Abstract group data - 648.725

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [4, 12, 4, 8, 3, 6, 3, 3], 'aut_gens': [[15484366, 23554882, 14520385, 37858024, 21125207, 18187580, 23548240], [14383819, 14520385, 26068879, 29321758, 18546248, 41472812, 22873591], [26736886, 15477724, 15471082, 37858024, 41796083, 14786794, 26106544], [26068879, 15484366, 14421484, 39912184, 24885146, 25096313, 15433417], [25667362, 26736886, 22911256, 29348326, 18559532, 38083123, 15576625], [15484366, 23554882, 14520385, 37818172, 24313853, 21376226, 23548240], [14507101, 14513743, 26606962, 37786420, 24327137, 34086503, 25575103], [15484366, 23554882, 14520385, 36723538, 18481286, 25096313, 23548240], [15484366, 23554882, 14520385, 40961782, 24923540, 21907667, 23548240]], 'aut_group': '31104.mg', 'aut_hash': 7361170441374917732, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 31104, 'aut_permdeg': 36, 'aut_perms': [226902803166164964828450736661567486443062, 102503951025700100526428240811454549200444, 77069415677107471044888558962329860106226, 191316775111502191938623096649537188711951, 3250696627691849239767998962981274563056, 47899084835849649493666785149315950608812, 214789546979731070755183673259820895957389, 77280900467992974715510986634134878118338], 'aut_phi_ratio': 144.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 18, 2, 1], [2, 81, 1, 1], [3, 4, 8, 1], [3, 8, 6, 1], [4, 162, 1, 1], [6, 36, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:\\GL(2,3):D_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '31104.mg', 'autcentquo_hash': 7361170441374917732, 'autcentquo_nilpotent': False, 'autcentquo_order': 31104, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:\\GL(2,3):D_4', 'cc_stats': [[1, 1, 1], [2, 18, 2], [2, 81, 1], [3, 4, 8], [3, 8, 6], [4, 162, 1], [6, 36, 8]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '648.725', 'commutator_count': 1, 'commutator_label': '162.54', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 725, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 18, 1, 2], [2, 81, 1, 1], [3, 4, 1, 8], [3, 8, 1, 6], [4, 162, 1, 1], [6, 36, 1, 8]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 3, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '648.725', 'hash': 725, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [3, 3, 3, 2, 4, 2, 3], 'inner_gens': [[15484366, 23554882, 14520385, 37319941, 22194731, 17656139, 23548240], [15484366, 23554882, 14520385, 40430341, 25461623, 20844785, 23548240], [15484366, 23554882, 14520385, 37773136, 18468002, 25096313, 23548240], [14946283, 26068879, 14377177, 37858024, 21216737, 25096313, 26075521], [14421484, 14520385, 26068879, 29308474, 21125207, 42017537, 15038542], [14421484, 14520385, 23554882, 28823527, 30498527, 18187580, 15576625], [15484366, 23554882, 14520385, 40443625, 24398741, 21376226, 23548240]], 'inner_hash': 725, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': False, 'inner_tex': 'C_3^4:D_4', 'inner_used': [1, 2, 3, 4, 5, 6], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 4], [2, 1], [4, 16], [8, 6]], 'label': '648.725', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^4:D4', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 7, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 27, 'number_divisions': 27, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 50, 'number_subgroup_classes': 277, 'number_subgroups': 4450, 'old_label': None, 'order': 648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 117], [3, 80], [4, 162], [6, 288]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2], 'outer_gen_pows': [14408200, 34893992, 14408200, 37333225, 37333225], 'outer_gens': [[23554882, 15484366, 14421484, 29808163, 21165059, 21376226, 15576625], [15477724, 23411674, 26099902, 37326583, 25429871, 30012607, 22348792], [23554882, 26606962, 14383819, 29808163, 21203453, 24564872, 26637985], [22478716, 23016799, 14513743, 29283364, 21131849, 18719021, 22880233], [26606962, 22478716, 14507101, 41006818, 21138491, 17656139, 22393099]], 'outer_group': '48.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 6, 'outer_perms': [693, 136, 547, 134, 16], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times S_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 16], [8, 6]], 'representations': {'PC': {'code': 94609601690980989995618200011523671337443599, 'gens': [1, 2, 4, 5, 6, 7], 'pres': [7, -2, -2, -2, -3, 3, 3, 3, 85, 36, 2243, 2250, 129, 9244, 7431, 438, 6053, 1860, 1531, 9421, 5312]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [15484366, 23554882, 14520385, 37858024, 21125207, 18187580, 23548240]}, 'Perm': {'d': 12, 'gens': [263727360, 131725915, 3633865, 79879108, 43626388, 79914484, 79914387]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:D_4', 'transitive_degree': 12, 'wreath_data': ['C_3:S_3', 'C_2', '2T1'], 'wreath_product': True}
• 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: 144416895
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 725, 'group_order': 648, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 14408200, 'size': 1}
  • id: 144416906
    {'aut_label': '2A', 'centralizer': '18.c1', 'counter': 2, 'group_counter': 725, 'group_order': 648, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 34086503, 'size': 18}
  • id: 144416915
    {'aut_label': '2A', 'centralizer': '18.c1', 'counter': 3, 'group_counter': 725, 'group_order': 648, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 14748400, 'size': 18}
  • id: 144416916
    {'aut_label': '2C', 'centralizer': '81.a1', 'counter': 4, 'group_counter': 725, 'group_order': 648, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 37864666, 'size': 81}
  • id: 144416917
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 5, 'group_counter': 725, 'group_order': 648, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 15471082, 'size': 4}
  • id: 144416918
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 6, 'group_counter': 725, 'group_order': 648, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 26068879, 'size': 4}
  • id: 144416919
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 7, 'group_counter': 725, 'group_order': 648, 'label': '3C', 'order': 3, 'powers': [7, 1], 'representative': 25530796, 'size': 4}
  • id: 144416920
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 8, 'group_counter': 725, 'group_order': 648, 'label': '3D', 'order': 3, 'powers': [8, 1], 'representative': 14946283, 'size': 4}
  • id: 144416921
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 9, 'group_counter': 725, 'group_order': 648, 'label': '3E', 'order': 3, 'powers': [9, 1], 'representative': 14513743, 'size': 4}
  • id: 144416896
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 10, 'group_counter': 725, 'group_order': 648, 'label': '3F', 'order': 3, 'powers': [10, 1], 'representative': 23411674, 'size': 4}
  • id: 144416897
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 11, 'group_counter': 725, 'group_order': 648, 'label': '3G', 'order': 3, 'powers': [11, 1], 'representative': 22342150, 'size': 4}
  • id: 144416898
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 12, 'group_counter': 725, 'group_order': 648, 'label': '3H', 'order': 3, 'powers': [12, 1], 'representative': 26736886, 'size': 4}
  • id: 144416899
    {'aut_label': '3I', 'centralizer': '8.a1', 'counter': 13, 'group_counter': 725, 'group_order': 648, 'label': '3I', 'order': 3, 'powers': [13, 1], 'representative': 15038542, 'size': 8}
  • id: 144416900
    {'aut_label': '3I', 'centralizer': '8.a1', 'counter': 14, 'group_counter': 725, 'group_order': 648, 'label': '3J', 'order': 3, 'powers': [14, 1], 'representative': 15569983, 'size': 8}
  • id: 144416901
    {'aut_label': '3I', 'centralizer': '8.a1', 'counter': 15, 'group_counter': 725, 'group_order': 648, 'label': '3K', 'order': 3, 'powers': [15, 1], 'representative': 26198803, 'size': 8}
  • id: 144416902
    {'aut_label': '3I', 'centralizer': '8.a1', 'counter': 16, 'group_counter': 725, 'group_order': 648, 'label': '3L', 'order': 3, 'powers': [16, 1], 'representative': 15045184, 'size': 8}
  • id: 144416903
    {'aut_label': '3I', 'centralizer': '8.a1', 'counter': 17, 'group_counter': 725, 'group_order': 648, 'label': '3M', 'order': 3, 'powers': [17, 1], 'representative': 25575103, 'size': 8}
  • id: 144416904
    {'aut_label': '3I', 'centralizer': '8.a1', 'counter': 18, 'group_counter': 725, 'group_order': 648, 'label': '3N', 'order': 3, 'powers': [18, 1], 'representative': 22386457, 'size': 8}
  • id: 144416905
    {'aut_label': '4A', 'centralizer': '162.b1', 'counter': 19, 'group_counter': 725, 'group_order': 648, 'label': '4A', 'order': 4, 'powers': [4, 19], 'representative': 22234583, 'size': 162}
  • id: 144416907
    {'aut_label': '6A', 'centralizer': '36.a1', 'counter': 20, 'group_counter': 725, 'group_order': 648, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 33555062, 'size': 36}
  • id: 144416908
    {'aut_label': '6A', 'centralizer': '36.a1', 'counter': 21, 'group_counter': 725, 'group_order': 648, 'label': '6B', 'order': 6, 'powers': [6, 3], 'representative': 23834575, 'size': 36}
  • id: 144416909
    {'aut_label': '6A', 'centralizer': '36.a1', 'counter': 22, 'group_counter': 725, 'group_order': 648, 'label': '6C', 'order': 6, 'powers': [7, 3], 'representative': 22765051, 'size': 36}
  • id: 144416910
    {'aut_label': '6A', 'centralizer': '36.a1', 'counter': 23, 'group_counter': 725, 'group_order': 648, 'label': '6D', 'order': 6, 'powers': [8, 3], 'representative': 15856318, 'size': 36}
  • id: 144416911
    {'aut_label': '6A', 'centralizer': '36.a1', 'counter': 24, 'group_counter': 725, 'group_order': 648, 'label': '6E', 'order': 6, 'powers': [9, 3], 'representative': 29430217, 'size': 36}
  • id: 144416912
    {'aut_label': '6A', 'centralizer': '36.a1', 'counter': 25, 'group_counter': 725, 'group_order': 648, 'label': '6F', 'order': 6, 'powers': [10, 2], 'representative': 24001679, 'size': 36}
  • id: 144416913
    {'aut_label': '6A', 'centralizer': '36.a1', 'counter': 26, 'group_counter': 725, 'group_order': 648, 'label': '6G', 'order': 6, 'powers': [11, 2], 'representative': 20806391, 'size': 36}
  • id: 144416914
    {'aut_label': '6A', 'centralizer': '36.a1', 'counter': 27, 'group_counter': 725, 'group_order': 648, 'label': '6H', 'order': 6, 'powers': [12, 2], 'representative': 18115976, 'size': 36}
• 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: 14056671
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.1a', '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], 'schur_index': 1}
  • id: 14056682
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 14056691
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 14056692
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 14056693
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 0, 0, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14056694
    {'cdim': 4, 'counter': 6, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4a', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 0, 2, 0, -2, -2, 1, -2, 4, 1, 1, 4, 1, -2, 1, 1, -2, -2, 0, 0, -1, -1, 0, 2, 0, -1, 0], 'schur_index': 1}
  • id: 14056695
    {'cdim': 4, 'counter': 7, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4b', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 0, 2, 0, -2, -2, 1, 4, 1, 1, 4, -2, -2, 1, -2, 1, -2, 1, 0, 0, -1, 2, 0, -1, 0, -1, 0], 'schur_index': 1}
  • id: 14056696
    {'cdim': 4, 'counter': 8, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4c', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 0, 2, 0, -2, 4, 4, -2, 1, 1, 1, -2, 1, -2, -2, -2, 1, 1, 0, 0, -1, -1, 0, -1, 0, 2, 0], 'schur_index': 1}
  • id: 14056697
    {'cdim': 4, 'counter': 9, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4d', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 0, 2, 0, 4, -2, 1, -2, 1, 4, 1, -2, -2, 1, 1, -2, 1, -2, 0, 0, 2, -1, 0, -1, 0, -1, 0], 'schur_index': 1}
  • id: 14056672
    {'cdim': 4, 'counter': 10, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4e', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 2, 0, 0, 1, 1, -2, 1, 4, -2, -2, 4, -2, 1, -2, -2, 1, 1, 0, -1, 0, 0, 2, 0, -1, 0, -1], 'schur_index': 1}
  • id: 14056673
    {'cdim': 4, 'counter': 11, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4f', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 2, 0, 0, 1, 1, -2, 4, -2, -2, 4, 1, 1, -2, 1, -2, 1, -2, 0, 2, 0, 0, -1, 0, -1, 0, -1], 'schur_index': 1}
  • id: 14056674
    {'cdim': 4, 'counter': 12, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4g', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 2, 0, 0, 1, 4, 4, 1, -2, -2, -2, 1, -2, 1, 1, 1, -2, -2, 0, -1, 0, 0, -1, 0, 2, 0, -1], 'schur_index': 1}
  • id: 14056675
    {'cdim': 4, 'counter': 13, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4h', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 2, 0, 0, 4, 1, -2, 1, -2, 4, -2, 1, 1, -2, -2, 1, -2, 1, 0, -1, 0, 0, -1, 0, -1, 0, 2], 'schur_index': 1}
  • id: 14056676
    {'cdim': 4, 'counter': 14, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4i', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, -2, 0, 0, 1, 1, -2, 1, 4, -2, -2, 4, -2, 1, -2, -2, 1, 1, 0, 1, 0, 0, -2, 0, 1, 0, 1], 'schur_index': 1}
  • id: 14056677
    {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4j', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, -2, 0, 0, 1, 1, -2, 4, -2, -2, 4, 1, 1, -2, 1, -2, 1, -2, 0, -2, 0, 0, 1, 0, 1, 0, 1], 'schur_index': 1}
  • id: 14056678
    {'cdim': 4, 'counter': 16, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4k', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, -2, 0, 0, 1, 4, 4, 1, -2, -2, -2, 1, -2, 1, 1, 1, -2, -2, 0, 1, 0, 0, 1, 0, -2, 0, 1], 'schur_index': 1}
  • id: 14056679
    {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4l', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, -2, 0, 0, 4, 1, -2, 1, -2, 4, -2, 1, 1, -2, -2, 1, -2, 1, 0, 1, 0, 0, 1, 0, 1, 0, -2], 'schur_index': 1}
  • id: 14056680
    {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4m', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 0, -2, 0, -2, -2, 1, -2, 4, 1, 1, 4, 1, -2, 1, 1, -2, -2, 0, 0, 1, 1, 0, -2, 0, 1, 0], 'schur_index': 1}
  • id: 14056681
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4n', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 0, -2, 0, -2, -2, 1, 4, 1, 1, 4, -2, -2, 1, -2, 1, -2, 1, 0, 0, 1, -2, 0, 1, 0, 1, 0], 'schur_index': 1}
  • id: 14056683
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4o', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 0, -2, 0, -2, 4, 4, -2, 1, 1, 1, -2, 1, -2, -2, -2, 1, 1, 0, 0, 1, 1, 0, 1, 0, -2, 0], 'schur_index': 1}
  • id: 14056684
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.4p', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 0, -2, 0, 4, -2, 1, -2, 1, 4, 1, -2, -2, 1, 1, -2, 1, -2, 0, 0, -2, 1, 0, 1, 0, 1, 0], 'schur_index': 1}
  • id: 14056685
    {'cdim': 8, 'counter': 22, 'faithful': True, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.8a', 'multiplicity': 1, 'nt': [12, 172], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, -4, 2, 2, -4, 2, -4, 2, -1, -1, -1, 2, 5, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14056686
    {'cdim': 8, 'counter': 23, 'faithful': True, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.8b', 'multiplicity': 1, 'nt': [12, 172], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, 2, -4, -4, -4, 2, 2, 2, 2, 5, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14056687
    {'cdim': 8, 'counter': 24, 'faithful': True, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.8c', 'multiplicity': 1, 'nt': [12, 172], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, 2, -4, 2, 2, 2, -4, -4, -1, -1, 5, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14056688
    {'cdim': 8, 'counter': 25, 'faithful': True, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.8d', 'multiplicity': 1, 'nt': [12, 172], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 2, -4, 2, -4, -4, -4, 2, 2, -1, -1, 2, -1, -1, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14056689
    {'cdim': 8, 'counter': 26, 'faithful': True, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.8e', 'multiplicity': 1, 'nt': [12, 172], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 2, -4, 2, 2, 2, -4, -4, -4, 5, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14056690
    {'cdim': 8, 'counter': 27, 'faithful': True, 'group': '648.725', 'group_order': 648, 'image': None, 'label': '648.725.8f', 'multiplicity': 1, 'nt': [12, 172], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 2, 2, -4, -4, 2, -4, 2, -4, -1, -1, -1, 5, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 33406115
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 648, 'label': '648.725.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33406126
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 324, 'label': '648.725.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33406135
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 324, 'label': '648.725.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 33406136
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 324, 'label': '648.725.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 33406137
    {'center': '4.a1', 'center_index': 4, 'center_order': 162, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 81, 'label': '648.725.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33406138
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 6, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4a', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 33406139
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 7, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4b', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 33406140
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 8, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4c', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]]]}
  • id: 33406141
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 9, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4d', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 33406116
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 10, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4e', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 33406117
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 11, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4f', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 33406118
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 12, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4g', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 33406119
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 13, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4h', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]]]}
  • id: 33406120
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 14, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4i', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 33406121
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 15, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4j', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 33406122
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 16, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4k', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]]]}
  • id: 33406123
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 17, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4l', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]]]}
  • id: 33406124
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 18, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4m', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 33406125
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 19, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4n', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 33406127
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 20, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4o', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
  • id: 33406128
    {'center': '72.a1', 'center_index': 72, 'center_order': 9, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.725.4p', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 33406129
    {'center': '648.a1', 'center_index': 648, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '648.725', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 1, 'label': '648.725.8a', 'nt': [12, 172], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33406130
    {'center': '648.a1', 'center_index': 648, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '648.725', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 1, 'label': '648.725.8b', 'nt': [12, 172], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33406131
    {'center': '648.a1', 'center_index': 648, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '648.725', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 1, 'label': '648.725.8c', 'nt': [12, 172], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33406132
    {'center': '648.a1', 'center_index': 648, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '648.725', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 1, 'label': '648.725.8d', 'nt': [12, 172], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33406133
    {'center': '648.a1', 'center_index': 648, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '648.725', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 1, 'label': '648.725.8e', 'nt': [12, 172], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33406134
    {'center': '648.a1', 'center_index': 648, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '648.725', 'group_counter': 725, 'group_order': 648, 'image': None, 'image_isoclass': '648.725', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 1, 'label': '648.725.8f', 'nt': [12, 172], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 116053424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '648.725.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.725', 'subgroup_hash': 725, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 116053435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.725.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053446
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 324, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.725.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 116053457
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 162, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.725.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053468
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 116053470
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 81, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '648.725.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'L2', 'D2', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 3}
  • id: 116053472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 116053473
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 116053426
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053427
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 116053432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 116053433
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 116053434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 116053436
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 116053437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053438
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053439
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053440
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053441
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f2', 'outer_equivalence': True, 'perfect': False, '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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.36.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 116053449
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.725.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\SOPlus(4,2)', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053450
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053451
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053452
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.72.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.72.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e2', 'outer_equivalence': True, 'perfect': False, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 116053456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '648.725.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, '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': 2}
  • id: 116053458
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.725.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': 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: 116053459
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053460
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053461
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053462
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.725.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': 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: 116053463
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.725.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': 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: 116053464
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.725.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053465
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.725.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 116053466
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.725.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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: 116053467
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.725.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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: 116053469
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.725', 'ambient_counter': 725, 'ambient_order': 648, 'ambient_tex': 'C_3^4:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 1, 'counter': 50, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '648.725.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '648.725', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 725, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4:D_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D3', 'C5'], '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: 116053424
    {'ambient': '648.725', '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': '648.a1', 'complements': ['648.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '9.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7564, 2383, 7583, 4041], 'generators': [23554882, 15484366, 28777033, 14421484, 14520385, 21125207, 18187580], 'label': '648.725.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '648.725'}
  • id: 116053425
    {'ambient': '648.725', 'aut_centralizer_order': 9, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '216.102', 'aut_weyl_index': 144, 'centralizer': '72.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.b1', '6.a1'], 'contains': ['24.b1', '36.b1', '36.c1', '36.d1'], 'core': '72.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1273, -1, 3636, -1], 'generators': [15484366, 14421484, 23442697, 18187580], 'label': '648.725.12.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 116053426
    {'ambient': '648.725', 'aut_centralizer_order': 1, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '432.741', 'aut_weyl_index': 72, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.a1'], 'contains': ['24.a1', '36.e1', '36.f1', '36.f2', '36.h1', '36.h2'], 'core': '648.a1', 'coset_action_label': '12T172', 'count': 72, 'diagramx': [7102, -1, 7271, -1], 'generators': [28777033, 23554882, 14421484, 15576625], 'label': '648.725.12.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '12.c1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 116053427
    {'ambient': '648.725', 'aut_centralizer_order': 1, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '648.555', 'aut_weyl_index': 48, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.a1', '6.a1'], 'contains': ['24.b1', '36.e1', '36.f1', '36.f2', '36.g1', '36.g2'], 'core': '72.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5476, -1, 5831, -1], 'generators': [28777033, 15484366, 23554882, 14421484], 'label': '648.725.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.d1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 116053428
    {'ambient': '648.725', 'aut_centralizer_order': 2, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '72.40', 'aut_weyl_index': 432, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.a1'], 'contains': ['36.b1', '36.f2', '54.a1'], 'core': '648.a1', 'coset_action_label': '18T216', 'count': 216, 'diagramx': [2558, -1, 4494, -1], 'generators': [15576625, 18187580, 29315116, 23548240], 'label': '648.725.18.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '18.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 116053429
    {'ambient': '648.725', 'aut_centralizer_order': 6, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '72.40', 'aut_weyl_index': 432, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.c1', '36.g1', '54.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4362, -1, 5055, -1], 'generators': [28777033, 15484366, 14421484, 18187580], 'label': '648.725.18.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 116053430
    {'ambient': '648.725', 'aut_centralizer_order': 2, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '432.734', 'aut_weyl_index': 72, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1'], 'contains': ['36.a1', '36.d1', '36.g2', '54.a1'], 'core': '648.a1', 'coset_action_label': '18T213', 'count': 36, 'diagramx': [3249, -1, 1406, -1], 'generators': [23411674, 15477724, 18187580, 29315116], 'label': '648.725.18.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '18.c1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 116053431
    {'ambient': '648.725', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '9.a1'], 'contains': ['36.g1', '162.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8182, -1, 8352, -1], 'generators': [15484366, 14421484, 21125207, 40468735], 'label': '648.725.18.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 116053432
    {'ambient': '648.725', 'aut_centralizer_order': 4, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.b1'], 'contains': ['36.h2', '162.b1'], 'core': '648.a1', 'coset_action_label': '18T214', 'count': 54, 'diagramx': [9675, -1, 9640, -1], 'generators': [21125207, 15576625, 26062237, 28790317], 'label': '648.725.18.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '18.e1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 116053433
    {'ambient': '648.725', 'aut_centralizer_order': 81, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1944, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '12.c1'], 'contains': ['72.b1', '72.c1', '72.c2', '72.e1', '72.e2'], 'core': '648.a1', 'coset_action_label': '24T1524', 'count': 24, 'diagramx': [6556, -1, 7901, -1], 'generators': [23554882, 14421484, 15576625], 'label': '648.725.24.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053434
    {'ambient': '648.725', 'aut_centralizer_order': 81, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1296, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.a1', '12.a1', '12.b1', '12.d1'], 'contains': ['72.a1', '72.b1', '72.c1', '72.c2', '72.d1'], 'core': '72.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4396, -1, 4806, -1], 'generators': [15484366, 23554882, 14421484], 'label': '648.725.24.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 116053435
    {'ambient': '648.725', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '15552.v', 'aut_weyl_index': 2, 'centralizer': '648.a1', 'complements': ['324.a1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '6.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5036, 681, 6018, 1711], 'generators': [23554882, 15484366, 28777033, 14421484, 14520385, 18187580], 'label': '648.725.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '648.725', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '648.725'}
  • id: 116053436
    {'ambient': '648.725', 'aut_centralizer_order': 18, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.29', 'aut_weyl_index': 648, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '18.c1'], 'contains': ['72.d1', '108.a1'], 'core': '648.a1', 'coset_action_label': '36T1112', 'count': 36, 'diagramx': [2341, -1, 409, -1], 'generators': [23411674, 15477724, 18187580], 'label': '648.725.36.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053437
    {'ambient': '648.725', 'aut_centralizer_order': 18, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, 'centralizer': '72.d1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['12.a1', '12.b1', '18.a1'], 'contains': ['72.c1', '108.a1', '108.b1'], 'core': '648.a1', 'coset_action_label': '36T1120', 'count': 144, 'diagramx': [325, -1, 1981, -1], 'generators': [15576625, 18187580, 23548240], 'label': '648.725.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '36.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 116053438
    {'ambient': '648.725', 'aut_centralizer_order': 54, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, 'centralizer': '72.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.a1', '12.b1', '18.b1'], 'contains': ['72.a1', '108.a1', '108.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1584, -1, 2915, -1], 'generators': [15484366, 14421484, 18187580], 'label': '648.725.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '36.c1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 116053439
    {'ambient': '648.725', 'aut_centralizer_order': 18, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '432.734', 'aut_weyl_index': 72, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '18.c1'], 'contains': ['72.d1', '108.b1'], 'core': '648.a1', 'coset_action_label': '36T1114', 'count': 4, 'diagramx': [955, -1, 1198, -1], 'generators': [14939641, 23442697, 18187580], 'label': '648.725.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.d1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 116053440
    {'ambient': '648.725', 'aut_centralizer_order': 1, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '108.17', 'aut_weyl_index': 288, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.c1', '12.d1'], 'contains': ['72.b1', '108.c1', '108.d1'], 'core': '648.a1', 'coset_action_label': '36T1189', 'count': 288, 'diagramx': [7681, -1, 6669, -1], 'generators': [28777033, 15484366, 23548240], 'label': '648.725.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '36.e1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 116053441
    {'ambient': '648.725', 'aut_centralizer_order': 1, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '72.40', 'aut_weyl_index': 432, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.c1', '12.d1'], 'contains': ['72.c2', '108.c1', '108.d1'], 'core': '648.a1', 'coset_action_label': '36T1187', 'count': 432, 'diagramx': [6935, -1, 7299, -1], 'generators': [28777033, 15484366, 23405032], 'label': '648.725.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1', 'old_label': '36.f1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 116053442
    {'ambient': '648.725', 'aut_centralizer_order': 2, 'aut_label': '36.f2', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '72.40', 'aut_weyl_index': 432, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.c1', '12.d1', '18.a1'], 'contains': ['72.c1', '108.c1', '108.d1'], 'core': '648.a1', 'coset_action_label': '36T1119', 'count': 216, 'diagramx': [5688, -1, 6039, -1], 'generators': [28777033, 15484366, 14513743], 'label': '648.725.36.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.f2', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 116053443
    {'ambient': '648.725', 'aut_centralizer_order': 6, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '18.b1', '18.d1'], 'contains': ['72.a1', '108.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5181, -1, 5408, -1], 'generators': [28777033, 15484366, 14421484], 'label': '648.725.36.g1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.g1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 116053444
    {'ambient': '648.725', 'aut_centralizer_order': 2, 'aut_label': '36.g2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '432.734', 'aut_weyl_index': 72, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '18.c1'], 'contains': ['72.d1', '108.c1'], 'core': '648.a1', 'coset_action_label': '36T1113', 'count': 36, 'diagramx': [3822, -1, 4204, -1], 'generators': [28777033, 23411674, 15477724], 'label': '648.725.36.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.g2', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 116053445
    {'ambient': '648.725', 'aut_centralizer_order': 2, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1'], 'contains': ['72.e1', '108.d1'], 'core': '648.a1', 'coset_action_label': '36T1234', 'count': 108, 'diagramx': [8204, -1, 8504, -1], 'generators': [28777033, 23405032, 15576625], 'label': '648.725.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '36.h1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 116053446
    {'ambient': '648.725', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '31104.mg', 'aut_weyl_index': 1, 'centralizer': '648.a1', 'complements': ['324.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '18.d1', '18.e1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7564, 4064, 8352, 6401], 'generators': [28777033, 15484366, 23554882, 14421484, 14520385, 21125207], 'label': '648.725.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '648.725', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '648.725'}
  • id: 116053447
    {'ambient': '648.725', 'aut_centralizer_order': 4, 'aut_label': '36.h2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '18.e1'], 'contains': ['72.e2', '108.d1'], 'core': '648.a1', 'coset_action_label': '36T1115', 'count': 54, 'diagramx': [9207, -1, 9640, -1], 'generators': [28777033, 15576625, 26062237], 'label': '648.725.36.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.h2', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h2', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 116053448
    {'ambient': '648.725', 'aut_centralizer_order': 12, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5184, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['18.a1', '18.b1', '18.c1'], 'contains': ['108.a1', '108.b1', '108.c1', '162.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3244, -1, 3636, -1], 'generators': [15477724, 28790317, 18187580], 'label': '648.725.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '54.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 116053449
    {'ambient': '648.725', 'aut_centralizer_order': 486, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '16.8', 'aut_weyl_index': 1944, 'centralizer': '8.a1', 'complements': ['9.a1'], 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '36.c1', '36.g1'], 'contains': ['216.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4434, 9319, 4370, 6932], 'generators': [15484366, 14421484], 'label': '648.725.72.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '648.725', 'quotient_action_image': '8.3', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 116053450
    {'ambient': '648.725', 'aut_centralizer_order': 81, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2592, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.a1', '24.b1', '36.e1'], 'contains': ['216.a1', '216.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6512, -1, 6572, -1], 'generators': [15484366, 23548240], 'label': '648.725.72.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053451
    {'ambient': '648.725', 'aut_centralizer_order': 162, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3888, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.a1', '24.b1', '36.b1', '36.f2'], 'contains': ['216.a1', '216.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4892, -1, 4938, -1], 'generators': [15484366, 14513743], 'label': '648.725.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.c1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 116053452
    {'ambient': '648.725', 'aut_centralizer_order': 81, 'aut_label': '72.c2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3888, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.a1', '24.b1', '36.f1'], 'contains': ['216.a1', '216.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5877, -1, 7140, -1], 'generators': [15484366, 23405032], 'label': '648.725.72.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.c2', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053453
    {'ambient': '648.725', 'aut_centralizer_order': 162, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.29', 'aut_weyl_index': 648, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '36.a1', '36.d1', '36.g2'], 'contains': ['216.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2697, -1, 3802, -1], 'generators': [23411674, 15477724], 'label': '648.725.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.d1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053454
    {'ambient': '648.725', 'aut_centralizer_order': 162, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.8', 'aut_weyl_index': 1944, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '36.h1'], 'contains': ['216.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7871, -1, 8206, -1], 'generators': [23405032, 15576625], 'label': '648.725.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.e1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053455
    {'ambient': '648.725', 'aut_centralizer_order': 324, 'aut_label': '72.e2', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.8', 'aut_weyl_index': 1944, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '36.h2'], 'contains': ['216.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9235, -1, 8774, -1], 'generators': [15576625, 26062237], 'label': '648.725.72.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '72.e2', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e2', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 116053456
    {'ambient': '648.725', 'aut_centralizer_order': 48, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3888, 'centralizer': '324.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1'], 'contains': ['162.a1', '162.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8934, -1, 9072, -1], 'generators': [18552890, 18187580, 29839915], 'label': '648.725.81.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 116053457
    {'ambient': '648.725', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '31104.mg', 'aut_weyl_index': 1, 'centralizer': '648.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '12.c1', '12.d1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5576, 2383, 6607, 4041], 'generators': [28777033, 15484366, 23554882, 14421484, 14520385], 'label': '648.725.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '648.725'}
  • id: 116053458
    {'ambient': '648.725', 'aut_centralizer_order': 108, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.a1', '36.b1', '36.c1', '54.a1'], 'contains': ['216.a1', '324.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2141, -1, 2770, -1], 'generators': [15477724, 18187580], 'label': '648.725.108.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '108.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053459
    {'ambient': '648.725', 'aut_centralizer_order': 108, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5184, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.b1', '36.c1', '36.d1', '54.a1'], 'contains': ['216.a1', '324.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1579, -1, 3269, -1], 'generators': [14939641, 18187580], 'label': '648.725.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '108.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 116053460
    {'ambient': '648.725', 'aut_centralizer_order': 12, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5184, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.e1', '36.f1', '36.f2', '36.g1', '36.g2', '54.a1'], 'contains': ['216.a1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5442, -1, 6039, -1], 'generators': [28777033, 14421484], 'label': '648.725.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.c1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 116053461
    {'ambient': '648.725', 'aut_centralizer_order': 8, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5184, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.e1', '36.f1', '36.f2', '36.h1', '36.h2'], 'contains': ['216.b1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [8204, -1, 7673, -1], 'generators': [28777033, 23548240], 'label': '648.725.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '108.d1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 116053462
    {'ambient': '648.725', 'aut_centralizer_order': 96, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '162.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '81.a1'], 'contains': ['324.a1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [5893, -1, 5506, -1], 'generators': [18187580, 29315116], 'label': '648.725.162.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053463
    {'ambient': '648.725', 'aut_centralizer_order': 192, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '162.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '18.e1', '81.a1'], 'contains': ['324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9568, -1, 9695, -1], 'generators': [21125207, 39937294], 'label': '648.725.162.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053464
    {'ambient': '648.725', 'aut_centralizer_order': 972, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.a1', '72.b1', '72.c1', '72.c2', '72.d1', '108.a1', '108.b1', '108.c1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4101, -1, 4938, -1], 'generators': [14421484], 'label': '648.725.216.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '216.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053465
    {'ambient': '648.725', 'aut_centralizer_order': 648, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 15552, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.b1', '72.c1', '72.c2', '72.e1', '72.e2', '108.d1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7112, -1, 7140, -1], 'generators': [23548240], 'label': '648.725.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 116053466
    {'ambient': '648.725', 'aut_centralizer_order': 864, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 31104, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.b1', '162.a1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3494, -1, 3857, -1], 'generators': [18187580], 'label': '648.725.324.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '324.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 116053467
    {'ambient': '648.725', 'aut_centralizer_order': 384, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 31104, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1', '108.d1', '162.a1', '162.b1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6228, -1, 6039, -1], 'generators': [28777033], 'label': '648.725.324.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 116053468
    {'ambient': '648.725', 'aut_centralizer_order': 9, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 36, 'centralizer': '72.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.a1', '12.a1', '12.b1'], 'core': '8.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2776, -1, 5422, -1], 'generators': [15484366, 23554882, 14421484, 14520385, 18187580], 'label': '648.725.4.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.b1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 116053469
    {'ambient': '648.725', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.b1', '324.a1', '324.b1'], 'contains': [], 'core': '648.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6077, 9213, 5485, 9204], 'generators': [], 'label': '648.725.648.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': ['72.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 116053470
    {'ambient': '648.725', 'aut_centralizer_order': 1, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '648.555', 'aut_weyl_index': 48, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.a1'], 'contains': ['12.a1', '12.b1', '12.d1', '18.a1', '18.b1', '18.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3249, -1, 4204, -1], 'generators': [28777033, 15484366, 23411674, 14421484, 18187580], 'label': '648.725.6.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '6.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 116053471
    {'ambient': '648.725', 'aut_centralizer_order': 81, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.18045', 'aut_weyl_index': 81, 'centralizer': '8.a1', 'complements': ['81.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1'], 'contains': ['24.a1', '24.b1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5242, 2383, 6565, 4041], 'generators': [15484366, 23554882, 14421484, 14520385], 'label': '648.725.8.a1', 'mobius_quo': 3, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['72.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '648.725', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 116053472
    {'ambient': '648.725', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.182', 'aut_weyl_index': 216, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['18.b1', '18.d1', '81.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8182, -1, 7687, -1], 'generators': [28777033, 15484366, 14421484, 18552890, 18187580], 'label': '648.725.9.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 116053473
    {'ambient': '648.725', 'aut_centralizer_order': 9, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '72.46', 'aut_weyl_index': 432, 'centralizer': '72.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.b1', '6.a1'], 'contains': ['24.b1', '36.a1', '36.b1', '36.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2246, -1, 2521, -1], 'generators': [15484366, 23411674, 14421484, 18187580], 'label': '648.725.12.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.a1', 'projective_image': '648.725', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}