel': '792.15', 'quotient_action_kernel_order': 792, 'quotient_fusion': None, 'short_label': '792.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219968
    {'ambient': '3168.c', 'aut_centralizer_order': 10560, 'aut_label': '792.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '264.c1.a1', '396.a1.a1', '396.e1.a1', '396.g1.a1'], 'contains': ['1584.a1.a1'], 'core': '792.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5435, 6264, 7644, 3562, 6719, 6007, 4219, 5350], 'generators': [20898638245, 24778026504], 'label': '3168.c.792.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '792.c1.a1', 'normal_contained_in': ['72.c1.a1', '264.c1.a1', '396.a1.a1'], 'normal_contains': ['1584.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '792.c1.a1', 'projective_image': '1584.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '396.4', 'quotient_action_kernel_order': 396, 'quotient_fusion': None, 'short_label': '792.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219969
    {'ambient': '3168.c', 'aut_centralizer_order': 480, 'aut_label': '792.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '264.d1.a1', '396.b1.a1', '396.d1.a1', '396.e1.a1'], 'contains': ['1584.a1.a1', '1584.c1.a1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4500, -1, 5450, -1, 6202, -1, 4031, -1], 'generators': [24778026504, 158006], 'label': '3168.c.792.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '792.d1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219970
    {'ambient': '3168.c', 'aut_centralizer_order': 480, 'aut_label': '792.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '264.e1.a1', '396.b1.a1', '396.d1.a1', '396.g1.a1'], 'contains': ['1584.a1.a1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4844, -1, 5776, -1, 6553, -1, 4607, -1], 'generators': [24778026504, 314821], 'label': '3168.c.792.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '792.e1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219971
    {'ambient': '3168.c', 'aut_centralizer_order': 2640, 'aut_label': '792.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '264.f1.a1', '396.c1.a1'], 'contains': ['1584.b1.a1'], 'core': '3168.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9070, -1, 2108, -1, 8240, -1, 8813, -1], 'generators': [20898638578, 24778026109], 'label': '3168.c.792.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '198.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '792.f1.a1', 'projective_image': '3168.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219972
    {'ambient': '3168.c', 'aut_centralizer_order': 2640, 'aut_label': '792.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.b1', '264.f1.b1', '396.c1.a1'], 'contains': ['1584.b1.a1'], 'core': '3168.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9070, -1, 2770, -1, 8240, -1, 8478, -1], 'generators': [3941958700, 24778026109], 'label': '3168.c.792.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '198.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '792.f1.b1', 'projective_image': '3168.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219974
    {'ambient': '3168.c', 'aut_centralizer_order': 21120, 'aut_label': '1584.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '528.a1.a1', '792.a1.a1', '792.b1.a1', '792.c1.a1', '792.d1.a1', '792.e1.a1'], 'contains': ['3168.a1.a1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4984, 4461, 5590, 5863, 6636, 4439, 4310, 5117], 'generators': [24778026504], 'label': '3168.c.1584.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1584.a1.a1', 'normal_contained_in': ['144.a1.a1', '528.a1.a1', '792.a1.a1', '792.b1.a1', '792.c1.a1'], 'normal_contains': ['3168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1584.a1.a1', 'projective_image': '1584.41', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1584.41', 'quotient_action_kernel_order': 1584, 'quotient_fusion': None, 'short_label': '1584.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219975
    {'ambient': '3168.c', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '88.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.f1.a1', '18.a1.a1', '66.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5230, 7855, 7811, 2256, 4813, 6689, 4031, 4563], 'generators': [24778026109, 7508493074, 23839464637, 16018118178, 15767835078, 158006], 'label': '3168.c.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60219976
    {'ambient': '3168.c', 'aut_centralizer_order': 10560, 'aut_label': '1584.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '528.b1.a1', '792.a1.a1', '792.f1.a1', '792.f1.b1'], 'contains': ['3168.a1.a1'], 'core': '3168.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7310, -1, 2868, -1, 7266, -1, 8120, -1], 'generators': [24778026109], 'label': '3168.c.1584.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '792.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '1584.b1.a1', 'projective_image': '3168.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1584.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219977
    {'ambient': '3168.c', 'aut_centralizer_order': 480, 'aut_label': '1584.c1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '1.1', 'aut_weyl_index': 21120, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '528.c1.a1', '792.d1.a1'], 'contains': ['3168.a1.a1'], 'core': '3168.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [3256, -1, 3804, -1, 5912, -1, 3331, -1], 'generators': [158006], 'label': '3168.c.1584.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.d1.a1', 'old_label': '1584.c1.a1', 'projective_image': '3168.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1584.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219978
    {'ambient': '3168.c', 'aut_centralizer_order': None, 'aut_label': '3168.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '1056.a1.a1', '1584.a1.a1', '1584.b1.a1', '1584.c1.a1'], 'contains': [], 'core': '3168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3423, 1980, 3618, 8643, 6352, 3215, 3977, 3927], 'generators': [], 'label': '3168.c.3168.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '3168.a1.a1', 'normal_contained_in': ['288.a1.a1', '1056.a1.a1', '1584.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '3168.a1.a1', 'projective_image': '3168.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219979
    {'ambient': '3168.c', 'aut_centralizer_order': 132, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '160.238', 'aut_weyl_index': 132, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '18.b1.a1', '66.a1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8788, 9491, 6685, 498, 8199, 4521, 8265, 6732], 'generators': [7508493074, 15767835078, 16018118178, 3941958700, 24778026109, 23839464637], 'label': '3168.c.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '18.b1.a1', '66.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '264.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219980
    {'ambient': '3168.c', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '88.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '18.c1.a1', '66.c1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7215, 6191, 9679, 4447, 7236, 5622, 6631, 5630], 'generators': [7508493074, 15767835078, 16018118178, 9929764, 24778026109, 23839464637], 'label': '3168.c.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60219981
    {'ambient': '3168.c', 'aut_centralizer_order': 176, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '120.47', 'aut_weyl_index': 176, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '24.a1.a1', '88.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4034, 2746, 1354, 8086, 3218, 1017, 5933, 1583], 'generators': [13640428742, 24778026109, 7508493074, 23839464637, 16018118178], 'label': '3168.c.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '176.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219982
    {'ambient': '3168.c', 'aut_centralizer_order': 176, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '120.47', 'aut_weyl_index': 176, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '88.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2986, 1544, 4246, 7163, 2531, 230, 3732, 796], 'generators': [13640428742, 7508493074, 23839464637, 16018118178, 9072762367], 'label': '3168.c.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1', '88.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '88.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219983
    {'ambient': '3168.c', 'aut_centralizer_order': 176, 'aut_label': '8.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '120.47', 'aut_weyl_index': 176, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '88.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2506, 4264, 5354, 5500, 2307, 2754, 833, 230], 'generators': [13640428742, 7508493074, 23839464637, 16018118178, 15767835078], 'label': '3168.c.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1', '88.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '176.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219984
    {'ambient': '3168.c', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1320.144', 'aut_weyl_index': 16, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.f1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '24.d1.a1', '88.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1014, -1, 2986, -1, 200, -1, 507, -1], 'generators': [13640428742, 7508493074, 23839464637, 16018118178, 158006], 'label': '3168.c.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60219985
    {'ambient': '3168.c', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '88.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.f1.a1', '6.a1.a1', '22.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3102, 7141, 5312, 4028, 2434, 3996, 2444, 2026], 'generators': [13640428742, 24778026109, 7508493074, 23839464637, 16018118178, 15767835078, 158006], 'label': '3168.c.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '88.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60219986
    {'ambient': '3168.c', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1320.144', 'aut_weyl_index': 16, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.a1', '4.f1.a1'], 'contains': ['16.a1.a1', '24.e1.a1', '88.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1607, -1, 3554, -1, 1654, -1, 1474, -1], 'generators': [314821, 13640428742, 7508493074, 23839464637, 16018118178], 'label': '3168.c.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60219987
    {'ambient': '3168.c', 'aut_centralizer_order': 44, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.47', 'aut_weyl_index': 176, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.b1.a1', '24.f1.a1', '88.f1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8003, -1, 417, -1, 6209, -1, 9910, -1], 'generators': [11450451583, 13640428742, 24778026109, 7508493074, 16018118178], 'label': '3168.c.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.f1.a1', 'projective_image': '352.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219988
    {'ambient': '3168.c', 'aut_centralizer_order': 44, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.47', 'aut_weyl_index': 176, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.b1.a1', '24.f1.b1', '88.f1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8003, -1, 991, -1, 6209, -1, 9298, -1], 'generators': [13640428742, 3941958700, 24778026109, 7508493074, 16018118178], 'label': '3168.c.8.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.f1.b1', 'projective_image': '352.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219989
    {'ambient': '3168.c', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '88.b1.a1', 'complements': ['352.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '99.a1.a1'], 'core': '9.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9430, 9353, 9199, 1370, 9016, 8100, 7540, 8073], 'generators': [3941958700, 24778026109, 23839464637, 16018118178, 15767835078, 158006], 'label': '3168.c.9.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '792.15', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60219990
    {'ambient': '3168.c', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '192.1531', 'aut_weyl_index': 110, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '22.b1.a1', '22.c1.a1', '33.a1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6016, -1, 5959, -1, 5768, -1, 6624, -1], 'generators': [20898638245, 24778026504, 2127406316, 3941958700, 24778026109, 19522081488, 158006], 'label': '3168.c.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '88.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60219991
    {'ambient': '3168.c', 'aut_centralizer_order': 264, 'aut_label': '12.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '80.52', 'aut_weyl_index': 264, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.a1.a1', '132.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7215, 6038, 7104, 5410, 6521, 3541, 5543, 5630], 'generators': [24778026109, 7508493074, 23839464637, 16018118178, 15767835078], 'label': '3168.c.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.a1.a1', '132.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '264.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219992
    {'ambient': '3168.c', 'aut_centralizer_order': 12, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 12, 'centralizer': '88.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '36.b1.a1', '132.e1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4616, 4930, 7516, 1693, 3606, 6607, 2562, 3519], 'generators': [7508493074, 23839464637, 16018118178, 15767835078, 158006], 'label': '3168.c.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60219993
    {'ambient': '3168.c', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 12, 'centralizer': '88.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '24.e1.a1', '36.c1.a1', '132.g1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4059, 7498, 8328, 3096, 5293, 5564, 2968, 4563], 'generators': [314821, 7508493074, 23839464637, 16018118178, 15767835078], 'label': '3168.c.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60219994
    {'ambient': '3168.c', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '880.210', 'aut_weyl_index': 24, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.e1.a1', '36.d1.a1', '132.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3086, -1, 3579, -1, 4019, -1, 4439, -1], 'generators': [24778026109, 7508493074, 23839464637, 16018118178, 158006], 'label': '3168.c.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60219995
    {'ambient': '3168.c', 'aut_centralizer_order': 132, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '80.52', 'aut_weyl_index': 264, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.f1.b1', '36.e1.a1', '132.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8837, -1, 2544, -1, 8579, -1, 9604, -1], 'generators': [7508493074, 16018118178, 3941958700, 24778026109, 23839464637], 'label': '3168.c.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.e1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60219996
    {'ambient': '3168.c', 'aut_centralizer_order': 44, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '480.1213', 'aut_weyl_index': 44, 'centralizer': '2.b1.a1', 'complements': ['1584.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '6.b1.a1', '22.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6649, 8408, 4891, 2948, 6230, 1827, 7884, 4195], 'generators': [7508493074, 15767835078, 16018118178, 3941958700, 24778026109, 23839464637, 13640428742], 'label': '3168.c.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.b1.a1', '22.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '88.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60219997
    {'ambient': '3168.c', 'aut_centralizer_order': 12, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '880.210', 'aut_weyl_index': 24, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.d1.a1', '24.e1.a1', '36.f1.a1', '132.d1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2396, -1, 4793, -1, 4465, -1, 3405, -1], 'generators': [44545782, 7508493074, 23839464637, 16018118178, 9072762367], 'label': '3168.c.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60219998
    {'ambient': '3168.c', 'aut_centralizer_order': 12, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '880.210', 'aut_weyl_index': 24, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.c1.a1'], 'contains': ['24.b1.a1', '36.g1.a1', '132.f1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5718, -1, 9483, -1, 7266, -1, 6547, -1], 'generators': [7508493074, 23839464637, 16018118178, 9929764, 9072762367], 'label': '3168.c.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '12.g1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60219999
    {'ambient': '3168.c', 'aut_centralizer_order': 352, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '60.13', 'aut_weyl_index': 352, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1'], 'contains': ['32.a1.a1', '48.a1.a1', '176.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1731, 1386, 1895, 8254, 1737, 242, 1336, 802], 'generators': [13640428742, 7508493074, 23839464637, 16018118178], 'label': '3168.c.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '48.a1.a1', '176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '176.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220000
    {'ambient': '3168.c', 'aut_centralizer_order': 176, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '60.13', 'aut_weyl_index': 352, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.f1.b1'], 'contains': ['32.a1.a1', '48.b1.a1', '176.b1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6031, -1, 346, -1, 2745, -1, 8206, -1], 'generators': [13640428742, 24778026109, 7508493074, 16018118178], 'label': '3168.c.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.b1.a1', 'projective_image': '352.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220001
    {'ambient': '3168.c', 'aut_centralizer_order': 8, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '660.17', 'aut_weyl_index': 32, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '176.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [188, -1, 1199, -1, 853, -1, 468, -1], 'generators': [13640428742, 7508493074, 16018118178, 158006], 'label': '3168.c.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.c1.a1', 'projective_image': '352.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 60220002
    {'ambient': '3168.c', 'aut_centralizer_order': 12, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 12, 'centralizer': '88.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '36.d1.a1', '36.f1.a1', '198.b1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7102, 8765, 8928, 1778, 6881, 9645, 5189, 7496], 'generators': [24778026109, 23839464637, 16018118178, 15767835078, 158006], 'label': '3168.c.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '9.a1.a1'], 'normal_contains': ['36.a1.a1', '36.b1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '792.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60220003
    {'ambient': '3168.c', 'aut_centralizer_order': 264, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '80.52', 'aut_weyl_index': 264, 'centralizer': '2.b1.a1', 'complements': ['176.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.e1.a1', '198.a1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9674, 9769, 7153, 549, 9793, 7564, 8634, 9577], 'generators': [3941958700, 24778026109, 23839464637, 16018118178, 15767835078], 'label': '3168.c.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.b1.a1', '9.a1.a1'], 'normal_contains': ['36.a1.a1', '198.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '792.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220004
    {'ambient': '3168.c', 'aut_centralizer_order': 12, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 12, 'centralizer': '88.b1.a1', 'complements': ['176.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.g1.a1', '198.c1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8713, 7082, 9904, 3949, 9016, 8636, 7501, 8505], 'generators': [24778026109, 23839464637, 16018118178, 9929764, 15767835078], 'label': '3168.c.18.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': ['6.c1.a1', '9.a1.a1'], 'normal_contains': ['36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '792.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60220005
    {'ambient': '3168.c', 'aut_centralizer_order': 440, 'aut_label': '22.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.52', 'aut_weyl_index': 440, 'centralizer': '2.b1.a1', 'complements': ['144.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.c1.a1', '66.a1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6485, 7511, 4205, 3575, 5976, 2154, 7884, 3618], 'generators': [20898638245, 24778026504, 2127406316, 3941958700, 24778026109, 19522081488], 'label': '3168.c.22.a1.a1', 'mobius_quo': 0, 'mobius_sub': 11, 'normal_closure': '22.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['44.a1.a1', '66.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '88.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220006
    {'ambient': '3168.c', 'aut_centralizer_order': 20, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.221', 'aut_weyl_index': 220, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.b1.a1', '44.d1.a1', '44.e1.a1', '44.g1.a1', '66.b1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3346, -1, 5168, -1, 2267, -1, 2281, -1], 'generators': [20898638245, 24778026504, 2127406316, 24778026109, 19522081488, 158006], 'label': '3168.c.22.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.a1', 'projective_image': '88.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220007
    {'ambient': '3168.c', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '88.b1.a1', 'complements': ['1584.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.g1.a1', '6.c1.a1', '22.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5815, 5934, 6256, 5230, 5268, 2929, 6132, 3093], 'generators': [7508493074, 15767835078, 16018118178, 9929764, 24778026109, 23839464637, 13640428742], 'label': '3168.c.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '88.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60220008
    {'ambient': '3168.c', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.221', 'aut_weyl_index': 220, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.f1.a1', '66.c1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5600, -1, 6388, -1, 5531, -1, 6148, -1], 'generators': [20898638245, 24778026504, 2127406316, 24778026109, 9929764, 19522081488], 'label': '3168.c.22.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.a1', 'projective_image': '88.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220009
    {'ambient': '3168.c', 'aut_centralizer_order': 528, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.d1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '72.a1.a1', '264.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7058, 3096, 2962, 7621, 6230, 3553, 7025, 4674], 'generators': [24778026109, 7508493074, 23839464637, 16018118178], 'label': '3168.c.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1', '264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '528.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220010
    {'ambient': '3168.c', 'aut_centralizer_order': 528, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '72.b1.a1', '264.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4421, 2237, 6146, 5895, 5554, 2795, 5142, 3916], 'generators': [7508493074, 23839464637, 16018118178, 9072762367], 'label': '3168.c.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '72.b1.a1', '264.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '264.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220011
    {'ambient': '3168.c', 'aut_centralizer_order': 528, 'aut_label': '24.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '72.c1.a1', '264.c1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4172, 5531, 7700, 3413, 5125, 5261, 2442, 3350], 'generators': [7508493074, 23839464637, 16018118178, 15767835078], 'label': '3168.c.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '72.c1.a1', '264.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '528.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220012
    {'ambient': '3168.c', 'aut_centralizer_order': 24, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.b1.a1', '12.d1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '72.d1.a1', '264.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1776, -1, 3552, -1, 3047, -1, 2145, -1], 'generators': [7508493074, 23839464637, 16018118178, 158006], 'label': '3168.c.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60220013
    {'ambient': '3168.c', 'aut_centralizer_order': 24, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.c1.a1', '12.d1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '72.e1.a1', '264.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2334, -1, 4084, -1, 4472, -1, 3084, -1], 'generators': [314821, 7508493074, 23839464637, 16018118178], 'label': '3168.c.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60220014
    {'ambient': '3168.c', 'aut_centralizer_order': 132, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '40.14', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.e1.a1'], 'contains': ['48.b1.a1', '72.f1.a1', '264.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8850, -1, 1380, -1, 8459, -1, 9788, -1], 'generators': [11450451583, 24778026109, 7508493074, 16018118178], 'label': '3168.c.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '1056.81', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220015
    {'ambient': '3168.c', 'aut_centralizer_order': 132, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '40.14', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '12.e1.a1'], 'contains': ['48.b1.a1', '72.f1.b1', '264.f1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8850, -1, 1865, -1, 8459, -1, 9199, -1], 'generators': [3941958700, 24778026109, 7508493074, 16018118178], 'label': '3168.c.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.b1', 'projective_image': '1056.81', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220016
    {'ambient': '3168.c', 'aut_centralizer_order': 352, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '60.13', 'aut_weyl_index': 352, 'centralizer': '2.b1.a1', 'complements': ['99.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'contains': ['96.a1.a1', '352.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [690, 231, 671, 9502, 1850, 1128, 2497, 1659], 'generators': [13640428742, 7508493074, 16018118178], 'label': '3168.c.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['96.a1.a1', '352.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '352.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.2', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220017
    {'ambient': '3168.c', 'aut_centralizer_order': 30, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '64.261', 'aut_weyl_index': 330, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '11.a1.a1'], 'contains': ['66.a1.a1', '66.b1.a1', '66.c1.a1', '99.a1.a1'], 'core': '66.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [8842, -1, 8330, -1, 7737, -1, 7123, -1], 'generators': [20898638245, 24778026504, 2127406316, 3941958700, 24778026109, 158006], 'label': '3168.c.33.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '33.a1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220018
    {'ambient': '3168.c', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 3, 'centralizer': '88.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '9.a1.a1', '33.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8577, 9543, 8152, 2140, 7486, 5622, 7123, 5630], 'generators': [7508493074, 15767835078, 16018118178, 158006, 3941958700, 24778026109, 23839464637], 'label': '3168.c.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60220019
    {'ambient': '3168.c', 'aut_centralizer_order': 528, 'aut_label': '36.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '396.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8577, 7537, 8994, 4066, 8759, 6503, 6656, 7787], 'generators': [24778026109, 23839464637, 16018118178, 15767835078], 'label': '3168.c.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'normal_contains': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '396.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '792.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220020
    {'ambient': '3168.c', 'aut_centralizer_order': 24, 'aut_label': '36.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '880.118', 'aut_weyl_index': 24, 'centralizer': '88.b1.a1', 'complements': ['88.f1.b1', '88.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '396.e1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6272, 6705, 8279, 1280, 6521, 7931, 4287, 6359], 'generators': [23839464637, 16018118178, 15767835078, 158006], 'label': '3168.c.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.b1.a1', '18.a1.a1'], 'normal_contains': ['72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '1584.41', 'quotient_action_image': '4.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60220021
    {'ambient': '3168.c', 'aut_centralizer_order': 24, 'aut_label': '36.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '880.118', 'aut_weyl_index': 24, 'centralizer': '88.b1.a1', 'complements': ['88.f1.b1', '88.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.a1'], 'contains': ['72.c1.a1', '72.e1.a1', '396.g1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5905, 8804, 9340, 2204, 7629, 7324, 4523, 6965], 'generators': [314821, 23839464637, 16018118178, 15767835078], 'label': '3168.c.36.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': ['12.c1.a1', '18.a1.a1'], 'normal_contains': ['72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '1584.41', 'quotient_action_image': '4.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60220022
    {'ambient': '3168.c', 'aut_centralizer_order': 24, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.a1.a1'], 'contains': ['72.a1.a1', '72.d1.a1', '72.e1.a1', '396.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5075, -1, 5914, -1, 6761, -1, 5597, -1], 'generators': [24778026109, 23839464637, 16018118178, 158006], 'label': '3168.c.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60220023
    {'ambient': '3168.c', 'aut_centralizer_order': 264, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '40.14', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.b1.a1'], 'contains': ['72.a1.a1', '72.f1.a1', '72.f1.b1', '396.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9833, -1, 2702, -1, 9833, -1, 9493, -1], 'generators': [3941958700, 24778026109, 23839464637, 16018118178], 'label': '3168.c.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.e1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220024
    {'ambient': '3168.c', 'aut_centralizer_order': 24, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.d1.a1', '72.e1.a1', '396.d1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4613, -1, 6989, -1, 7089, -1, 4845, -1], 'generators': [23839464637, 16018118178, 158006, 9072762367], 'label': '3168.c.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '792.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60220025
    {'ambient': '3168.c', 'aut_centralizer_order': 24, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 48, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.c1.a1'], 'contains': ['72.b1.a1', '396.f1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7530, -1, 9914, -1, 9085, -1, 7546, -1], 'generators': [23839464637, 16018118178, 9929764, 9072762367], 'label': '3168.c.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '36.g1.a1', 'projective_image': '792.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60220026
    {'ambient': '3168.c', 'aut_centralizer_order': 880, 'aut_label': '44.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 880, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '22.a1.a1', '22.b1.a1', '22.c1.a1'], 'contains': ['88.a1.a1', '88.b1.a1', '88.c1.a1', '132.a1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3833, 4250, 4624, 5753, 2831, 1997, 4845, 2563], 'generators': [20898638245, 24778026504, 2127406316, 24778026109, 19522081488], 'label': '3168.c.44.a1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.a1.a1', 'normal_contained_in': ['4.a1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1', '88.b1.a1', '88.c1.a1', '132.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '88.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.2', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220027
    {'ambient': '3168.c', 'aut_centralizer_order': 40, 'aut_label': '44.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.15', 'aut_weyl_index': 880, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '22.b1.a1'], 'contains': ['88.a1.a1', '88.d1.a1', '88.e1.a1', '132.b1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [1468, -1, 2360, -1, 894, -1, 2220, -1], 'generators': [24778026504, 2127406316, 24778026109, 19522081488, 158006], 'label': '3168.c.44.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.b1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60220028
    {'ambient': '3168.c', 'aut_centralizer_order': 440, 'aut_label': '44.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 880, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '22.a1.a1'], 'contains': ['88.a1.a1', '88.f1.a1', '88.f1.b1', '132.c1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7230, -1, 593, -1, 5909, -1, 9004, -1], 'generators': [24778026504, 2127406316, 3941958700, 24778026109, 19522081488], 'label': '3168.c.44.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '22.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '44.c1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220029
    {'ambient': '3168.c', 'aut_centralizer_order': 88, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '240.208', 'aut_weyl_index': 88, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1', '44.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3898, 4264, 4891, 5966, 3170, 1175, 5137, 2598], 'generators': [13640428742, 24778026109, 7508493074, 23839464637, 16018118178, 15767835078], 'label': '3168.c.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1', '44.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '88.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220030
    {'ambient': '3168.c', 'aut_centralizer_order': 40, 'aut_label': '44.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.15', 'aut_weyl_index': 880, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '22.b1.a1'], 'contains': ['88.b1.a1', '88.d1.a1', '88.e1.a1', '132.d1.a1'], 'core': '88.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [984, -1, 3663, -1, 1240, -1, 1880, -1], 'generators': [24778026504, 2127406316, 44545782, 3941958762, 19522081488], 'label': '3168.c.44.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.d1.a1', 'projective_image': '88.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220031
    {'ambient': '3168.c', 'aut_centralizer_order': 40, 'aut_label': '44.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '48.45', 'aut_weyl_index': 440, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '22.b1.a1'], 'contains': ['88.c1.a1', '88.d1.a1', '132.e1.a1'], 'core': '88.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3153, -1, 5087, -1, 578, -1, 135, -1], 'generators': [20898638245, 24778026504, 2127406316, 19522081488, 158006], 'label': '3168.c.44.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.e1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220032
    {'ambient': '3168.c', 'aut_centralizer_order': 40, 'aut_label': '44.f1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.15', 'aut_weyl_index': 880, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '22.c1.a1'], 'contains': ['88.b1.a1', '132.f1.a1'], 'core': '88.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [5443, -1, 6634, -1, 5618, -1, 6227, -1], 'generators': [24778026504, 2127406316, 3941958762, 9929764, 19522081488], 'label': '3168.c.44.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '44.f1.a1', 'projective_image': '88.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220033
    {'ambient': '3168.c', 'aut_centralizer_order': 40, 'aut_label': '44.g1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '48.45', 'aut_weyl_index': 440, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '22.b1.a1'], 'contains': ['88.c1.a1', '88.e1.a1', '132.g1.a1'], 'core': '88.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1921, -1, 5611, -1, 2037, -1, 1098, -1], 'generators': [20898638245, 24778026504, 2127406316, 314821, 19522081488], 'label': '3168.c.44.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.g1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220034
    {'ambient': '3168.c', 'aut_centralizer_order': 1056, 'aut_label': '48.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1'], 'contains': ['96.a1.a1', '144.a1.a1', '528.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2446, 2330, 3400, 7880, 5090, 2282, 3403, 2994], 'generators': [7508493074, 23839464637, 16018118178], 'label': '3168.c.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': ['96.a1.a1', '144.a1.a1', '528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '528.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.9', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220035
    {'ambient': '3168.c', 'aut_centralizer_order': 528, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.f1.a1', '24.f1.b1'], 'contains': ['96.a1.a1', '144.b1.a1', '528.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6937, -1, 1367, -1, 5810, -1, 8210, -1], 'generators': [24778026109, 7508493074, 16018118178], 'label': '3168.c.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.b1.a1', 'projective_image': '1056.81', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220036
    {'ambient': '3168.c', 'aut_centralizer_order': 24, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '220.7', 'aut_weyl_index': 96, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.d1.a1'], 'contains': ['96.a1.a1', '144.c1.a1', '528.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [334, -1, 2328, -1, 3105, -1, 2211, -1], 'generators': [7508493074, 16018118178, 158006], 'label': '3168.c.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '48.c1.a1', 'projective_image': '1056.81', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 60220037
    {'ambient': '3168.c', 'aut_centralizer_order': 1320, 'aut_label': '66.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1320, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '22.a1.a1', '33.a1.a1'], 'contains': ['132.a1.a1', '132.c1.a1', '198.a1.a1'], 'core': '66.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8873, 8454, 6413, 1693, 8192, 4521, 8265, 6609], 'generators': [20898638245, 24778026504, 2127406316, 3941958700, 24778026109], 'label': '3168.c.66.a1.a1', 'mobius_quo': 0, 'mobius_sub': -11, 'normal_closure': '66.a1.a1', 'normal_contained_in': ['6.b1.a1', '22.a1.a1'], 'normal_contains': ['132.a1.a1', '198.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '66.a1.a1', 'projective_image': '264.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '33.1', 'quotient_action_kernel_order': 33, 'quotient_fusion': None, 'short_label': '66.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220038
    {'ambient': '3168.c', 'aut_centralizer_order': 60, 'aut_label': '66.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 660, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '22.b1.a1', '33.a1.a1'], 'contains': ['132.a1.a1', '132.b1.a1', '132.d1.a1', '132.e1.a1', '132.g1.a1', '198.b1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5147, -1, 7563, -1, 4878, -1, 4031, -1], 'generators': [20898638245, 24778026504, 2127406316, 24778026109, 158006], 'label': '3168.c.66.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.b1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220039
    {'ambient': '3168.c', 'aut_centralizer_order': 60, 'aut_label': '66.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 660, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '22.c1.a1', '33.a1.a1'], 'contains': ['132.a1.a1', '132.f1.a1', '198.c1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [7597, -1, 9250, -1, 7746, -1, 7018, -1], 'generators': [20898638245, 24778026504, 2127406316, 24778026109, 9929764], 'label': '3168.c.66.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.c1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220040
    {'ambient': '3168.c', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '88.b1.a1', 'complements': ['792.f1.b1', '792.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '12.b1.a1', '44.e1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2883, 5227, 5342, 3949, 1192, 3670, 833, 1052], 'generators': [13640428742, 7508493074, 23839464637, 16018118178, 15767835078, 158006], 'label': '3168.c.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.c1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '176.13', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60220041
    {'ambient': '3168.c', 'aut_centralizer_order': 1056, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.a1.a1', '36.d1.a1', '36.e1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '792.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8378, 5062, 4673, 6147, 8321, 5348, 6656, 6575], 'generators': [24778026109, 23839464637, 16018118178], 'label': '3168.c.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '792.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '1584.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.5', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220042
    {'ambient': '3168.c', 'aut_centralizer_order': 1056, 'aut_label': '72.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.a1.a1', '36.f1.a1', '36.g1.a1'], 'contains': ['144.a1.a1', '792.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6532, 4230, 8296, 4351, 7716, 4614, 5538, 5840], 'generators': [23839464637, 16018118178, 9072762367], 'label': '3168.c.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.b1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '792.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '792.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.2', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220043
    {'ambient': '3168.c', 'aut_centralizer_order': 1056, 'aut_label': '72.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.a1.a1', '36.b1.a1', '36.c1.a1'], 'contains': ['144.a1.a1', '792.c1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6157, 7161, 8620, 3329, 7310, 6876, 4233, 5327], 'generators': [23839464637, 16018118178, 15767835078], 'label': '3168.c.72.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.c1.a1', 'normal_contained_in': ['24.c1.a1', '36.a1.a1', '36.b1.a1', '36.c1.a1'], 'normal_contains': ['144.a1.a1', '792.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '1584.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.2', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220044
    {'ambient': '3168.c', 'aut_centralizer_order': 48, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 96, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.b1.a1', '36.d1.a1', '36.f1.a1'], 'contains': ['144.a1.a1', '144.c1.a1', '792.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3977, -1, 5729, -1, 6015, -1, 4031, -1], 'generators': [23839464637, 16018118178, 158006], 'label': '3168.c.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60220045
    {'ambient': '3168.c', 'aut_centralizer_order': 48, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 96, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.c1.a1', '36.d1.a1', '36.f1.a1'], 'contains': ['144.a1.a1', '792.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4441, -1, 6266, -1, 6904, -1, 4632, -1], 'generators': [314821, 23839464637, 16018118178], 'label': '3168.c.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '1584.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60220046
    {'ambient': '3168.c', 'aut_centralizer_order': 264, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.e1.a1'], 'contains': ['144.b1.a1', '792.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9609, -1, 2130, -1, 9092, -1, 9441, -1], 'generators': [11450451583, 24778026109, 16018118178], 'label': '3168.c.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.f1.a1', 'projective_image': '3168.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220047
    {'ambient': '3168.c', 'aut_centralizer_order': 264, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '36.e1.a1'], 'contains': ['144.b1.a1', '792.f1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9609, -1, 2719, -1, 9092, -1, 9176, -1], 'generators': [3941958700, 24778026109, 16018118178], 'label': '3168.c.72.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.f1.b1', 'projective_image': '3168.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220048
    {'ambient': '3168.c', 'aut_centralizer_order': 1760, 'aut_label': '88.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1760, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1'], 'contains': ['176.a1.a1', '176.b1.a1', '264.a1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3455, 2231, 890, 8113, 2445, 1519, 6286, 2592], 'generators': [24778026504, 2127406316, 24778026109, 19522081488], 'label': '3168.c.88.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '88.a1.a1', 'normal_contained_in': ['8.a1.a1', '44.a1.a1'], 'normal_contains': ['176.a1.a1', '264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '88.a1.a1', 'projective_image': '176.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '44.4', 'quotient_action_kernel_order': 44, 'quotient_fusion': None, 'short_label': '88.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220049
    {'ambient': '3168.c', 'aut_centralizer_order': 1760, 'aut_label': '88.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1760, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.a1.a1', '44.d1.a1', '44.f1.a1'], 'contains': ['176.a1.a1', '264.b1.a1'], 'core': '88.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3034, 1399, 4239, 6807, 2154, 784, 3775, 1857], 'generators': [24778026504, 2127406316, 3941958762, 19522081488], 'label': '3168.c.88.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '88.b1.a1', 'normal_contained_in': ['8.b1.a1', '44.a1.a1'], 'normal_contains': ['176.a1.a1', '264.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '88.b1.a1', 'projective_image': '88.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '88.5', 'quotient_action_kernel_order': 88, 'quotient_fusion': None, 'short_label': '88.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220050
    {'ambient': '3168.c', 'aut_centralizer_order': 1760, 'aut_label': '88.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1760, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '44.a1.a1', '44.e1.a1', '44.g1.a1'], 'contains': ['176.a1.a1', '264.c1.a1'], 'core': '88.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2188, 3815, 5202, 5410, 1951, 2253, 1125, 1344], 'generators': [20898638245, 24778026504, 2127406316, 19522081488], 'label': '3168.c.88.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '88.c1.a1', 'normal_contained_in': ['8.c1.a1', '44.a1.a1'], 'normal_contains': ['176.a1.a1', '264.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '88.c1.a1', 'projective_image': '176.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '44.2', 'quotient_action_kernel_order': 44, 'quotient_fusion': None, 'short_label': '88.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220051
    {'ambient': '3168.c', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '88.b1.a1', 'complements': ['792.f1.b1', '792.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.e1.a1', '12.c1.a1', '44.g1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2493, 7082, 5634, 4719, 2597, 2976, 1474, 1746], 'generators': [314821, 13640428742, 7508493074, 23839464637, 16018118178, 15767835078], 'label': '3168.c.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.c1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '176.13', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '88.5'}
  • id: 60220052
    {'ambient': '3168.c', 'aut_centralizer_order': 80, 'aut_label': '88.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1760, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '44.b1.a1', '44.d1.a1', '44.e1.a1'], 'contains': ['176.a1.a1', '176.c1.a1', '264.d1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [950, -1, 1851, -1, 1231, -1, 840, -1], 'generators': [24778026504, 2127406316, 19522081488, 158006], 'label': '3168.c.88.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '88.d1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220053
    {'ambient': '3168.c', 'aut_centralizer_order': 80, 'aut_label': '88.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1760, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '44.b1.a1', '44.d1.a1', '44.g1.a1'], 'contains': ['176.a1.a1', '264.e1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [1389, -1, 3501, -1, 1522, -1, 1547, -1], 'generators': [24778026504, 2127406316, 314821, 19522081488], 'label': '3168.c.88.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '88.e1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220054
    {'ambient': '3168.c', 'aut_centralizer_order': 440, 'aut_label': '88.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1760, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '44.c1.a1'], 'contains': ['176.b1.a1', '264.f1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7957, -1, 86, -1, 5339, -1, 8988, -1], 'generators': [2127406316, 20898638578, 24778026109, 19522081488], 'label': '3168.c.88.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '22.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '88.f1.a1', 'projective_image': '352.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220055
    {'ambient': '3168.c', 'aut_centralizer_order': 440, 'aut_label': '88.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1760, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '44.c1.a1'], 'contains': ['176.b1.a1', '264.f1.b1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7957, -1, 487, -1, 5339, -1, 8417, -1], 'generators': [2127406316, 3941958700, 24778026109, 19522081488], 'label': '3168.c.88.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '22.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '88.f1.b1', 'projective_image': '352.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220056
    {'ambient': '3168.c', 'aut_centralizer_order': 1056, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'contains': ['288.a1.a1', '1056.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [496, 357, 1758, 9418, 4905, 2306, 3421, 3018], 'generators': [7508493074, 16018118178], 'label': '3168.c.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1'], 'normal_contains': ['288.a1.a1', '1056.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '1056.81', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.20', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220057
    {'ambient': '3168.c', 'aut_centralizer_order': 60, 'aut_label': '99.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 660, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '33.a1.a1'], 'contains': ['198.a1.a1', '198.b1.a1', '198.c1.a1'], 'core': '198.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9663, -1, 9041, -1, 9429, -1, 7907, -1], 'generators': [20898638245, 24778026504, 3941958700, 24778026109, 158006], 'label': '3168.c.99.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '99.a1.a1', 'projective_image': '792.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '99.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220058
    {'ambient': '3168.c', 'aut_centralizer_order': 2640, 'aut_label': '132.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '44.a1.a1', '66.a1.a1', '66.b1.a1', '66.c1.a1'], 'contains': ['264.a1.a1', '264.b1.a1', '264.c1.a1', '396.a1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6998, 6540, 6909, 4351, 5854, 4503, 5917, 5624], 'generators': [20898638245, 24778026504, 2127406316, 24778026109], 'label': '3168.c.132.a1.a1', 'mobius_quo': 0, 'mobius_sub': 22, 'normal_closure': '132.a1.a1', 'normal_contained_in': ['12.a1.a1', '44.a1.a1', '66.a1.a1'], 'normal_contains': ['264.a1.a1', '264.b1.a1', '264.c1.a1', '396.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.a1.a1', 'projective_image': '264.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '66.4', 'quotient_action_kernel_order': 66, 'quotient_fusion': None, 'short_label': '132.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220059
    {'ambient': '3168.c', 'aut_centralizer_order': 120, 'aut_label': '132.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '44.b1.a1', '66.b1.a1'], 'contains': ['264.a1.a1', '264.d1.a1', '264.e1.a1', '396.b1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [2868, -1, 3896, -1, 3712, -1, 4031, -1], 'generators': [24778026504, 2127406316, 24778026109, 158006], 'label': '3168.c.132.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '132.b1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60220060
    {'ambient': '3168.c', 'aut_centralizer_order': 1320, 'aut_label': '132.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '44.c1.a1', '66.a1.a1'], 'contains': ['264.a1.a1', '264.f1.a1', '264.f1.b1', '396.c1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8670, -1, 1974, -1, 8159, -1, 8702, -1], 'generators': [24778026504, 2127406316, 3941958700, 24778026109], 'label': '3168.c.132.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '66.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '132.c1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220061
    {'ambient': '3168.c', 'aut_centralizer_order': 120, 'aut_label': '132.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '44.d1.a1', '66.b1.a1'], 'contains': ['264.b1.a1', '264.d1.a1', '264.e1.a1', '396.d1.a1'], 'core': '264.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [1212, -1, 5045, -1, 4058, -1, 3489, -1], 'generators': [24778026504, 2127406316, 44545782, 3941958762], 'label': '3168.c.132.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '132.d1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220062
    {'ambient': '3168.c', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '12.d1.a1', '44.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2007, -1, 3129, -1, 1467, -1, 2605, -1], 'generators': [13640428742, 24778026109, 7508493074, 23839464637, 16018118178, 158006], 'label': '3168.c.4.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '176.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60220063
    {'ambient': '3168.c', 'aut_centralizer_order': 120, 'aut_label': '132.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '44.e1.a1', '66.b1.a1'], 'contains': ['264.c1.a1', '264.d1.a1', '396.e1.a1'], 'core': '264.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4683, -1, 7465, -1, 3396, -1, 1803, -1], 'generators': [20898638245, 24778026504, 2127406316, 158006], 'label': '3168.c.132.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.e1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220064
    {'ambient': '3168.c', 'aut_centralizer_order': 120, 'aut_label': '132.f1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '44.f1.a1', '66.c1.a1'], 'contains': ['264.b1.a1', '396.f1.a1'], 'core': '264.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [5681, -1, 8588, -1, 7869, -1, 7311, -1], 'generators': [24778026504, 2127406316, 3941958762, 9929764], 'label': '3168.c.132.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '132.f1.a1', 'projective_image': '264.15', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220065
    {'ambient': '3168.c', 'aut_centralizer_order': 120, 'aut_label': '132.g1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1320, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '44.g1.a1', '66.b1.a1'], 'contains': ['264.c1.a1', '264.e1.a1', '396.g1.a1'], 'core': '264.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3620, -1, 7800, -1, 4855, -1, 2707, -1], 'generators': [20898638245, 24778026504, 2127406316, 314821], 'label': '3168.c.132.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.g1.a1', 'projective_image': '528.41', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60220066
    {'ambient': '3168.c', 'aut_centralizer_order': 2112, 'aut_label': '144.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2112, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.a1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1'], 'contains': ['288.a1.a1', '1584.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5202, 4264, 6063, 6108, 6904, 4672, 4400, 4883], 'generators': [23839464637, 16018118178], 'label': '3168.c.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '72.a1.a1', '72.b1.a1', '72.c1.a1'], 'normal_contains': ['288.a1.a1', '1584.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '1584.41', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.9', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60220067
    {'ambient': '3168.c', 'aut_centralizer_order': 1056, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '10.2', 'aut_weyl_index': 2112, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.a1.a1', '72.f1.a1', '72.f1.b1'], 'contains': ['288.a1.a1', '1584.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7957, -1, 2945, -1, 7462, -1, 8210, -1], 'generators': [24778026109, 16018118178], 'label': '3168.c.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '144.b1.a1', 'projective_image': '3168.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220068
    {'ambient': '3168.c', 'aut_centralizer_order': 48, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '110.1', 'aut_weyl_index': 192, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '72.d1.a1'], 'contains': ['288.a1.a1', '1584.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3163, -1, 3851, -1, 5732, -1, 3220, -1], 'generators': [16018118178, 158006], 'label': '3168.c.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '144.c1.a1', 'projective_image': '3168.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 60220069
    {'ambient': '3168.c', 'aut_centralizer_order': 3520, 'aut_label': '176.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3520, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '88.a1.a1', '88.b1.a1', '88.c1.a1', '88.d1.a1', '88.e1.a1'], 'contains': ['352.a1.a1', '528.a1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2090, 1934, 1587, 7950, 2053, 1641, 2696, 2172], 'generators': [24778026504, 2127406316, 19522081488], 'label': '3168.c.176.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '176.a1.a1', 'normal_contained_in': ['16.a1.a1', '88.a1.a1', '88.b1.a1', '88.c1.a1'], 'normal_contains': ['352.a1.a1', '528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '176.a1.a1', 'projective_image': '176.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '176.13', 'quotient_action_kernel_order': 176, 'quotient_fusion': None, 'short_label': '176.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220070
    {'ambient': '3168.c', 'aut_centralizer_order': 1760, 'aut_label': '176.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3520, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '88.a1.a1', '88.f1.a1', '88.f1.b1'], 'contains': ['352.a1.a1', '528.b1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6102, -1, 175, -1, 3396, -1, 8011, -1], 'generators': [2127406316, 24778026109, 19522081488], 'label': '3168.c.176.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '88.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '176.b1.a1', 'projective_image': '352.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220071
    {'ambient': '3168.c', 'aut_centralizer_order': 80, 'aut_label': '176.c1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3520, 'centralizer': '44.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '88.d1.a1'], 'contains': ['352.a1.a1', '528.c1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [218, -1, 640, -1, 1388, -1, 1352, -1], 'generators': [2127406316, 19522081488, 158006], 'label': '3168.c.176.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.d1.a1', 'old_label': '176.c1.a1', 'projective_image': '352.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60220072
    {'ambient': '3168.c', 'aut_centralizer_order': 2640, 'aut_label': '198.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2640, 'centralizer': '2.b1.a1', 'complements': ['16.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '66.a1.a1', '99.a1.a1'], 'contains': ['396.a1.a1', '396.c1.a1'], 'core': '198.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9515, 8454, 6514, 1693, 9549, 5786, 8002, 8505], 'generators': [20898638245, 24778026504, 3941958700, 24778026109], 'label': '3168.c.198.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '198.a1.a1', 'normal_contained_in': ['18.b1.a1', '66.a1.a1'], 'normal_contains': ['396.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '198.a1.a1', 'projective_image': '792.15', 'quotient_action_image': '2.1', 'quotient_action_kernel': '99.1', 'quotient_action_kernel_order': 99, 'quotient_fusion': None, 'short_label': '198.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}