Abstract group data - 20736.hv

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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': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [12, 12, 18, 12, 12], 'aut_gens': [[2628844618652, 22237257739413], [148029337610683, 63293475561642], [87906979654172, 62799592259924], [27911510721697, 28782295685370], [129841167494554, 154860741919763], [128533453178037, 154861344689779]], 'aut_group': None, 'aut_hash': 6683667874813135431, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 82944, 'aut_permdeg': 108, 'aut_perms': [242187027323233967926571829195132134876284357166537420070505719122971453085224704653267159914910590101130838720351586646826760237070181194143413961077286446258716343561725971, 1012277844436035937971325539638235878450028786409617228810303947472003155791874812402524668793110729982467254002351187131026863591784231270775152250519752695730970402231754344, 1032351914116608941339541801480746264718644786736713806283855370820346294112215933653602854058157772240691087946680261704366994803317450201439270131351476474552356004643421225, 4447635179532760400599818624474499942743854374601438049627048021279756389345448741792562948821426958055017439259090687148617958635464318151643223504994293555598898696265869, 436845279292090544210199402136294737527076486228688117523507716601934207975984135525851586329699854444237770344234885442028042096111982457581738522893482565397673250062057905], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 1, 2], [2, 27, 2, 1], [2, 36, 1, 1], [2, 54, 1, 3], [2, 72, 1, 1], [2, 108, 1, 1], [2, 108, 2, 1], [2, 216, 1, 1], [3, 6, 1, 1], [3, 8, 1, 1], [3, 12, 1, 1], [3, 1152, 1, 1], [4, 36, 1, 1], [4, 72, 1, 2], [4, 144, 1, 1], [4, 216, 1, 1], [4, 216, 2, 1], [4, 324, 1, 1], [4, 432, 1, 2], [4, 648, 2, 1], [4, 1296, 1, 1], [6, 6, 1, 1], [6, 12, 1, 4], [6, 24, 1, 6], [6, 24, 2, 1], [6, 48, 1, 3], [6, 54, 2, 1], [6, 108, 1, 3], [6, 144, 1, 4], [6, 216, 2, 1], [6, 288, 1, 1], [6, 432, 1, 1], [6, 3456, 1, 1], [9, 2304, 1, 1], [12, 144, 1, 6], [12, 144, 2, 1], [12, 288, 1, 3], [12, 288, 2, 1], [12, 432, 1, 1], [12, 432, 2, 2], [12, 864, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.C_2^6.C_6.C_2^3', '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': 36, 'autcentquo_group': None, 'autcentquo_hash': 6683667874813135431, 'autcentquo_nilpotent': False, 'autcentquo_order': 82944, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3.C_2^6.D_6.C_2^2', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 6, 2], [2, 27, 2], [2, 36, 1], [2, 54, 3], [2, 72, 1], [2, 108, 3], [2, 216, 1], [3, 6, 1], [3, 8, 1], [3, 12, 1], [3, 1152, 1], [4, 36, 1], [4, 72, 2], [4, 144, 1], [4, 216, 3], [4, 324, 1], [4, 432, 2], [4, 648, 2], [4, 1296, 1], [6, 6, 1], [6, 12, 4], [6, 24, 8], [6, 48, 3], [6, 54, 2], [6, 108, 3], [6, 144, 4], [6, 216, 2], [6, 288, 1], [6, 432, 1], [6, 3456, 1], [9, 2304, 1], [12, 144, 8], [12, 288, 5], [12, 432, 5], [12, 864, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '20736.hv', 'commutator_count': 1, 'commutator_label': '5184.me', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 204, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 1, 2], [2, 27, 1, 2], [2, 36, 1, 1], [2, 54, 1, 3], [2, 72, 1, 1], [2, 108, 1, 3], [2, 216, 1, 1], [3, 6, 1, 1], [3, 8, 1, 1], [3, 12, 1, 1], [3, 1152, 1, 1], [4, 36, 1, 1], [4, 72, 1, 2], [4, 144, 1, 1], [4, 216, 1, 3], [4, 324, 1, 1], [4, 432, 1, 2], [4, 648, 1, 2], [4, 1296, 1, 1], [6, 6, 1, 1], [6, 12, 1, 4], [6, 24, 1, 6], [6, 24, 2, 1], [6, 48, 1, 3], [6, 54, 1, 2], [6, 108, 1, 3], [6, 144, 1, 4], [6, 216, 1, 2], [6, 288, 1, 1], [6, 432, 1, 1], [6, 3456, 1, 1], [9, 2304, 1, 1], [12, 144, 1, 6], [12, 144, 2, 1], [12, 288, 1, 3], [12, 288, 2, 1], [12, 432, 1, 3], [12, 432, 2, 1], [12, 864, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [8, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2], [12, 1, 6], [24, 0, 4], [24, 1, 8], [48, 1, 3]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '5184.br', 'hash': 8762208741585009387, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [12, 6], 'inner_gens': [[2628844618652, 63029948483924], [43329167857787, 22237257739413]], 'inner_hash': 8762208741585009387, 'inner_nilpotent': False, 'inner_order': 20736, 'inner_split': True, 'inner_tex': '(S_3\\times D_6^2).S_4', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 2], [3, 12], [6, 18], [8, 2], [12, 24], [16, 1], [24, 16], [48, 3]], 'label': '20736.hv', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(S3*D6^2).S4', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 71, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 82, 'number_divisions': 78, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': None, 'number_subgroup_classes': 6918, 'number_subgroups': 476956, 'old_label': None, 'order': 20736, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 879], [3, 1178], [4, 4752], [6, 6006], [9, 2304], [12, 5616]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[2628844638899, 22237257770668], [7866168279452, 22237257739413]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 8, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 12], [6, 18], [8, 2], [12, 20], [16, 1], [24, 14], [48, 5]], 'representations': {'PC': {'code': '110747984445725528613028473451048301256947518948195584537664756460066466480186176303699087405579711342938983623206059561426615957926140575377823280997255979492624335378413800271694060339761096384406762594606648039927198229', 'gens': [1, 2, 4, 5, 6, 7, 9, 11], 'pres': [12, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 3, 118224, 16945, 61, 271586, 584643, 1743, 146187, 832324, 376, 1108, 1733, 438065, 461, 529206, 490410, 76638, 19530, 50118, 4938, 246, 811015, 119827, 175135, 12331, 29239, 3139, 373256, 461396, 102740, 13016, 320, 829449, 990741, 207393, 11577, 76042, 897358, 193282, 190126, 47590, 394, 165899, 165911, 297251, 165935, 41543]}, 'Perm': {'d': 17, 'gens': [2628844618652, 22237257739413]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 81, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(S_3\\times D_6^2).S_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 154651946
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 204, 'group_order': 20736, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 154651957
    {'aut_label': '2A', 'centralizer': '3.a1', 'counter': 2, 'group_counter': 204, 'group_order': 20736, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 16687, 'size': 3}
  • id: 154651968
    {'aut_label': '2B', 'centralizer': '6.o1', 'counter': 3, 'group_counter': 204, 'group_order': 20736, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 25181, 'size': 6}
  • id: 154651979
    {'aut_label': '2C', 'centralizer': '6.n1', 'counter': 4, 'group_counter': 204, 'group_order': 20736, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 4264, 'size': 6}
  • id: 154651990
    {'aut_label': '2D', 'centralizer': '27.b1', 'counter': 5, 'group_counter': 204, 'group_order': 20736, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 5325060787200, 'size': 27}
  • id: 154652001
    {'aut_label': '2D', 'centralizer': '27.b1', 'counter': 6, 'group_counter': 204, 'group_order': 20736, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 126957537937435, 'size': 27}
  • id: 154652012
    {'aut_label': '2F', 'centralizer': '36.da1', 'counter': 7, 'group_counter': 204, 'group_order': 20736, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 123747256, 'size': 36}
  • id: 154652023
    {'aut_label': '2G', 'centralizer': '54.r1', 'counter': 8, 'group_counter': 204, 'group_order': 20736, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 1078117201, 'size': 54}
  • id: 154652027
    {'aut_label': '2H', 'centralizer': '54.q1', 'counter': 9, 'group_counter': 204, 'group_order': 20736, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 1078140940, 'size': 54}
  • id: 154651947
    {'aut_label': '2I', 'centralizer': '54.s1', 'counter': 10, 'group_counter': 204, 'group_order': 20736, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 88176230542, 'size': 54}
  • id: 154651948
    {'aut_label': '2J', 'centralizer': '72.bw1', 'counter': 11, 'group_counter': 204, 'group_order': 20736, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 8395548135087, 'size': 72}
  • id: 154651949
    {'aut_label': '2K', 'centralizer': None, 'counter': 12, 'group_counter': 204, 'group_order': 20736, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 26468478743, 'size': 108}
  • id: 154651950
    {'aut_label': '2L', 'centralizer': None, 'counter': 13, 'group_counter': 204, 'group_order': 20736, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 85447222992714, 'size': 108}
  • id: 154651951
    {'aut_label': '2L', 'centralizer': None, 'counter': 14, 'group_counter': 204, 'group_order': 20736, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 25514093521, 'size': 108}
  • id: 154651952
    {'aut_label': '2N', 'centralizer': None, 'counter': 15, 'group_counter': 204, 'group_order': 20736, 'label': '2N', 'order': 2, 'powers': [1, 15], 'representative': 91917101208715, 'size': 216}
  • id: 154651953
    {'aut_label': '3A', 'centralizer': '6.l1', 'counter': 16, 'group_counter': 204, 'group_order': 20736, 'label': '3A', 'order': 3, 'powers': [16, 1], 'representative': 436414003200, 'size': 6}
  • id: 154651954
    {'aut_label': '3B', 'centralizer': '8.a1', 'counter': 17, 'group_counter': 204, 'group_order': 20736, 'label': '3B', 'order': 3, 'powers': [17, 1], 'representative': 135225987321600, 'size': 8}
  • id: 154651955
    {'aut_label': '3C', 'centralizer': '12.bv1', 'counter': 18, 'group_counter': 204, 'group_order': 20736, 'label': '3C', 'order': 3, 'powers': [18, 1], 'representative': 9683982604800, 'size': 12}
  • id: 154651956
    {'aut_label': '3D', 'centralizer': None, 'counter': 19, 'group_counter': 204, 'group_order': 20736, 'label': '3D', 'order': 3, 'powers': [19, 1], 'representative': 41858037828891, 'size': 1152}
  • id: 154651958
    {'aut_label': '4A', 'centralizer': '36.db1', 'counter': 20, 'group_counter': 204, 'group_order': 20736, 'label': '4A', 'order': 4, 'powers': [2, 20], 'representative': 123777702, 'size': 36}
  • id: 154651959
    {'aut_label': '4B', 'centralizer': '72.jk1', 'counter': 21, 'group_counter': 204, 'group_order': 20736, 'label': '4B', 'order': 4, 'powers': [2, 21], 'representative': 123752302, 'size': 72}
  • id: 154651960
    {'aut_label': '4C', 'centralizer': '72.bx1', 'counter': 22, 'group_counter': 204, 'group_order': 20736, 'label': '4C', 'order': 4, 'powers': [2, 22], 'representative': 8395548164048, 'size': 72}
  • id: 154651961
    {'aut_label': '4D', 'centralizer': None, 'counter': 23, 'group_counter': 204, 'group_order': 20736, 'label': '4D', 'order': 4, 'powers': [4, 23], 'representative': 20923276515070, 'size': 144}
  • id: 154651962
    {'aut_label': '4E', 'centralizer': None, 'counter': 24, 'group_counter': 204, 'group_order': 20736, 'label': '4E', 'order': 4, 'powers': [6, 24], 'representative': 148028778386386, 'size': 216}
  • id: 154651963
    {'aut_label': '4F', 'centralizer': None, 'counter': 25, 'group_counter': 204, 'group_order': 20736, 'label': '4F', 'order': 4, 'powers': [2, 25], 'representative': 110299705699817, 'size': 216}
  • id: 154651964
    {'aut_label': '4E', 'centralizer': None, 'counter': 26, 'group_counter': 204, 'group_order': 20736, 'label': '4G', 'order': 4, 'powers': [5, 26], 'representative': 43171978764341, 'size': 216}
  • id: 154651965
    {'aut_label': '4H', 'centralizer': None, 'counter': 27, 'group_counter': 204, 'group_order': 20736, 'label': '4H', 'order': 4, 'powers': [2, 27], 'representative': 5344224492646, 'size': 324}
  • id: 154651966
    {'aut_label': '4I', 'centralizer': None, 'counter': 28, 'group_counter': 204, 'group_order': 20736, 'label': '4I', 'order': 4, 'powers': [3, 28], 'representative': 21365913555760, 'size': 432}
  • id: 154651967
    {'aut_label': '4J', 'centralizer': None, 'counter': 29, 'group_counter': 204, 'group_order': 20736, 'label': '4J', 'order': 4, 'powers': [10, 29], 'representative': 148222338579707, 'size': 432}
  • id: 154651969
    {'aut_label': '4K', 'centralizer': None, 'counter': 30, 'group_counter': 204, 'group_order': 20736, 'label': '4K', 'order': 4, 'powers': [5, 30], 'representative': 175502877138006, 'size': 648}
  • id: 154651970
    {'aut_label': '4K', 'centralizer': None, 'counter': 31, 'group_counter': 204, 'group_order': 20736, 'label': '4L', 'order': 4, 'powers': [6, 31], 'representative': 68262039031634, 'size': 648}
  • id: 154651971
    {'aut_label': '4M', 'centralizer': None, 'counter': 32, 'group_counter': 204, 'group_order': 20736, 'label': '4M', 'order': 4, 'powers': [8, 32], 'representative': 47090168295776, 'size': 1296}
  • id: 154651972
    {'aut_label': '6A', 'centralizer': '6.l1', 'counter': 33, 'group_counter': 204, 'group_order': 20736, 'label': '6A', 'order': 6, 'powers': [16, 2], 'representative': 436414019887, 'size': 6}
  • id: 154651973
    {'aut_label': '6B', 'centralizer': '12.bt1', 'counter': 34, 'group_counter': 204, 'group_order': 20736, 'label': '6B', 'order': 6, 'powers': [16, 3], 'representative': 112608946781, 'size': 12}
  • id: 154651974
    {'aut_label': '6C', 'centralizer': '12.bq1', 'counter': 35, 'group_counter': 204, 'group_order': 20736, 'label': '6C', 'order': 6, 'powers': [16, 2], 'representative': 436414027660, 'size': 12}
  • id: 154651975
    {'aut_label': '6D', 'centralizer': '12.bv1', 'counter': 36, 'group_counter': 204, 'group_order': 20736, 'label': '6D', 'order': 6, 'powers': [18, 2], 'representative': 5673901347340, 'size': 12}
  • id: 154651976
    {'aut_label': '6E', 'centralizer': '12.br1', 'counter': 37, 'group_counter': 204, 'group_order': 20736, 'label': '6E', 'order': 6, 'powers': [16, 4], 'representative': 436414003921, 'size': 12}
  • id: 154651977
    {'aut_label': '6F', 'centralizer': '24.dz1', 'counter': 38, 'group_counter': 204, 'group_order': 20736, 'label': '6F', 'order': 6, 'powers': [16, 4], 'representative': 112608925864, 'size': 24}
  • id: 154651978
    {'aut_label': '6G', 'centralizer': '24.dz1', 'counter': 39, 'group_counter': 204, 'group_order': 20736, 'label': '6G', 'order': 6, 'powers': [16, 3], 'representative': 112608940942, 'size': 24}
  • id: 154651980
    {'aut_label': '6H', 'centralizer': '24.ee1', 'counter': 40, 'group_counter': 204, 'group_order': 20736, 'label': '6H', 'order': 6, 'powers': [18, 3], 'representative': 89109745789661, 'size': 24}
  • id: 154651981
    {'aut_label': '6I', 'centralizer': '24.eb1', 'counter': 41, 'group_counter': 204, 'group_order': 20736, 'label': '6I', 'order': 6, 'powers': [18, 4], 'representative': 89109745780446, 'size': 24}
  • id: 154651982
    {'aut_label': '6J', 'centralizer': '24.ea1', 'counter': 42, 'group_counter': 204, 'group_order': 20736, 'label': '6J', 'order': 6, 'powers': [18, 2], 'representative': 85442469259660, 'size': 24}
  • id: 154651983
    {'aut_label': '6K', 'centralizer': '24.eb1', 'counter': 43, 'group_counter': 204, 'group_order': 20736, 'label': '6K', 'order': 6, 'powers': [17, 2], 'representative': 135225987351835, 'size': 24}
  • id: 154651984
    {'aut_label': '6L1', 'centralizer': '24.eb1', 'counter': 44, 'group_counter': 204, 'group_order': 20736, 'label': '6L1', 'order': 6, 'powers': [17, 4], 'representative': 132361681496401, 'size': 24}
  • id: 154651985
    {'aut_label': '6L1', 'centralizer': '24.eb1', 'counter': 45, 'group_counter': 204, 'group_order': 20736, 'label': '6L-1', 'order': 6, 'powers': [17, 4], 'representative': 93382359840721, 'size': 24}
  • id: 154651986
    {'aut_label': '6M', 'centralizer': '48.a1', 'counter': 46, 'group_counter': 204, 'group_order': 20736, 'label': '6M', 'order': 6, 'powers': [18, 4], 'representative': 5431047512401, 'size': 48}
  • id: 154651987
    {'aut_label': '6N', 'centralizer': '48.a1', 'counter': 47, 'group_counter': 204, 'group_order': 20736, 'label': '6N', 'order': 6, 'powers': [18, 3], 'representative': 5431047531022, 'size': 48}
  • id: 154651988
    {'aut_label': '6O', 'centralizer': '48.a1', 'counter': 48, 'group_counter': 204, 'group_order': 20736, 'label': '6O', 'order': 6, 'powers': [17, 3], 'representative': 89209857118222, 'size': 48}
  • id: 154651989
    {'aut_label': '6P', 'centralizer': '54.i1', 'counter': 49, 'group_counter': 204, 'group_order': 20736, 'label': '6P', 'order': 6, 'powers': [16, 6], 'representative': 132275932981915, 'size': 54}
  • id: 154651991
    {'aut_label': '6P', 'centralizer': '54.i1', 'counter': 50, 'group_counter': 204, 'group_order': 20736, 'label': '6Q', 'order': 6, 'powers': [16, 5], 'representative': 5344348222080, 'size': 54}
  • id: 154651992
    {'aut_label': '6R', 'centralizer': None, 'counter': 51, 'group_counter': 204, 'group_order': 20736, 'label': '6R', 'order': 6, 'powers': [16, 8], 'representative': 113646759121, 'size': 108}
  • id: 154651993
    {'aut_label': '6S', 'centralizer': None, 'counter': 52, 'group_counter': 204, 'group_order': 20736, 'label': '6S', 'order': 6, 'powers': [16, 9], 'representative': 113646782860, 'size': 108}
  • id: 154651994
    {'aut_label': '6T', 'centralizer': None, 'counter': 53, 'group_counter': 204, 'group_order': 20736, 'label': '6T', 'order': 6, 'powers': [16, 10], 'representative': 9335741566222, 'size': 108}
  • id: 154651995
    {'aut_label': '6U', 'centralizer': None, 'counter': 54, 'group_counter': 204, 'group_order': 20736, 'label': '6U', 'order': 6, 'powers': [16, 7], 'representative': 112692389176, 'size': 144}
  • id: 154651996
    {'aut_label': '6V', 'centralizer': None, 'counter': 55, 'group_counter': 204, 'group_order': 20736, 'label': '6V', 'order': 6, 'powers': [18, 11], 'representative': 1569772069167, 'size': 144}
  • id: 154651997
    {'aut_label': '6W', 'centralizer': None, 'counter': 56, 'group_counter': 204, 'group_order': 20736, 'label': '6W', 'order': 6, 'powers': [18, 7], 'representative': 5431526518456, 'size': 144}
  • id: 154651998
    {'aut_label': '6X', 'centralizer': None, 'counter': 57, 'group_counter': 204, 'group_order': 20736, 'label': '6X', 'order': 6, 'powers': [16, 11], 'representative': 21035881440007, 'size': 144}
  • id: 154651999
    {'aut_label': '6Y', 'centralizer': None, 'counter': 58, 'group_counter': 204, 'group_order': 20736, 'label': '6Y', 'order': 6, 'powers': [16, 13], 'representative': 93386638224714, 'size': 216}
  • id: 154652000
    {'aut_label': '6Y', 'centralizer': None, 'counter': 59, 'group_counter': 204, 'group_order': 20736, 'label': '6Z', 'order': 6, 'powers': [16, 14], 'representative': 126956623450321, 'size': 216}
  • id: 154652002
    {'aut_label': '6AA', 'centralizer': None, 'counter': 60, 'group_counter': 204, 'group_order': 20736, 'label': '6AA', 'order': 6, 'powers': [17, 11], 'representative': 128531979882206, 'size': 288}
  • id: 154652003
    {'aut_label': '6AB', 'centralizer': None, 'counter': 61, 'group_counter': 204, 'group_order': 20736, 'label': '6AB', 'order': 6, 'powers': [18, 15], 'representative': 87713898819595, 'size': 432}
  • id: 154652004
    {'aut_label': '6AC', 'centralizer': None, 'counter': 62, 'group_counter': 204, 'group_order': 20736, 'label': '6AC', 'order': 6, 'powers': [19, 12], 'representative': 22251188731349, 'size': 3456}
  • id: 154652005
    {'aut_label': '9A', 'centralizer': None, 'counter': 63, 'group_counter': 204, 'group_order': 20736, 'label': '9A', 'order': 9, 'powers': [63, 17], 'representative': 28782255788571, 'size': 2304}
  • id: 154652006
    {'aut_label': '12A', 'centralizer': None, 'counter': 64, 'group_counter': 204, 'group_order': 20736, 'label': '12A', 'order': 12, 'powers': [33, 21], 'representative': 112692390497, 'size': 144}
  • id: 154652007
    {'aut_label': '12B', 'centralizer': None, 'counter': 65, 'group_counter': 204, 'group_order': 20736, 'label': '12B', 'order': 12, 'powers': [35, 21], 'representative': 112692391600, 'size': 144}
  • id: 154652008
    {'aut_label': '12C', 'centralizer': None, 'counter': 66, 'group_counter': 204, 'group_order': 20736, 'label': '12C', 'order': 12, 'powers': [35, 20], 'representative': 112692392321, 'size': 144}
  • id: 154652009
    {'aut_label': '12D', 'centralizer': None, 'counter': 67, 'group_counter': 204, 'group_order': 20736, 'label': '12D', 'order': 12, 'powers': [36, 22], 'representative': 1569772085581, 'size': 144}
  • id: 154652010
    {'aut_label': '12E', 'centralizer': None, 'counter': 68, 'group_counter': 204, 'group_order': 20736, 'label': '12E', 'order': 12, 'powers': [36, 20], 'representative': 5431526520880, 'size': 144}
  • id: 154652011
    {'aut_label': '12F', 'centralizer': None, 'counter': 69, 'group_counter': 204, 'group_order': 20736, 'label': '12F', 'order': 12, 'powers': [33, 22], 'representative': 21035881464475, 'size': 144}
  • id: 154652013
    {'aut_label': '12G1', 'centralizer': None, 'counter': 70, 'group_counter': 204, 'group_order': 20736, 'label': '12G1', 'order': 12, 'powers': [37, 23], 'representative': 21035881444271, 'size': 144}
  • id: 154652014
    {'aut_label': '12G1', 'centralizer': None, 'counter': 71, 'group_counter': 204, 'group_order': 20736, 'label': '12G-1', 'order': 12, 'powers': [37, 23], 'representative': 21035881461055, 'size': 144}
  • id: 154652015
    {'aut_label': '12H', 'centralizer': None, 'counter': 72, 'group_counter': 204, 'group_order': 20736, 'label': '12H', 'order': 12, 'powers': [41, 23], 'representative': 175415658956088, 'size': 288}
  • id: 154652016
    {'aut_label': '12I', 'centralizer': None, 'counter': 73, 'group_counter': 204, 'group_order': 20736, 'label': '12I', 'order': 12, 'powers': [42, 21], 'representative': 127043801754167, 'size': 288}
  • id: 154652017
    {'aut_label': '12J', 'centralizer': None, 'counter': 74, 'group_counter': 204, 'group_order': 20736, 'label': '12J', 'order': 12, 'powers': [43, 22], 'representative': 153017184879314, 'size': 288}
  • id: 154652018
    {'aut_label': '12K1', 'centralizer': None, 'counter': 75, 'group_counter': 204, 'group_order': 20736, 'label': '12K1', 'order': 12, 'powers': [44, 23], 'representative': 27905283685336, 'size': 288}
  • id: 154652019
    {'aut_label': '12K1', 'centralizer': None, 'counter': 76, 'group_counter': 204, 'group_order': 20736, 'label': '12K-1', 'order': 12, 'powers': [45, 23], 'representative': 167589367564937, 'size': 288}
  • id: 154652020
    {'aut_label': '12L', 'centralizer': None, 'counter': 77, 'group_counter': 204, 'group_order': 20736, 'label': '12L', 'order': 12, 'powers': [49, 24], 'representative': 72209538407539, 'size': 432}
  • id: 154652021
    {'aut_label': '12M', 'centralizer': None, 'counter': 78, 'group_counter': 204, 'group_order': 20736, 'label': '12M', 'order': 12, 'powers': [36, 25], 'representative': 27911510692582, 'size': 432}
  • id: 154652022
    {'aut_label': '12L', 'centralizer': None, 'counter': 79, 'group_counter': 204, 'group_order': 20736, 'label': '12N', 'order': 12, 'powers': [50, 26], 'representative': 51013670775221, 'size': 432}
  • id: 154652024
    {'aut_label': '12O1', 'centralizer': None, 'counter': 80, 'group_counter': 204, 'group_order': 20736, 'label': '12O1', 'order': 12, 'powers': [53, 29], 'representative': 153373086355003, 'size': 432}
  • id: 154652025
    {'aut_label': '12O1', 'centralizer': None, 'counter': 81, 'group_counter': 204, 'group_order': 20736, 'label': '12O5', 'order': 12, 'powers': [53, 29], 'representative': 155994578649403, 'size': 432}
  • id: 154652026
    {'aut_label': '12P', 'centralizer': None, 'counter': 82, 'group_counter': 204, 'group_order': 20736, 'label': '12P', 'order': 12, 'powers': [40, 28], 'representative': 175770602413302, 'size': 864}
• 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: 15002065
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15002076
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 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: 15002087
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 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: 15002098
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 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: 15002109
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, -1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, -1, -1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002120
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 0, 2, -2, 2, 0, 2, 2, 2, -1, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 2, 2, 0, 0, 1, -1, 0, 0, -2, -2, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002131
    {'cdim': 3, 'counter': 7, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, -1, -1, 3, 3, -1, 1, -1, 3, -1, 1, 3, 3, 3, 0, 3, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 3, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, 3, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, -1, 1, 3, -1, 3, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 15002141
    {'cdim': 3, 'counter': 8, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3b', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, 3, -1, -1, 3, 1, -1, 3, -1, 1, 3, 3, 3, 0, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 3, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, -1, 3, -1, 1, 1, 3, 3, -1, -1, 1, 1, 0, 0, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 15002142
    {'cdim': 3, 'counter': 9, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3c', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 1, -1, 3, -1, 1, 3, 3, 3, 0, -1, -1, 1, 1, -1, 1, -1, 3, 1, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 15002066
    {'cdim': 3, 'counter': 10, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3d', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, 3, 3, 3, 0, 3, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 3, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 1, -1, 3, -1, 3, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 15002067
    {'cdim': 3, 'counter': 11, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3e', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, 3, -1, -1, 3, -1, -1, 3, -1, -1, 3, 3, 3, 0, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 3, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, -1, 0, 0, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 15002068
    {'cdim': 3, 'counter': 12, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3f', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, 3, 3, 3, 0, -1, -1, -1, -1, 1, -1, 1, 3, -1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 15002069
    {'cdim': 3, 'counter': 13, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, -1, 1, 3, 3, -1, -1, -1, -3, -1, 1, 3, 3, 3, 0, -3, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 3, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, 1, 1, -1, -1, -1, 1, 0, 0, 1, -1, -3, 1, -3, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 15002070
    {'cdim': 3, 'counter': 14, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, -1, 1, 3, 3, -1, 1, -1, -3, -1, -1, 3, 3, 3, 0, -3, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 3, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, 3, 1, 1, 1, 1, -1, -1, 1, -1, 0, 0, -1, 1, -3, 1, -3, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 15002071
    {'cdim': 3, 'counter': 15, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3i', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, -3, -1, -1, 3, -1, -1, -3, -1, 1, 3, 3, 3, 0, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 3, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, -1, 3, -1, -1, -1, -3, -3, -1, -1, -1, 1, 0, 0, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 15002072
    {'cdim': 3, 'counter': 16, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3j', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, -3, -1, -1, 3, 1, -1, -3, -1, -1, 3, 3, 3, 0, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 3, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, -1, 3, -1, 1, 1, -3, -3, -1, -1, 1, -1, 0, 0, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 15002073
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3k', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, 1, -1, -1, -1, -1, -1, -3, -1, 1, 3, 3, 3, 0, 1, 1, -1, -1, -1, 1, -1, -3, 1, -1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 0, 0, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 15002074
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.3l', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, 1, -1, -1, -1, 1, -1, -3, -1, -1, 3, 3, 3, 0, 1, 1, 1, 1, 1, -1, 1, -3, -1, 1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 15002075
    {'cdim': 6, 'counter': 19, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6a', 'multiplicity': 1, 'nt': [8, 34], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -2, -2, -2, -2, -2, -2, 0, 2, 6, 2, 0, 6, 6, 6, 0, -2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 6, -2, 6, 6, -2, -2, 6, 6, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002077
    {'cdim': 6, 'counter': 20, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6b', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, -2, -2, 2, -2, 6, 0, -2, 2, -2, 2, -2, 0, 2, 0, 6, 6, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 2, 2, -2, -2, 6, -2, 2, -2, -2, 2, 2, 0, 0, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002078
    {'cdim': 6, 'counter': 21, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6c', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, -2, -2, 2, 6, -2, 0, -2, 2, -2, 2, 2, 0, -2, 0, 6, 6, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 2, 2, -2, -2, -2, 6, 2, -2, -2, 2, 2, 0, 0, -2, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002079
    {'cdim': 6, 'counter': 22, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6d', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, -2, 2, -2, -2, 6, 0, 2, -2, -2, 0, 2, 0, -2, 2, 6, 6, 6, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, 6, -2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, -2, 0, 0], 'schur_index': 1}
  • id: 15002080
    {'cdim': 6, 'counter': 23, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6e', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, -2, 2, -2, 6, -2, 0, 2, -2, -2, 0, -2, 0, 2, 2, 6, 6, 6, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, 6, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0], 'schur_index': 1}
  • id: 15002081
    {'cdim': 6, 'counter': 24, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6f', 'multiplicity': 1, 'nt': [9, 31], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, 4, 2, 2, 2, 2, 2, 0, 2, 0, 3, -3, 0, 0, 4, 4, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 3, 3, 3, 0, 3, -3, 0, -3, -3, 3, 0, 0, 3, 0, 0, -3, -1, -1, -1, -1, -1, 2, -1, -2, 1, -1, -1, -1, 0, 0, 0, -1, -1, 1, 1, -2, 2, 1, -1, 2, -2, -1, -1, -1, -1, -1, -1, 0, -1, 0], 'schur_index': 1}
  • id: 15002082
    {'cdim': 6, 'counter': 25, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6g', 'multiplicity': 1, 'nt': [12, 100], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -2, -2, 2, -2, -2, -2, 0, 2, -6, 2, 0, 6, 6, 6, 0, 2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, -2, 6, 6, -2, -2, 6, 6, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002083
    {'cdim': 6, 'counter': 26, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6h', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, -2, -2, 2, -2, 6, 0, -2, 2, -2, -2, -2, 0, 2, 0, 6, 6, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 2, 2, -2, -2, 6, -2, 2, -2, -2, -2, -2, 0, 0, 2, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002084
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6i', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, -2, -2, 2, 6, -2, 0, -2, 2, -2, -2, 2, 0, -2, 0, 6, 6, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 2, 2, -2, -2, -2, 6, 2, -2, -2, -2, -2, 0, 0, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002085
    {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6j', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, -2, 2, -2, -2, 6, 0, 2, -2, -2, 0, 2, 0, -2, -2, 6, 6, 6, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, 6, -2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 2, 0, 0], 'schur_index': 1}
  • id: 15002086
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6k', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, -2, 2, -2, 6, -2, 0, 2, -2, -2, 0, -2, 0, 2, -2, 6, 6, 6, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, 6, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, 0, 0], 'schur_index': 1}
  • id: 15002088
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6l', 'multiplicity': 1, 'nt': [18, 300], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, -4, 2, 2, 2, -2, 2, 0, 2, 0, 3, -3, 0, 0, -4, -4, -2, -2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 3, 3, 3, 0, 3, -3, 0, -3, -3, 3, 0, 0, 3, 0, 0, -3, -1, -1, -1, -1, -1, -2, 1, 2, -1, -1, -1, 1, 0, 0, 0, 1, 1, -1, -1, 2, -2, -1, 1, -2, 2, 1, 1, 1, -1, -1, -1, 0, -1, 0], 'schur_index': 1}
  • id: 15002089
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6m', 'multiplicity': 1, 'nt': [18, 311], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, -4, 2, 2, 2, 2, 2, 0, 2, 0, 3, -3, 0, 0, -4, -4, 2, 2, -2, 0, -2, 0, 0, -2, 0, 0, 0, 3, 3, 3, 0, 3, -3, 0, -3, -3, 3, 0, 0, 3, 0, 0, -3, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, 1, 1, 1, 0, 1, 0], 'schur_index': 1}
  • id: 15002090
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6n', 'multiplicity': 1, 'nt': [18, 319], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, 4, 2, 2, 2, -2, 2, 0, 2, 0, 3, -3, 0, 0, 4, 4, -2, -2, -2, 0, -2, 0, 0, -2, 0, 0, 0, 3, 3, 3, 0, 3, -3, 0, -3, -3, 3, 0, 0, 3, 0, 0, -3, -1, -1, -1, -1, -1, -2, 1, -2, 1, -1, -1, 1, 0, 0, 0, 1, 1, 1, 1, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 1, 0], 'schur_index': 1}
  • id: 15002091
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6o', 'multiplicity': 1, 'nt': [18, 483], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 2, 2, -4, 2, 2, 2, 2, -2, 0, -2, 0, 3, -3, 0, 0, 4, 0, 2, -2, -2, 0, -2, 0, 0, 2, 0, 0, 0, 3, -5, 3, 0, -5, 1, 0, -3, 1, 1, 4, 4, 1, -2, -2, 1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 1, 1, -1, 0, 0, 0, 1, -1, 1, -3, -2, 2, 3, 1, -2, 0, 1, -1, 1, 1, -1, 1, 0, -1, 0], 'schur_index': 1}
  • id: 15002092
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6p', 'multiplicity': 1, 'nt': [18, 483], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 2, 2, 4, 2, 2, 2, 2, -2, 0, -2, 0, 3, -3, 0, 0, -4, 0, 2, -2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 3, -5, 3, 0, -5, 1, 0, -3, 1, 1, 4, 4, 1, -2, -2, 1, -1, -1, -1, -1, -1, 2, -1, -2, 1, 1, 1, -1, 0, 0, 0, 1, -1, -1, 3, 2, 2, -3, 1, -2, 0, 1, -1, 1, -1, 1, -1, 0, 1, 0], 'schur_index': 1}
  • id: 15002093
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6q', 'multiplicity': 1, 'nt': [18, 484], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 2, 2, -4, 2, 2, 2, -2, -2, 0, -2, 0, 3, -3, 0, 0, 4, 0, -2, 2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 3, -5, 3, 0, -5, 1, 0, -3, 1, 1, 4, 4, 1, -2, -2, 1, -1, -1, -1, -1, -1, -2, 1, 2, -1, 1, 1, 1, 0, 0, 0, -1, 1, 1, -3, -2, -2, 3, -1, 2, 0, -1, 1, -1, -1, 1, -1, 0, 1, 0], 'schur_index': 1}
  • id: 15002094
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.6r', 'multiplicity': 1, 'nt': [18, 484], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 2, 2, 4, 2, 2, 2, -2, -2, 0, -2, 0, 3, -3, 0, 0, -4, 0, -2, 2, -2, 0, -2, 0, 0, 2, 0, 0, 0, 3, -5, 3, 0, -5, 1, 0, -3, 1, 1, 4, 4, 1, -2, -2, 1, -1, -1, -1, -1, -1, -2, 1, -2, 1, 1, 1, 1, 0, 0, 0, -1, 1, -1, 3, 2, -2, -3, -1, 2, 0, -1, 1, -1, 1, -1, 1, 0, -1, 0], 'schur_index': 1}
  • id: 15002095
    {'cdim': 8, 'counter': 37, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.8a', 'multiplicity': 1, 'nt': [12, 213], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, -1, 2, 2, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, -4, -1, 2, -1, -1, -4, 2, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 0, 0, -1, -2, -2, 0, 0, 0, -2, 0, -2, -2, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002096
    {'cdim': 8, 'counter': 38, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.8b', 'multiplicity': 1, 'nt': [24, 2893], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, -1, 2, 2, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, -4, -1, 2, -1, -1, -4, 2, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -1, 0, 0, -1, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002097
    {'cdim': 12, 'counter': 39, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12a', 'multiplicity': 1, 'nt': [16, 1068], 'qdim': 12, 'qvalues': [12, -4, -4, 4, -4, -4, 0, 4, -4, 4, 0, 0, 0, 0, 0, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, -4, -4, 4, -4, -4, 4, 4, 4, -4, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002099
    {'cdim': 12, 'counter': 40, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12b', 'multiplicity': 1, 'nt': [16, 1068], 'qdim': 12, 'qvalues': [12, -4, 4, -4, -4, -4, 0, -4, 4, 4, 0, 0, 0, 0, 0, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -4, -4, -4, -4, -4, -4, 4, 4, -4, -4, -4, 4, 4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002100
    {'cdim': 12, 'counter': 41, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12c', 'multiplicity': 1, 'nt': [18, 315], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 3, -3, 0, 4, 4, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, -3, 3, 3, 0, -3, -3, 0, -3, -3, 3, 0, 0, 0, 0, 0, -1, 2, 1, -2, 0, 0, -1, -1, 0, 0, 2, 2, -2, -2, 1, -1, -2, 2, -1, 1, -1, -1, -1, 0, 0, 0, -1, 0, -1], 'schur_index': 1}
  • id: 15002101
    {'cdim': 12, 'counter': 42, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12d', 'multiplicity': 1, 'nt': [36, 2210], 'qdim': 12, 'qvalues': [12, 12, 12, 12, -4, -4, 0, -4, -4, -4, 0, -4, 0, -4, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 6, -6, 0, -6, -6, 6, 0, 0, 6, 0, 0, -6, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002102
    {'cdim': 12, 'counter': 43, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12e', 'multiplicity': 1, 'nt': [36, 2214], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, -2, 0, 3, -3, 0, -4, -4, 2, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, -3, 3, 3, 0, -3, -3, 0, -3, -3, 3, 0, 0, 0, 0, 0, -1, 2, -1, 2, 0, 0, -1, 1, 0, 0, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, 0, 1, 0, 1], 'schur_index': 1}
  • id: 15002103
    {'cdim': 12, 'counter': 44, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12f', 'multiplicity': 1, 'nt': [36, 2216], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, -2, 0, 3, -3, 0, 4, 4, -2, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, -3, 3, 3, 0, -3, -3, 0, -3, -3, 3, 0, 0, 0, 0, 0, 1, -2, 1, -2, 0, 0, 1, 1, 0, 0, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1], 'schur_index': 1}
  • id: 15002104
    {'cdim': 12, 'counter': 45, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12g', 'multiplicity': 1, 'nt': [36, 2217], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 2, 0, 3, -3, 0, -4, -4, -2, -2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, -3, 3, 3, 0, -3, -3, 0, -3, -3, 3, 0, 0, 0, 0, 0, 1, -2, -1, 2, 0, 0, 1, -1, 0, 0, -2, -2, 2, 2, -1, 1, 2, -2, 1, -1, 1, 1, 1, 0, 0, 0, -1, 0, -1], 'schur_index': 1}
  • id: 15002105
    {'cdim': 12, 'counter': 46, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12h', 'multiplicity': 1, 'nt': [36, 5945], 'qdim': 12, 'qvalues': [12, 12, -4, -4, -4, -4, 0, -4, -4, -4, 0, 4, 0, 4, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -10, 6, 0, -10, 2, 0, -6, 2, 2, 8, 8, 2, -4, -4, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002106
    {'cdim': 12, 'counter': 47, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12i', 'multiplicity': 1, 'nt': [36, 5978], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, -2, 0, 3, -3, 0, 4, -4, -2, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, -3, 8, -1, -3, 3, -1, -4, 5, 5, -4, -1, -1, -1, 0, 0, 0, 0, 0, 1, -2, 1, -2, 0, 0, 1, 1, 0, 0, 2, -2, -2, 2, 1, 1, 2, 2, -1, -1, -1, 1, -1, 0, 0, 0, 1, 0, -1], 'schur_index': 1}
  • id: 15002107
    {'cdim': 12, 'counter': 48, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12j', 'multiplicity': 1, 'nt': [36, 5979], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 3, -3, 0, 4, -4, 2, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, -3, 8, -1, -3, 3, -1, -4, 5, 5, -4, -1, -1, -1, 0, 0, 0, 0, 0, -1, 2, 1, -2, 0, 0, -1, -1, 0, 0, -2, 2, -2, 2, 1, -1, 2, -2, 1, -1, 1, -1, 1, 0, 0, 0, -1, 0, 1], 'schur_index': 1}
  • id: 15002108
    {'cdim': 12, 'counter': 49, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12k', 'multiplicity': 1, 'nt': [36, 5991], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 2, 0, 3, -3, 0, -4, 4, -2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, -3, 8, -1, -3, 3, -1, -4, 5, 5, -4, -1, -1, -1, 0, 0, 0, 0, 0, 1, -2, -1, 2, 0, 0, 1, -1, 0, 0, 2, -2, 2, -2, -1, 1, -2, 2, -1, 1, -1, 1, -1, 0, 0, 0, -1, 0, 1], 'schur_index': 1}
  • id: 15002110
    {'cdim': 12, 'counter': 50, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12l', 'multiplicity': 1, 'nt': [36, 5998], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, -2, 0, 3, -3, 0, -4, 4, 2, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, -3, 8, -1, -3, 3, -1, -4, 5, 5, -4, -1, -1, -1, 0, 0, 0, 0, 0, -1, 2, -1, 2, 0, 0, -1, 1, 0, 0, -2, 2, 2, -2, -1, -1, -2, -2, 1, 1, 1, -1, 1, 0, 0, 0, 1, 0, -1], 'schur_index': 1}
  • id: 15002111
    {'cdim': 12, 'counter': 51, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12m', 'multiplicity': 1, 'nt': [36, 6028], 'qdim': 12, 'qvalues': [12, 12, -4, -4, -4, -4, 0, 4, 4, -4, 0, 0, 0, 0, 0, 6, -6, 0, 0, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 6, 0, 2, 2, 0, -6, 2, -4, -4, -4, -4, 2, 2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002112
    {'cdim': 12, 'counter': 52, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12n', 'multiplicity': 1, 'nt': [36, 6028], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 4, 4, 8, -4, -4, 4, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 6, 0, 2, 2, 0, -6, 2, -4, -4, -4, -4, 2, 2, 2, -2, -2, 2, -2, 2, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002113
    {'cdim': 12, 'counter': 53, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12o', 'multiplicity': 1, 'nt': [36, 6029], 'qdim': 12, 'qvalues': [12, 12, -4, -4, -4, -4, 0, 4, 4, -4, 0, 0, 0, 0, 0, 6, -6, 0, 0, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 6, 0, 2, 2, 0, -6, 2, -4, -4, -4, -4, 2, 2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002114
    {'cdim': 12, 'counter': 54, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12p', 'multiplicity': 1, 'nt': [36, 6029], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 4, 4, -8, -4, -4, 4, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 6, 0, 2, 2, 0, -6, 2, -4, -4, -4, -4, 2, 2, 2, -2, -2, 2, -2, 2, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002115
    {'cdim': 12, 'counter': 55, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12q', 'multiplicity': 1, 'nt': [36, 11984], 'qdim': 12, 'qvalues': [12, -4, 4, -4, 4, 4, 0, 4, -4, -4, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, -10, -2, 2, 8, 2, 2, -4, 2, 2, 4, 4, -4, -4, 2, -2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0], 'schur_index': 1}
  • id: 15002116
    {'cdim': 12, 'counter': 56, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12r', 'multiplicity': 1, 'nt': [36, 11984], 'qdim': 12, 'qvalues': [12, -4, 4, -4, 4, 4, 0, 4, -4, -4, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, -10, -2, 2, 8, 2, 2, -4, 2, 2, 4, 4, -4, -4, 2, -2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0], 'schur_index': 1}
  • id: 15002117
    {'cdim': 12, 'counter': 57, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12s', 'multiplicity': 1, 'nt': [36, 11998], 'qdim': 12, 'qvalues': [12, -4, -4, 4, 4, 4, 0, -4, 4, -4, -4, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 2, 2, 8, -2, -2, -4, 2, -2, -4, -4, 4, 4, -2, 2, 2, -2, -2, -2, 2, 2, -4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002118
    {'cdim': 12, 'counter': 58, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12t', 'multiplicity': 1, 'nt': [36, 11999], 'qdim': 12, 'qvalues': [12, -4, -4, 4, 4, 4, 0, -4, 4, -4, 4, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 2, 2, 8, -2, -2, -4, 2, -2, -4, -4, 4, 4, -2, 2, 2, -2, -2, -2, 2, 2, 4, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002122
    {'cdim': 16, 'counter': 61, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.16a', 'multiplicity': 1, 'nt': [24, 2912], 'qdim': 16, 'qvalues': [16, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 4, -8, -2, 4, -2, -2, -8, 4, 4, -8, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002119
    {'cdim': 12, 'counter': 59, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12u', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -8, 8, -8, -8, 0, 8, -8, 8, 0, 0, 0, 0, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 4, 4, 16, -4, -4, -8, 4, -4, -8, -8, 8, 8, -4, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002121
    {'cdim': 12, 'counter': 60, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.12v', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 8, -8, -8, -8, 0, -8, 8, 8, 0, 0, 0, 0, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, -4, 4, 16, 4, 4, -8, 4, 4, 8, 8, -8, -8, 4, -4, -4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002123
    {'cdim': 24, 'counter': 62, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, 24, -8, -8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -12, -3, 6, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 4, -12, 6, 4, 1, 6, -3, 1, 4, -2, -2, 4, -2, -2, 1, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, 2, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002124
    {'cdim': 24, 'counter': 63, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -8, 8, -8, 8, 0, 0, 0, 0, 0, -4, 0, 4, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, -8, -8, 8, -4, 4, 4, -4, -2, 4, -4, 2, 2, -2, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002125
    {'cdim': 24, 'counter': 64, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24c', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -8, 8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -8, -8, 10, 8, 2, -2, -2, 2, 4, -2, 2, -4, -4, 4, -2, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002126
    {'cdim': 24, 'counter': 65, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -8, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -8, -8, 10, 8, 2, -2, -2, 2, 4, -2, 2, -4, -4, 4, -2, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002127
    {'cdim': 24, 'counter': 66, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24e', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -8, 8, 8, -8, 0, 0, 0, 0, 0, 4, 0, -4, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, -8, -8, 8, -4, 4, 4, -4, -2, 4, -4, 2, 2, -2, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002128
    {'cdim': 24, 'counter': 67, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24f', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 8, -8, -8, 8, 0, 0, 0, 0, 0, 4, 0, -4, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, -8, -8, -8, 4, 4, 4, 4, 2, -4, 4, -2, -2, 2, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002129
    {'cdim': 24, 'counter': 68, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24g', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 6, -6, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 16, 8, -8, 10, -8, -2, -2, -2, -2, -4, 2, -2, 4, 4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 15002130
    {'cdim': 24, 'counter': 69, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24h', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, -6, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 16, 8, -8, 10, -8, -2, -2, -2, -2, -4, 2, -2, 4, 4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
  • id: 15002132
    {'cdim': 24, 'counter': 70, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24i', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 8, -8, 8, -8, 0, 0, 0, 0, 0, -4, 0, 4, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, -8, -8, -8, 4, 4, 4, 4, 2, -4, 4, -2, -2, 2, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002133
    {'cdim': 24, 'counter': 71, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24j', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 24, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -6, -8, -2, -6, 6, -2, 4, -2, -2, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002134
    {'cdim': 24, 'counter': 72, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24k', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 24, -8, -8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -12, -3, 6, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 4, -12, 6, 4, 1, 6, -3, 1, 4, -2, -2, 4, -2, -2, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, -2, -2, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002135
    {'cdim': 24, 'counter': 73, 'faithful': False, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24l', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 24, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -6, -8, -2, -6, 6, -2, 4, -2, -2, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002136
    {'cdim': 24, 'counter': 74, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24m', 'multiplicity': 2, 'nt': [96, 0], 'qdim': 48, 'qvalues': [48, -16, -16, 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -24, -6, 12, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, -4, -8, -2, -4, 2, -2, 8, -4, 4, -8, 4, -4, 2, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002137
    {'cdim': 24, 'counter': 75, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.24n', 'multiplicity': 2, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, -16, -16, 16, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -24, -6, 12, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, -4, -8, -2, -4, 2, -2, 8, -4, 4, -8, 4, -4, 2, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002138
    {'cdim': 48, 'counter': 76, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.48a', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 48, 'qvalues': [48, -16, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, -4, 8, 2, -4, 2, 2, -8, 4, -4, 8, -4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002139
    {'cdim': 48, 'counter': 77, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.48b', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, -16, -16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 8, 8, -4, -8, 4, 8, -4, 4, -4, 8, -8, 4, -2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15002140
    {'cdim': 48, 'counter': 78, 'faithful': True, 'group': '20736.hv', 'group_order': 20736, 'image': None, 'label': '20736.hv.48c', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, -16, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -8, 8, -4, 8, -4, 8, -4, -4, 4, -8, 8, -4, 2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 34711768
    {'center': None, 'center_index': 1, 'center_order': 20736, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 20736, 'label': '20736.hv.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 34711779
    {'center': None, 'center_index': 1, 'center_order': 20736, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 10368, 'label': '20736.hv.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 34711790
    {'center': None, 'center_index': 1, 'center_order': 20736, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 10368, 'label': '20736.hv.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 34711801
    {'center': None, 'center_index': 1, 'center_order': 20736, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 10368, 'label': '20736.hv.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 34711812
    {'center': None, 'center_index': 6, 'center_order': 3456, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': None, 'kernel_order': 3456, 'label': '20736.hv.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711823
    {'center': None, 'center_index': 6, 'center_order': 3456, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 1728, 'label': '20736.hv.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711834
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 7, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 864, 'label': '20736.hv.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 34711845
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 8, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 864, 'label': '20736.hv.3b', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34711849
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 9, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 864, 'label': '20736.hv.3c', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34711769
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 10, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 864, 'label': '20736.hv.3d', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34711770
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 11, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 864, 'label': '20736.hv.3e', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34711771
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 12, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 864, 'label': '20736.hv.3f', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 34711772
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 13, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 432, 'label': '20736.hv.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 34711773
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 14, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 432, 'label': '20736.hv.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34711774
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 15, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 432, 'label': '20736.hv.3i', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34711775
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 16, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 432, 'label': '20736.hv.3j', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34711776
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 17, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 432, 'label': '20736.hv.3k', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34711777
    {'center': None, 'center_index': 24, 'center_order': 864, 'counter': 18, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 432, 'label': '20736.hv.3l', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 34711778
    {'center': None, 'center_index': 96, 'center_order': 216, 'counter': 19, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '96.227', 'image_order': 96, 'indicator': 1, 'kernel': None, 'kernel_order': 216, 'label': '20736.hv.6a', 'nt': [8, 34], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711780
    {'center': None, 'center_index': 192, 'center_order': 108, 'counter': 20, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 108, 'label': '20736.hv.6b', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 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]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711781
    {'center': None, 'center_index': 192, 'center_order': 108, 'counter': 21, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 108, 'label': '20736.hv.6c', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 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]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711782
    {'center': None, 'center_index': 192, 'center_order': 108, 'counter': 22, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 108, 'label': '20736.hv.6d', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711783
    {'center': None, 'center_index': 192, 'center_order': 108, 'counter': 23, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 108, 'label': '20736.hv.6e', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711784
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 24, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.6f', 'nt': [9, 31], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 34711785
    {'center': None, 'center_index': 96, 'center_order': 216, 'counter': 25, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 108, 'label': '20736.hv.6g', 'nt': [12, 100], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711786
    {'center': None, 'center_index': 192, 'center_order': 108, 'counter': 26, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 108, 'label': '20736.hv.6h', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 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]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711787
    {'center': None, 'center_index': 192, 'center_order': 108, 'counter': 27, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 108, 'label': '20736.hv.6i', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 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]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711788
    {'center': None, 'center_index': 192, 'center_order': 108, 'counter': 28, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 108, 'label': '20736.hv.6j', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711789
    {'center': None, 'center_index': 192, 'center_order': 108, 'counter': 29, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 108, 'label': '20736.hv.6k', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711791
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 30, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.6l', 'nt': [18, 300], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 34711792
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 31, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.6m', 'nt': [18, 311], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 34711793
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 32, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.6n', 'nt': [18, 319], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 34711794
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 33, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.6o', 'nt': [18, 483], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[3, 0]], [[0, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 34711795
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 34, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.6p', 'nt': [18, 483], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[3, 0]], [[0, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 34711796
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 35, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.6q', 'nt': [18, 484], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[3, 0]], [[0, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 34711797
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 36, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.6r', 'nt': [18, 484], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[3, 0]], [[0, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 34711798
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 37, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.8a', 'nt': [12, 213], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711799
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 38, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.8b', 'nt': [24, 2893], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711800
    {'center': None, 'center_index': 768, 'center_order': 27, 'counter': 39, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '768.1090070', 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '20736.hv.12a', 'nt': [16, 1068], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711802
    {'center': None, 'center_index': 768, 'center_order': 27, 'counter': 40, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '768.1090070', 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '20736.hv.12b', 'nt': [16, 1068], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711803
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 41, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.12c', 'nt': [18, 315], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 34711804
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 42, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.12d', 'nt': [36, 2210], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711805
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 43, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.12e', 'nt': [36, 2214], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 34711806
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 44, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.12f', 'nt': [36, 2216], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 34711807
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 45, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.12g', 'nt': [36, 2217], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 34711808
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 46, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.12h', 'nt': [36, 5945], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-10, 0]], [[6, 0]], [[0, 0]], [[-10, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[8, 0]], [[8, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711809
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 47, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.12i', 'nt': [36, 5978], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-3, 0]], [[8, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-4, 0]], [[5, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 34711810
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 48, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.12j', 'nt': [36, 5979], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-3, 0]], [[8, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-4, 0]], [[5, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 34711811
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 49, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.12k', 'nt': [36, 5991], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-3, 0]], [[8, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-4, 0]], [[5, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 34711813
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 50, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.12l', 'nt': [36, 5998], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-3, 0]], [[8, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-4, 0]], [[5, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 34711814
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 51, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.12m', 'nt': [36, 6028], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711815
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 52, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.12n', 'nt': [36, 6028], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711816
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 53, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.12o', 'nt': [36, 6029], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711817
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 54, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.12p', 'nt': [36, 6029], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711818
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 55, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.12q', 'nt': [36, 11984], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[-2, 0]], [[2, 0]], [[8, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711819
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 56, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.12r', 'nt': [36, 11984], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[-2, 0]], [[2, 0]], [[8, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711820
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 57, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.12s', 'nt': [36, 11998], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[2, 0]], [[2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711821
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 58, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.12t', 'nt': [36, 11999], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[2, 0]], [[2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711822
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 59, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.12u1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[2, 0]], [[2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711824
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 60, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.12u2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[2, 0]], [[2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711825
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 61, 'cyclotomic_n': 12, 'dim': 12, 'faithful': True, 'field': [-3, 0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.12v1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[-2, 0]], [[2, 0]], [[8, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]]]}
  • id: 34711826
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 62, 'cyclotomic_n': 12, 'dim': 12, 'faithful': True, 'field': [-3, 0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.12v2', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[-2, 0]], [[2, 0]], [[8, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]]]}
  • id: 34711827
    {'center': None, 'center_index': 1296, 'center_order': 16, 'counter': 63, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '20736.hv.16a', 'nt': [24, 2912], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711828
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 64, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.24a', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[24, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[4, 0]], [[-12, 0]], [[6, 0]], [[4, 0]], [[1, 0]], [[6, 0]], [[-3, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711829
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 65, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24b', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711830
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 66, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24c', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-8, 0]], [[-8, 0]], [[10, 0]], [[8, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711831
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 67, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24d', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-8, 0]], [[-8, 0]], [[10, 0]], [[8, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711832
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 68, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24e', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711833
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 69, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24f', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711835
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 70, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24g', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[8, 0]], [[-8, 0]], [[10, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711836
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 71, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24h', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[8, 0]], [[-8, 0]], [[10, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711837
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 72, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24i', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711838
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 73, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.24j', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[24, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[-6, 0]], [[-8, 0]], [[-2, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711839
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 74, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.24k', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[24, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[4, 0]], [[-12, 0]], [[6, 0]], [[4, 0]], [[1, 0]], [[6, 0]], [[-3, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711840
    {'center': None, 'center_index': 5184, 'center_order': 4, 'counter': 75, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': None, 'image_order': 5184, 'indicator': 1, 'kernel': None, 'kernel_order': 4, 'label': '20736.hv.24l', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[24, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[-6, 0]], [[-8, 0]], [[-2, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711841
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 76, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24m1', 'nt': [96, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[-7, 0], [-12, 1]], [[-2, 0]], [[1, 0]], [[5, 0], [12, 1]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711842
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 77, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24m2', 'nt': [96, 2], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[5, 0], [12, 1]], [[-2, 0]], [[1, 0]], [[-7, 0], [-12, 1]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711843
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 78, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24n1', 'nt': [144, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[-7, 0], [-12, 1]], [[-2, 0]], [[1, 0]], [[5, 0], [12, 1]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711844
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 79, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.24n2', 'nt': [144, 2], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[5, 0], [12, 1]], [[-2, 0]], [[1, 0]], [[-7, 0], [-12, 1]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711846
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 80, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.48a', 'nt': [96, 0], 'q_character': None, 'values': [[[48, 0]], [[-16, 0]], [[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-6, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-8, 0]], [[4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711847
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 81, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.48b', 'nt': [144, 0], 'q_character': None, 'values': [[[48, 0]], [[-16, 0]], [[-16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-8, 0]], [[4, 0]], [[8, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[8, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34711848
    {'center': None, 'center_index': 20736, 'center_order': 1, 'counter': 82, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '20736.hv', 'group_counter': 204, 'group_order': 20736, 'image': None, 'image_isoclass': '20736.hv', 'image_order': 20736, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '20736.hv.48c', 'nt': [144, 0], 'q_character': None, 'values': [[[48, 0]], [[-16, 0]], [[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[-8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-8, 0]], [[8, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 165831686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 20736, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '20736.hv.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': None, 'standard_generators': False, 'stem': False, 'subgroup': '20736.hv', 'subgroup_hash': 8762208741585009387, 'subgroup_order': 20736, 'subgroup_tex': '(S_3\\times D_6^2).S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 10368, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1758954285288529209, 'subgroup_order': 10368, 'subgroup_tex': 'C_3^3.C_2^6.C_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 10368, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10368.ko', 'subgroup_hash': 167106407630815206, 'subgroup_order': 10368, 'subgroup_tex': '(C_2\\times C_6^3):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 10368, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7883340048705160529, 'subgroup_order': 10368, 'subgroup_tex': 'C_3^3.C_2^6.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 165832130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 3456, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 525722683067195112, 'subgroup_order': 6912, 'subgroup_tex': 'C_3^3.C_2^6.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165832241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5184, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.me', 'subgroup_hash': 975037636565507688, 'subgroup_order': 5184, 'subgroup_tex': '(C_2\\times C_6^3).A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 864, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.4.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.iw', 'subgroup_hash': 6727255864635961679, 'subgroup_order': 5184, 'subgroup_tex': '(C_2\\times C_6^3):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 864, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.4.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.br', 'subgroup_hash': 8516518659742523003, 'subgroup_order': 5184, 'subgroup_tex': 'S_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 864, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.4.d1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '5184.lt', 'subgroup_hash': 5374838751090567370, 'subgroup_order': 5184, 'subgroup_tex': 'C_2^2.S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 165831687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 3456, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2446017018021023618, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^6.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165831698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 864, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5778261595966716331, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 864, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2715466972124711132, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2425803580201813803, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8335550775717024997, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 864, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6165631590696015220, 'subgroup_order': 3456, 'subgroup_tex': '(C_6\\times C_3:S_3).C_2^5', 'supersolvable': False, 'sylow': 0}
  • id: 165831753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 864, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3480226012340062552, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2366672597493260842, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2961508002222461711, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 864, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 8889029366698179586, 'subgroup_order': 3456, 'subgroup_tex': 'C_6^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 165831798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 864, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 6841718500386749446, 'subgroup_order': 3456, 'subgroup_tex': 'C_6^3.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165831809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 5115304581320845519, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^2.(C_2^4\\times C_6).C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 3052190559826990109, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1728, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 4495812781084944206, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^6.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165831842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1728, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.6.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 9205376649829030111, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^3.C_2^6.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165831853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8874309035082440433, 'subgroup_order': 2592, 'subgroup_tex': 'C_2^4:\\He_3.C_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 864, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.go', 'subgroup_hash': 929290681673135987, 'subgroup_order': 2592, 'subgroup_tex': '(C_2\\times C_6^3):C_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5019823450070533420, 'subgroup_order': 2592, 'subgroup_tex': 'C_6^2.C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 864, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ch', 'subgroup_hash': 9178653712281623659, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 659196483080109522, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^3:C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.cf', 'subgroup_hash': 2849964587609183046, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 659196483080109522, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^3:C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 864, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8244346645530609879, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times C_6^2).A_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165831942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.cf', 'subgroup_hash': 2849964587609183046, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 216, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8244346645530609879, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times C_6^2).A_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165831964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.cf', 'subgroup_hash': 2849964587609183046, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ce', 'subgroup_hash': 659196483080109522, 'subgroup_order': 2592, 'subgroup_tex': '(C_3\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.9.a1', 'maximal': False, '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': '2304.fm', 'subgroup_hash': 7637583695901725631, 'subgroup_order': 2304, 'subgroup_tex': 'C_6^2.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 1728, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47930', 'subgroup_hash': 47930, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1728.47186', 'subgroup_hash': 47186, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1728.33373', 'subgroup_hash': 33373, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1728.46674', 'subgroup_hash': 46674, 'subgroup_order': 1728, 'subgroup_tex': 'C_3^3:D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 165832042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46610', 'subgroup_hash': 46610, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165832053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47234', 'subgroup_hash': 47234, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.33646', 'subgroup_hash': 33646, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46672', 'subgroup_hash': 46672, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46595', 'subgroup_hash': 46595, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165832097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47412', 'subgroup_hash': 47412, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.38805', 'subgroup_hash': 38805, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23039', 'subgroup_hash': 23039, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47073', 'subgroup_hash': 47073, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165832142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.32654', 'subgroup_hash': 32654, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2.(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 165832153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.38805', 'subgroup_hash': 38805, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47120', 'subgroup_hash': 47120, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.38801', 'subgroup_hash': 38801, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47189', 'subgroup_hash': 47189, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.32920', 'subgroup_hash': 32920, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.33339', 'subgroup_hash': 33339, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.38801', 'subgroup_hash': 38801, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.32920', 'subgroup_hash': 32920, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23037', 'subgroup_hash': 23037, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.33337', 'subgroup_hash': 33337, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23040', 'subgroup_hash': 23040, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.20990', 'subgroup_hash': 20990, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.21110', 'subgroup_hash': 21110, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.20913', 'subgroup_hash': 20913, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165832308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.20911', 'subgroup_hash': 20911, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165832319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47186', 'subgroup_hash': 47186, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47234', 'subgroup_hash': 47234, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.33373', 'subgroup_hash': 33373, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.33646', 'subgroup_hash': 33646, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47410', 'subgroup_hash': 47410, 'subgroup_order': 1728, 'subgroup_tex': 'D_6:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47186', 'subgroup_hash': 47186, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47234', 'subgroup_hash': 47234, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.38706', 'subgroup_hash': 38706, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.33373', 'subgroup_hash': 33373, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.33646', 'subgroup_hash': 33646, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23049', 'subgroup_hash': 23049, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.23052', 'subgroup_hash': 23052, 'subgroup_order': 1728, 'subgroup_tex': 'C_2^3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.44164', 'subgroup_hash': 44164, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.41187', 'subgroup_hash': 41187, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.41187', 'subgroup_hash': 41187, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.44869', 'subgroup_hash': 44869, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.39381', 'subgroup_hash': 39381, 'subgroup_order': 1728, 'subgroup_tex': '(C_2\\times C_6^3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.39507', 'subgroup_hash': 39507, 'subgroup_order': 1728, 'subgroup_tex': '(C_2\\times C_6^3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.24805', 'subgroup_hash': 24805, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 864, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.27525', 'subgroup_hash': 27525, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.12469', 'subgroup_hash': 12469, 'subgroup_order': 1728, 'subgroup_tex': '(C_2^2\\times C_6^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.46612', 'subgroup_hash': 46612, 'subgroup_order': 1728, 'subgroup_tex': '(S_3\\times C_6^2):D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.46614', 'subgroup_hash': 46614, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 864, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.46671', 'subgroup_hash': 46671, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.46604', 'subgroup_hash': 46604, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165832597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.31632', 'subgroup_hash': 31632, 'subgroup_order': 1728, 'subgroup_tex': '(S_3\\times D_6):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.31632', 'subgroup_hash': 31632, 'subgroup_order': 1728, 'subgroup_tex': '(S_3\\times D_6):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.31633', 'subgroup_hash': 31633, 'subgroup_order': 1728, 'subgroup_tex': '(S_3\\times D_6):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 864, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.12.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1728.31633', 'subgroup_hash': 31633, 'subgroup_order': 1728, 'subgroup_tex': '(S_3\\times D_6):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.1900', 'subgroup_hash': 1900, 'subgroup_order': 1296, 'subgroup_tex': '(C_2\\times C_6^3):C_3', 'supersolvable': False, 'sylow': 0}
  • id: 165832612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3544', 'subgroup_hash': 3544, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times C_6^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 432, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3544', 'subgroup_hash': 3544, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times C_6^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 216, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.1790', 'subgroup_hash': 1790, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3544', 'subgroup_hash': 3544, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times C_6^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3544', 'subgroup_hash': 3544, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times C_6^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3544', 'subgroup_hash': 3544, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times C_6^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3544', 'subgroup_hash': 3544, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times C_6^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3544', 'subgroup_hash': 3544, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times C_6^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3490', 'subgroup_hash': 3490, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 165831694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1152.99278', 'subgroup_hash': 2368459875340991891, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1152.21963', 'subgroup_hash': 7981665237764246853, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165831696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1152.26828', 'subgroup_hash': 7140287825457423678, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1152.26828', 'subgroup_hash': 7140287825457423678, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1152.138373', 'subgroup_hash': 2700593171953895555, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 165831700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1152.18620', 'subgroup_hash': 5271839691138937371, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1152.22265', 'subgroup_hash': 2348707964752874473, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1152.22265', 'subgroup_hash': 2348707964752874473, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1152.99264', 'subgroup_hash': 1594526254796960368, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1152.99265', 'subgroup_hash': 4963667966820280558, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1152.21946', 'subgroup_hash': 3171567106034984609, 'subgroup_order': 1152, 'subgroup_tex': 'C_6^2.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165831706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1152.26827', 'subgroup_hash': 9130782718890453194, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1152.26827', 'subgroup_hash': 9130782718890453194, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1152.134261', 'subgroup_hash': 7928613971095736285, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1152.90180', 'subgroup_hash': 8731392349183348047, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.18.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1152.90180', 'subgroup_hash': 8731392349183348047, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3961', 'subgroup_hash': 3961, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4704', 'subgroup_hash': 4704, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2919', 'subgroup_hash': 2919, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831715
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4719', 'subgroup_hash': 4719, 'subgroup_order': 864, 'subgroup_tex': 'C_6:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4524', 'subgroup_hash': 4524, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 165831717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3266', 'subgroup_hash': 3266, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4488', 'subgroup_hash': 4488, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4719', 'subgroup_hash': 4719, 'subgroup_order': 864, 'subgroup_tex': 'C_6:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3273', 'subgroup_hash': 3273, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4407', 'subgroup_hash': 4407, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4375', 'subgroup_hash': 4375, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4240', 'subgroup_hash': 4240, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 165831725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4264', 'subgroup_hash': 4264, 'subgroup_order': 864, 'subgroup_tex': 'C_3\\times C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4286', 'subgroup_hash': 4286, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6).D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4407', 'subgroup_hash': 4407, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4701', 'subgroup_hash': 4701, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4312', 'subgroup_hash': 4312, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4312', 'subgroup_hash': 4312, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4407', 'subgroup_hash': 4407, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4701', 'subgroup_hash': 4701, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4312', 'subgroup_hash': 4312, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4312', 'subgroup_hash': 4312, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4383', 'subgroup_hash': 4383, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2738', 'subgroup_hash': 2738, 'subgroup_order': 864, 'subgroup_tex': '(C_6\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4719', 'subgroup_hash': 4719, 'subgroup_order': 864, 'subgroup_tex': 'C_6:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4599', 'subgroup_hash': 4599, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4475', 'subgroup_hash': 4475, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3690', 'subgroup_hash': 3690, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4719', 'subgroup_hash': 4719, 'subgroup_order': 864, 'subgroup_tex': 'C_6:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3694', 'subgroup_hash': 3694, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4405', 'subgroup_hash': 4405, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 165831749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4377', 'subgroup_hash': 4377, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4241', 'subgroup_hash': 4241, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 165831751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4263', 'subgroup_hash': 4263, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4299', 'subgroup_hash': 4299, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times C_6^2):D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4255', 'subgroup_hash': 4255, 'subgroup_order': 864, 'subgroup_tex': 'C_3\\times C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4407', 'subgroup_hash': 4407, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4700', 'subgroup_hash': 4700, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 165831757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4283', 'subgroup_hash': 4283, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times C_6^2).D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4283', 'subgroup_hash': 4283, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times C_6^2).D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4407', 'subgroup_hash': 4407, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4700', 'subgroup_hash': 4700, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 165831761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4283', 'subgroup_hash': 4283, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times C_6^2).D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4283', 'subgroup_hash': 4283, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times C_6^2).D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4385', 'subgroup_hash': 4385, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2712', 'subgroup_hash': 2712, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4080', 'subgroup_hash': 4080, 'subgroup_order': 864, 'subgroup_tex': 'S_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4082', 'subgroup_hash': 4082, 'subgroup_order': 864, 'subgroup_tex': 'D_6:\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165831770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4083', 'subgroup_hash': 4083, 'subgroup_order': 864, 'subgroup_tex': 'D_6:\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165831771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4089', 'subgroup_hash': 4089, 'subgroup_order': 864, 'subgroup_tex': 'D_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165831772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4091', 'subgroup_hash': 4091, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6).D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4084', 'subgroup_hash': 4084, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times S_3^2):D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4085', 'subgroup_hash': 4085, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6).D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4090', 'subgroup_hash': 4090, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6).D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4686', 'subgroup_hash': 4686, 'subgroup_order': 864, 'subgroup_tex': 'S_3^3:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4079', 'subgroup_hash': 4079, 'subgroup_order': 864, 'subgroup_tex': 'D_6:\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165831779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4080', 'subgroup_hash': 4080, 'subgroup_order': 864, 'subgroup_tex': 'S_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4074', 'subgroup_hash': 4074, 'subgroup_order': 864, 'subgroup_tex': 'S_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4085', 'subgroup_hash': 4085, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6).D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4077', 'subgroup_hash': 4077, 'subgroup_order': 864, 'subgroup_tex': 'S_3^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 165831783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4078', 'subgroup_hash': 4078, 'subgroup_order': 864, 'subgroup_tex': 'C_3^3:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165831784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4087', 'subgroup_hash': 4087, 'subgroup_order': 864, 'subgroup_tex': 'C_3:S_3^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 165831785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4576', 'subgroup_hash': 4576, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4576', 'subgroup_hash': 4576, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4524', 'subgroup_hash': 4524, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 165831789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4524', 'subgroup_hash': 4524, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 165831790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4524', 'subgroup_hash': 4524, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 165831791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4719', 'subgroup_hash': 4719, 'subgroup_order': 864, 'subgroup_tex': 'C_6:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4599', 'subgroup_hash': 4599, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3266', 'subgroup_hash': 3266, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3587', 'subgroup_hash': 3587, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3266', 'subgroup_hash': 3266, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4475', 'subgroup_hash': 4475, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3690', 'subgroup_hash': 3690, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4475', 'subgroup_hash': 4475, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4488', 'subgroup_hash': 4488, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4488', 'subgroup_hash': 4488, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 432, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4719', 'subgroup_hash': 4719, 'subgroup_order': 864, 'subgroup_tex': 'C_6:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3587', 'subgroup_hash': 3587, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3266', 'subgroup_hash': 3266, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 432, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4719', 'subgroup_hash': 4719, 'subgroup_order': 864, 'subgroup_tex': 'C_6:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3273', 'subgroup_hash': 3273, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3601', 'subgroup_hash': 3601, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3273', 'subgroup_hash': 3273, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4525', 'subgroup_hash': 4525, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3273', 'subgroup_hash': 3273, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3601', 'subgroup_hash': 3601, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.1963', 'subgroup_hash': 1963, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3603', 'subgroup_hash': 3603, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3273', 'subgroup_hash': 3273, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4578', 'subgroup_hash': 4578, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.1963', 'subgroup_hash': 1963, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2029', 'subgroup_hash': 2029, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3603', 'subgroup_hash': 3603, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3694', 'subgroup_hash': 3694, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2031', 'subgroup_hash': 2031, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.1964', 'subgroup_hash': 1964, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2030', 'subgroup_hash': 2030, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4723', 'subgroup_hash': 4723, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3789', 'subgroup_hash': 3789, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3789', 'subgroup_hash': 3789, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4022', 'subgroup_hash': 4022, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.736', 'subgroup_hash': 736, 'subgroup_order': 864, 'subgroup_tex': '(C_2^2\\times C_6^2):C_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.3875', 'subgroup_hash': 3875, 'subgroup_order': 864, 'subgroup_tex': 'C_6^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4019', 'subgroup_hash': 4019, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4017', 'subgroup_hash': 4017, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4391', 'subgroup_hash': 4391, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4406', 'subgroup_hash': 4406, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4391', 'subgroup_hash': 4391, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4239', 'subgroup_hash': 4239, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 165831839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4389', 'subgroup_hash': 4389, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 165831840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4263', 'subgroup_hash': 4263, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4389', 'subgroup_hash': 4389, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 165831843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4298', 'subgroup_hash': 4298, 'subgroup_order': 864, 'subgroup_tex': 'D_6^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 165831844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2872', 'subgroup_hash': 2872, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.2872', 'subgroup_hash': 2872, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4374', 'subgroup_hash': 4374, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4255', 'subgroup_hash': 4255, 'subgroup_order': 864, 'subgroup_tex': 'C_3\\times C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2872', 'subgroup_hash': 2872, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4284', 'subgroup_hash': 4284, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times C_6^2).D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4228', 'subgroup_hash': 4228, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 165831854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831856
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4379', 'subgroup_hash': 4379, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4382', 'subgroup_hash': 4382, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2918', 'subgroup_hash': 2918, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2918', 'subgroup_hash': 2918, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2694', 'subgroup_hash': 2694, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2918', 'subgroup_hash': 2918, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2918', 'subgroup_hash': 2918, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4387', 'subgroup_hash': 4387, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2712', 'subgroup_hash': 2712, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2712', 'subgroup_hash': 2712, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2919', 'subgroup_hash': 2919, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2695', 'subgroup_hash': 2695, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 165831871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2737', 'subgroup_hash': 2737, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times C_6^2).D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2737', 'subgroup_hash': 2737, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times C_6^2).D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 432, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.2919', 'subgroup_hash': 2919, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4321', 'subgroup_hash': 4321, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165831883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.24.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4297', 'subgroup_hash': 4297, 'subgroup_order': 864, 'subgroup_tex': '(S_3\\times D_6):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.27.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090070', 'subgroup_hash': 1090070, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.201144', 'subgroup_hash': 201144, 'subgroup_order': 768, 'subgroup_tex': '(C_2^2\\times D_{12}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.266', 'subgroup_hash': 266, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 216, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.294', 'subgroup_hash': 294, 'subgroup_order': 648, 'subgroup_tex': '(C_3\\times C_6^2):C_6', 'supersolvable': False, 'sylow': 0}
  • id: 165831890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.281', 'subgroup_hash': 281, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.281', 'subgroup_hash': 281, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.266', 'subgroup_hash': 266, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.705', 'subgroup_hash': 705, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 165831894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.704', 'subgroup_hash': 704, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.703', 'subgroup_hash': 703, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.705', 'subgroup_hash': 705, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 165831898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.703', 'subgroup_hash': 703, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.32.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.704', 'subgroup_hash': 704, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '576.8418', 'subgroup_hash': 8418, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '576.5394', 'subgroup_hash': 5394, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '576.8399', 'subgroup_hash': 8399, 'subgroup_order': 576, 'subgroup_tex': 'C_3^2:D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '576.8400', 'subgroup_hash': 8400, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '576.8418', 'subgroup_hash': 8418, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '576.5394', 'subgroup_hash': 5394, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '576.8399', 'subgroup_hash': 8399, 'subgroup_order': 576, 'subgroup_tex': 'C_3^2:D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '576.8400', 'subgroup_hash': 8400, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8556', 'subgroup_hash': 8556, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.6139', 'subgroup_hash': 6139, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.2285', 'subgroup_hash': 2285, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.6139', 'subgroup_hash': 6139, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.6139', 'subgroup_hash': 6139, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7159', 'subgroup_hash': 7159, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7159', 'subgroup_hash': 7159, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7159', 'subgroup_hash': 7159, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.3408', 'subgroup_hash': 3408, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times D_{12}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.2285', 'subgroup_hash': 2285, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7160', 'subgroup_hash': 7160, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8557', 'subgroup_hash': 8557, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.3409', 'subgroup_hash': 3409, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times D_4).D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165831924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8524', 'subgroup_hash': 8524, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.(C_2^2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165831925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5699', 'subgroup_hash': 5699, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.(C_2^2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 165831926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7160', 'subgroup_hash': 7160, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.6140', 'subgroup_hash': 6140, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8420', 'subgroup_hash': 8420, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8420', 'subgroup_hash': 8420, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5372', 'subgroup_hash': 5372, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5372', 'subgroup_hash': 5372, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.6140', 'subgroup_hash': 6140, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5372', 'subgroup_hash': 5372, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.2286', 'subgroup_hash': 2286, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5372', 'subgroup_hash': 5372, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.2286', 'subgroup_hash': 2286, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.1959', 'subgroup_hash': 1959, 'subgroup_order': 576, 'subgroup_tex': 'C_2^3.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165831939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.1959', 'subgroup_hash': 1959, 'subgroup_order': 576, 'subgroup_tex': 'C_2^3.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165831940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.2037', 'subgroup_hash': 2037, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.2037', 'subgroup_hash': 2037, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8418', 'subgroup_hash': 8418, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8418', 'subgroup_hash': 8418, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5394', 'subgroup_hash': 5394, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5394', 'subgroup_hash': 5394, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8553', 'subgroup_hash': 8553, 'subgroup_order': 576, 'subgroup_tex': 'C_4:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8553', 'subgroup_hash': 8553, 'subgroup_order': 576, 'subgroup_tex': 'C_4:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.6134', 'subgroup_hash': 6134, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8418', 'subgroup_hash': 8418, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8418', 'subgroup_hash': 8418, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.6134', 'subgroup_hash': 6134, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5394', 'subgroup_hash': 5394, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5394', 'subgroup_hash': 5394, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.3413', 'subgroup_hash': 3413, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times C_{12}):D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.3412', 'subgroup_hash': 3412, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times C_{12}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.2289', 'subgroup_hash': 2289, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times D_6):D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.3414', 'subgroup_hash': 3414, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times C_{12}):D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.2289', 'subgroup_hash': 2289, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times D_6):D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.2292', 'subgroup_hash': 2292, 'subgroup_order': 576, 'subgroup_tex': '(C_2\\times D_6):D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165831962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7405', 'subgroup_hash': 7405, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7405', 'subgroup_hash': 7405, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7567', 'subgroup_hash': 7567, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 165831966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7567', 'subgroup_hash': 7567, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 165831967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7405', 'subgroup_hash': 7405, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7941', 'subgroup_hash': 7941, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 165831969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7409', 'subgroup_hash': 7409, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7409', 'subgroup_hash': 7409, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.7409', 'subgroup_hash': 7409, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5729', 'subgroup_hash': 5729, 'subgroup_order': 576, 'subgroup_tex': '(C_2^2\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5729', 'subgroup_hash': 5729, 'subgroup_order': 576, 'subgroup_tex': '(C_2^2\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165831974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8675', 'subgroup_hash': 8675, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.4011', 'subgroup_hash': 4011, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165831977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.4011', 'subgroup_hash': 4011, 'subgroup_order': 576, 'subgroup_tex': 'C_3\\times C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165831978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.3607', 'subgroup_hash': 3607, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.4613', 'subgroup_hash': 4613, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times C_{12}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165831980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5126', 'subgroup_hash': 5126, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.3607', 'subgroup_hash': 3607, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.3607', 'subgroup_hash': 3607, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.3607', 'subgroup_hash': 3607, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8420', 'subgroup_hash': 8420, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8394', 'subgroup_hash': 8394, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8418', 'subgroup_hash': 8418, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.8392', 'subgroup_hash': 8392, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5399', 'subgroup_hash': 5399, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5399', 'subgroup_hash': 5399, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5296', 'subgroup_hash': 5296, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.36.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.5296', 'subgroup_hash': 5296, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 165831993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 432, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.775', 'subgroup_hash': 775, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_6^3', 'supersolvable': True, 'sylow': 0}
  • id: 165831994
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 432, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 432, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831998
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165831999
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832002
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832005
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832006
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.709', 'subgroup_hash': 709, 'subgroup_order': 432, 'subgroup_tex': 'D_6:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.479', 'subgroup_hash': 479, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.765', 'subgroup_hash': 765, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.692', 'subgroup_hash': 692, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.692', 'subgroup_hash': 692, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.765', 'subgroup_hash': 765, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.641', 'subgroup_hash': 641, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832026
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832027
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.653', 'subgroup_hash': 653, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.694', 'subgroup_hash': 694, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.461', 'subgroup_hash': 461, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.641', 'subgroup_hash': 641, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.675', 'subgroup_hash': 675, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.694', 'subgroup_hash': 694, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.461', 'subgroup_hash': 461, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.719', 'subgroup_hash': 719, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.495', 'subgroup_hash': 495, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832050
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.767', 'subgroup_hash': 767, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.696', 'subgroup_hash': 696, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.654', 'subgroup_hash': 654, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.654', 'subgroup_hash': 654, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.634', 'subgroup_hash': 634, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.766', 'subgroup_hash': 766, 'subgroup_order': 432, 'subgroup_tex': 'C_2^2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.766', 'subgroup_hash': 766, 'subgroup_order': 432, 'subgroup_tex': 'C_2^2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.658', 'subgroup_hash': 658, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.652', 'subgroup_hash': 652, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.656', 'subgroup_hash': 656, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.696', 'subgroup_hash': 696, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.427', 'subgroup_hash': 427, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.634', 'subgroup_hash': 634, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.656', 'subgroup_hash': 656, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.684', 'subgroup_hash': 684, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.427', 'subgroup_hash': 427, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.678', 'subgroup_hash': 678, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.602', 'subgroup_hash': 602, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.602', 'subgroup_hash': 602, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.600', 'subgroup_hash': 600, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.600', 'subgroup_hash': 600, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.599', 'subgroup_hash': 599, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.602', 'subgroup_hash': 602, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.602', 'subgroup_hash': 602, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.595', 'subgroup_hash': 595, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.568', 'subgroup_hash': 568, 'subgroup_order': 432, 'subgroup_tex': '(C_3^2\\times D_6):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.di2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.di2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.754', 'subgroup_hash': 754, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.600', 'subgroup_hash': 600, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.574', 'subgroup_hash': 574, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.580', 'subgroup_hash': 580, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.596', 'subgroup_hash': 596, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.600', 'subgroup_hash': 600, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.594', 'subgroup_hash': 594, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.574', 'subgroup_hash': 574, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.596', 'subgroup_hash': 596, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.604', 'subgroup_hash': 604, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.567', 'subgroup_hash': 567, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 165832111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ea2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ea2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.569', 'subgroup_hash': 569, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_{12}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.575', 'subgroup_hash': 575, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.581', 'subgroup_hash': 581, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.596', 'subgroup_hash': 596, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.600', 'subgroup_hash': 600, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.608', 'subgroup_hash': 608, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.597', 'subgroup_hash': 597, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.607', 'subgroup_hash': 607, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.598', 'subgroup_hash': 598, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.el2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.en2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.601', 'subgroup_hash': 601, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.602', 'subgroup_hash': 602, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.600', 'subgroup_hash': 600, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.602', 'subgroup_hash': 602, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.609', 'subgroup_hash': 609, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.598', 'subgroup_hash': 598, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.612', 'subgroup_hash': 612, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.611', 'subgroup_hash': 611, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ey2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.607', 'subgroup_hash': 607, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832146
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.709', 'subgroup_hash': 709, 'subgroup_order': 432, 'subgroup_tex': 'D_6:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.709', 'subgroup_hash': 709, 'subgroup_order': 432, 'subgroup_tex': 'D_6:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.709', 'subgroup_hash': 709, 'subgroup_order': 432, 'subgroup_tex': 'D_6:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.773', 'subgroup_hash': 773, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.729', 'subgroup_hash': 729, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.719', 'subgroup_hash': 719, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.479', 'subgroup_hash': 479, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.479', 'subgroup_hash': 479, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.479', 'subgroup_hash': 479, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.511', 'subgroup_hash': 511, 'subgroup_order': 432, 'subgroup_tex': 'C_6^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.495', 'subgroup_hash': 495, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.555', 'subgroup_hash': 555, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.554', 'subgroup_hash': 554, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.768', 'subgroup_hash': 768, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.767', 'subgroup_hash': 767, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832168
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.696', 'subgroup_hash': 696, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.654', 'subgroup_hash': 654, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.677', 'subgroup_hash': 677, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832172
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.677', 'subgroup_hash': 677, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.654', 'subgroup_hash': 654, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.634', 'subgroup_hash': 634, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.641', 'subgroup_hash': 641, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.656', 'subgroup_hash': 656, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.680', 'subgroup_hash': 680, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.658', 'subgroup_hash': 658, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.656', 'subgroup_hash': 656, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.656', 'subgroup_hash': 656, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.680', 'subgroup_hash': 680, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.682', 'subgroup_hash': 682, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.696', 'subgroup_hash': 696, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.427', 'subgroup_hash': 427, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.450', 'subgroup_hash': 450, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.427', 'subgroup_hash': 427, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.634', 'subgroup_hash': 634, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.641', 'subgroup_hash': 641, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 216, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.652', 'subgroup_hash': 652, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.676', 'subgroup_hash': 676, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.523', 'subgroup_hash': 523, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.682', 'subgroup_hash': 682, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.427', 'subgroup_hash': 427, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.450', 'subgroup_hash': 450, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.450', 'subgroup_hash': 450, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.427', 'subgroup_hash': 427, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.696', 'subgroup_hash': 696, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.634', 'subgroup_hash': 634, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832207
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832211
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832212
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.641', 'subgroup_hash': 641, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832227
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832228
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.696', 'subgroup_hash': 696, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.634', 'subgroup_hash': 634, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 165832234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 165832246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.659', 'subgroup_hash': 659, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.641', 'subgroup_hash': 641, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 27, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.769', 'subgroup_hash': 769, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.48.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '384.4427', 'subgroup_hash': 4427, 'subgroup_order': 384, 'subgroup_tex': '(C_2^2\\times C_{12}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '384.2613', 'subgroup_hash': 2613, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '384.11260', 'subgroup_hash': 11260, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '384.1538', 'subgroup_hash': 1538, 'subgroup_order': 384, 'subgroup_tex': '(C_2^2\\times C_4):D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '384.18884', 'subgroup_hash': 18884, 'subgroup_order': 384, 'subgroup_tex': 'C_2^3:(S_3\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 165832261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '384.2611', 'subgroup_hash': 2611, 'subgroup_order': 384, 'subgroup_tex': '(C_2^2\\times D_{12}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '384.2612', 'subgroup_hash': 2612, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 165832263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '384.1546', 'subgroup_hash': 1546, 'subgroup_order': 384, 'subgroup_tex': '(C_2^2\\times D_{12}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5312', 'subgroup_hash': 5312, 'subgroup_order': 384, 'subgroup_tex': 'C_3\\times C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.4247', 'subgroup_hash': 4247, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.15179', 'subgroup_hash': 15179, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.2075', 'subgroup_hash': 2075, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.12882', 'subgroup_hash': 12882, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr C_2^2\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 165832270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.18221', 'subgroup_hash': 18221, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.18491', 'subgroup_hash': 18491, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.15188', 'subgroup_hash': 15188, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.54.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.6437', 'subgroup_hash': 6437, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 108, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.60', 'subgroup_hash': 60, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.60', 'subgroup_hash': 60, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.60', 'subgroup_hash': 60, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.64.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.64.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.64.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.39', 'subgroup_hash': 39, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.64.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '288.651', 'subgroup_hash': 651, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '288.941', 'subgroup_hash': 941, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.708', 'subgroup_hash': 708, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.653', 'subgroup_hash': 653, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.959', 'subgroup_hash': 959, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.960', 'subgroup_hash': 960, 'subgroup_order': 288, 'subgroup_tex': 'D_4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.890', 'subgroup_hash': 890, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.881', 'subgroup_hash': 881, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1031', 'subgroup_hash': 1031, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1031', 'subgroup_hash': 1031, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.961', 'subgroup_hash': 961, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.386', 'subgroup_hash': 386, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.616', 'subgroup_hash': 616, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.941', 'subgroup_hash': 941, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.624', 'subgroup_hash': 624, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.953', 'subgroup_hash': 953, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.960', 'subgroup_hash': 960, 'subgroup_order': 288, 'subgroup_tex': 'D_4:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.890', 'subgroup_hash': 890, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.881', 'subgroup_hash': 881, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1031', 'subgroup_hash': 1031, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1031', 'subgroup_hash': 1031, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.955', 'subgroup_hash': 955, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.386', 'subgroup_hash': 386, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.890', 'subgroup_hash': 890, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.890', 'subgroup_hash': 890, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.881', 'subgroup_hash': 881, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.879', 'subgroup_hash': 879, 'subgroup_order': 288, 'subgroup_tex': 'C_4:\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.878', 'subgroup_hash': 878, 'subgroup_order': 288, 'subgroup_tex': 'S_3^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.878', 'subgroup_hash': 878, 'subgroup_order': 288, 'subgroup_tex': 'S_3^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.869', 'subgroup_hash': 869, 'subgroup_order': 288, 'subgroup_tex': 'C_4.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1031', 'subgroup_hash': 1031, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.878', 'subgroup_hash': 878, 'subgroup_order': 288, 'subgroup_tex': 'S_3^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 165832383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.868', 'subgroup_hash': 868, 'subgroup_order': 288, 'subgroup_tex': 'S_3^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 165832384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832394
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.616', 'subgroup_hash': 616, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.651', 'subgroup_hash': 651, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.616', 'subgroup_hash': 616, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.651', 'subgroup_hash': 651, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.616', 'subgroup_hash': 616, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.616', 'subgroup_hash': 616, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.651', 'subgroup_hash': 651, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.616', 'subgroup_hash': 616, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.616', 'subgroup_hash': 616, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.651', 'subgroup_hash': 651, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.737', 'subgroup_hash': 737, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.941', 'subgroup_hash': 941, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.941', 'subgroup_hash': 941, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.941', 'subgroup_hash': 941, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.941', 'subgroup_hash': 941, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832426
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.737', 'subgroup_hash': 737, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.708', 'subgroup_hash': 708, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.708', 'subgroup_hash': 708, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.794', 'subgroup_hash': 794, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.994', 'subgroup_hash': 994, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.708', 'subgroup_hash': 708, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.794', 'subgroup_hash': 794, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.268', 'subgroup_hash': 268, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.624', 'subgroup_hash': 624, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.653', 'subgroup_hash': 653, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.624', 'subgroup_hash': 624, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.624', 'subgroup_hash': 624, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.653', 'subgroup_hash': 653, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.994', 'subgroup_hash': 994, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.624', 'subgroup_hash': 624, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.653', 'subgroup_hash': 653, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.624', 'subgroup_hash': 624, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.739', 'subgroup_hash': 739, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.708', 'subgroup_hash': 708, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1009', 'subgroup_hash': 1009, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.268', 'subgroup_hash': 268, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.309', 'subgroup_hash': 309, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.653', 'subgroup_hash': 653, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.624', 'subgroup_hash': 624, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.739', 'subgroup_hash': 739, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.281', 'subgroup_hash': 281, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.229', 'subgroup_hash': 229, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.229', 'subgroup_hash': 229, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.229', 'subgroup_hash': 229, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.240', 'subgroup_hash': 240, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.228', 'subgroup_hash': 228, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.229', 'subgroup_hash': 229, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.281', 'subgroup_hash': 281, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1043', 'subgroup_hash': 1043, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832496
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1043', 'subgroup_hash': 1043, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832498
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1044', 'subgroup_hash': 1044, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 165832499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.817', 'subgroup_hash': 817, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.817', 'subgroup_hash': 817, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.411', 'subgroup_hash': 411, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hs1', 'outer_equivalence': True, 'perfect': False, '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': '288.810', 'subgroup_hash': 810, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ht1', 'outer_equivalence': True, 'perfect': False, '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': '288.810', 'subgroup_hash': 810, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hu1', 'outer_equivalence': True, 'perfect': False, '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': '288.810', 'subgroup_hash': 810, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hv1', 'outer_equivalence': True, 'perfect': False, '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': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hw1', 'outer_equivalence': True, 'perfect': False, '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': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hx1', 'outer_equivalence': True, 'perfect': False, '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': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hy1', 'outer_equivalence': True, 'perfect': False, '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': '288.810', 'subgroup_hash': 810, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 165832516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hz1', 'outer_equivalence': True, 'perfect': False, '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': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ia1', 'outer_equivalence': True, 'perfect': False, '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': '288.836', 'subgroup_hash': 836, 'subgroup_order': 288, 'subgroup_tex': 'C_2^4:D_9', 'supersolvable': False, 'sylow': 0}
  • id: 165832518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ib1', 'outer_equivalence': True, 'perfect': False, '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': '288.951', 'subgroup_hash': 951, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ic1', 'outer_equivalence': True, 'perfect': False, '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': '288.951', 'subgroup_hash': 951, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.id1', 'outer_equivalence': True, 'perfect': False, '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': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ie1', 'outer_equivalence': True, 'perfect': False, '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': '288.951', 'subgroup_hash': 951, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.if1', 'outer_equivalence': True, 'perfect': False, '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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ig1', 'outer_equivalence': True, 'perfect': False, '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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ih1', 'outer_equivalence': True, 'perfect': False, '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': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ii1', 'outer_equivalence': True, 'perfect': False, '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': '288.568', 'subgroup_hash': 568, 'subgroup_order': 288, 'subgroup_tex': 'D_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ij1', 'outer_equivalence': True, 'perfect': False, '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': '288.568', 'subgroup_hash': 568, 'subgroup_order': 288, 'subgroup_tex': 'D_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ik1', 'outer_equivalence': True, 'perfect': False, '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': '288.568', 'subgroup_hash': 568, 'subgroup_order': 288, 'subgroup_tex': 'D_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.il1', 'outer_equivalence': True, 'perfect': False, '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': '288.568', 'subgroup_hash': 568, 'subgroup_order': 288, 'subgroup_tex': 'D_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.im1', 'outer_equivalence': True, 'perfect': False, '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': '288.959', 'subgroup_hash': 959, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.in1', 'outer_equivalence': True, 'perfect': False, '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': '288.568', 'subgroup_hash': 568, 'subgroup_order': 288, 'subgroup_tex': 'D_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.io1', 'outer_equivalence': True, 'perfect': False, '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': '288.568', 'subgroup_hash': 568, 'subgroup_order': 288, 'subgroup_tex': 'D_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ip1', 'outer_equivalence': True, 'perfect': False, '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': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iq1', 'outer_equivalence': True, 'perfect': False, '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': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ir1', 'outer_equivalence': True, 'perfect': False, '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': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.is1', 'outer_equivalence': True, 'perfect': False, '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': '288.941', 'subgroup_hash': 941, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.it1', 'outer_equivalence': True, 'perfect': False, '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': '288.952', 'subgroup_hash': 952, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iu1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iv1', 'outer_equivalence': True, 'perfect': False, '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': '288.952', 'subgroup_hash': 952, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iw1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ix1', 'outer_equivalence': True, 'perfect': False, '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': '288.569', 'subgroup_hash': 569, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iy1', 'outer_equivalence': True, 'perfect': False, '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': '288.569', 'subgroup_hash': 569, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iz1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ja1', 'outer_equivalence': True, 'perfect': False, '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': '288.954', 'subgroup_hash': 954, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jb1', 'outer_equivalence': True, 'perfect': False, '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': '288.881', 'subgroup_hash': 881, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jc1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jd1', 'outer_equivalence': True, 'perfect': False, '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': '288.569', 'subgroup_hash': 569, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.je1', 'outer_equivalence': True, 'perfect': False, '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': '288.881', 'subgroup_hash': 881, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jf1', 'outer_equivalence': True, 'perfect': False, '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': '288.934', 'subgroup_hash': 934, 'subgroup_order': 288, 'subgroup_tex': '(C_6\\times C_{12}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jg1', 'outer_equivalence': True, 'perfect': False, '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': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jh1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ji1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jj1', 'outer_equivalence': True, 'perfect': False, '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': '288.950', 'subgroup_hash': 950, 'subgroup_order': 288, 'subgroup_tex': 'C_2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jk1', 'outer_equivalence': True, 'perfect': False, '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': '288.950', 'subgroup_hash': 950, 'subgroup_order': 288, 'subgroup_tex': 'C_2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jl1', 'outer_equivalence': True, 'perfect': False, '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': '288.631', 'subgroup_hash': 631, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jm1', 'outer_equivalence': True, 'perfect': False, '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': '288.978', 'subgroup_hash': 978, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jn1', 'outer_equivalence': True, 'perfect': False, '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': '288.631', 'subgroup_hash': 631, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jo1', 'outer_equivalence': True, 'perfect': False, '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': '288.434', 'subgroup_hash': 434, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jp1', 'outer_equivalence': True, 'perfect': False, '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': '288.631', 'subgroup_hash': 631, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jq1', 'outer_equivalence': True, 'perfect': False, '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': '288.631', 'subgroup_hash': 631, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 165832565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jr1', 'outer_equivalence': True, 'perfect': False, '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': '288.961', 'subgroup_hash': 961, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.js1', 'outer_equivalence': True, 'perfect': False, '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': '288.570', 'subgroup_hash': 570, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jt1', 'outer_equivalence': True, 'perfect': False, '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': '288.570', 'subgroup_hash': 570, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ju1', 'outer_equivalence': True, 'perfect': False, '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': '288.570', 'subgroup_hash': 570, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jv1', 'outer_equivalence': True, 'perfect': False, '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': '288.570', 'subgroup_hash': 570, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jw1', 'outer_equivalence': True, 'perfect': False, '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': '288.570', 'subgroup_hash': 570, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jx1', 'outer_equivalence': True, 'perfect': False, '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': '288.570', 'subgroup_hash': 570, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jy1', 'outer_equivalence': True, 'perfect': False, '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': '288.962', 'subgroup_hash': 962, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jz1', 'outer_equivalence': True, 'perfect': False, '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': '288.571', 'subgroup_hash': 571, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ka1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kb1', 'outer_equivalence': True, 'perfect': False, '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': '288.956', 'subgroup_hash': 956, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 165832578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kc1', 'outer_equivalence': True, 'perfect': False, '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': '288.386', 'subgroup_hash': 386, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kd1', 'outer_equivalence': True, 'perfect': False, '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': '288.386', 'subgroup_hash': 386, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ke1', 'outer_equivalence': True, 'perfect': False, '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': '288.571', 'subgroup_hash': 571, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kf1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kg1', 'outer_equivalence': True, 'perfect': False, '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': '288.422', 'subgroup_hash': 422, 'subgroup_order': 288, 'subgroup_tex': '(C_6\\times C_{12}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kh1', 'outer_equivalence': True, 'perfect': False, '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': '288.386', 'subgroup_hash': 386, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ki1', 'outer_equivalence': True, 'perfect': False, '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': '288.386', 'subgroup_hash': 386, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 165832585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kj1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kk1', 'outer_equivalence': True, 'perfect': False, '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': '288.571', 'subgroup_hash': 571, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kl1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.km1', 'outer_equivalence': True, 'perfect': False, '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': '288.571', 'subgroup_hash': 571, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 165832590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kn1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ko1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kp1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kq1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kr1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ks1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.kt1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.72.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ku1', 'outer_equivalence': True, 'perfect': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 165832599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '20736.hv.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 165832600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 216, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.96.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.227', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 227, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 165832601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 108, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.192.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1538', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1538, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 108, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.192.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.955', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 955, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 165832603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '20736.hv.256.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 3}
  • id: 165832604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 27, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.768.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '768.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '768.1090070', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1090070, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5:S_4', 'simple': False, 'solvable': True, 'special_labels': ['D3', 'C6'], '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: 165832605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 16, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.1296.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1296.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1296.3490', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3490, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\wr S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 165832606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3456, 'characteristic': True, 'core_order': 4, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20736.hv.5184.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '5184.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '5184.br', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8516518659742523003, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 5184, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^3:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], '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: 165832607
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20736.hv', 'ambient_counter': 204, 'ambient_order': 20736, 'ambient_tex': '(S_3\\times D_6^2).S_4', 'central': True, 'central_factor': False, 'centralizer_order': 20736, 'characteristic': True, 'core_order': 1, 'counter': 929, 'cyclic': True, 'direct': None, 'hall': 1, 'label': '20736.hv.20736.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20736.a1.N', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '20736.hv', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8762208741585009387, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 20736, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(S_3\\times D_6^2).S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D4', 'C7'], 'split': None, '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: 165831686
    {'ambient': '20736.hv', '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': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '3.a1', '4.b1', '4.c1', '4.d1', '27.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [277, 2951, 228, 5768], 'generators': [25514092800, 26468500904, 1078117201, 16687, 9360177523200, 2628844618652, 4985, 46036847791741, 134983133510400, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.1.a1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '20736.hv', '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': None}
  • id: 165831687
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.k1', '12.o1', '12.q1', '12.u1', '12.bh1', '12.bk1', '12.bp1', '12.bq1', '18.n1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3813, 5031, 5439, 3968], 'generators': [25514092800, 26468500904, 1078117201, 16687, 9360177523200, 4985, 134983133510400, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.6.a1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '24.a1', '24.b1', '24.c1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '20736.hv', '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': '10000.da'}
  • id: 165831688
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.j1'], 'contains': ['48.hd1', '64.a1', '64.i1'], 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': [202, -1, 199, -1], 'generators': [134983133510400, 16687, 26428551121, 112608921600, 46036847791741, 30235, 25514097785, 9360177523200], 'label': '20736.hv.16.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.j1', 'old_label': '16.e1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '200000.p'}
  • id: 165831689
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '8.k1'], 'contains': ['48.ig1', '64.b1', '64.d1', '64.g1', '64.i1'], 'core': '192.B', 'coset_action_label': None, 'count': 16, 'diagramx': [119, -1, 83, -1], 'generators': [134983133510400, 1078138249, 29514, 25514092800, 1078116480, 112608921600, 46036847791741, 9360177523200], 'label': '20736.hv.16.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.k1', 'old_label': '16.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831690
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['48.ih1', '64.b1', '64.e1', '64.f1', '64.i1'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': [149, -1, 151, -1], 'generators': [134983133510400, 26428555385, 1078117201, 112608921600, 46036847791741, 1078140940, 26428567087, 9360177523200], 'label': '20736.hv.16.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1', 'old_label': '16.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '1296.3544'}
  • id: 165831691
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '8.l1'], 'contains': ['48.iu1', '64.c1', '64.d1', '64.e1', '64.i1'], 'core': '192.B', 'coset_action_label': None, 'count': 16, 'diagramx': [280, -1, 700, -1], 'generators': [134983133510400, 26428580635, 721, 4985, 1078133167, 112608921600, 46036847791741, 9360177523200], 'label': '20736.hv.16.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.l1', 'old_label': '16.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '8748.c'}
  • id: 165831692
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['48.iv1', '64.c1', '64.g1', '64.f1', '64.i1'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': [167, -1, 135, -1], 'generators': [134983133510400, 26428551121, 112608921600, 46036847791741, 1078140940, 25514097785, 26428567087, 9360177523200], 'label': '20736.hv.16.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.i1', 'old_label': '16.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '1296.3544'}
  • id: 165831693
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1'], 'contains': ['32.f1', '32.g1', '32.h1', '48.ix1', '64.h1'], 'core': '192.B', 'coset_action_label': None, 'count': 32, 'diagramx': [55, -1, 40, -1], 'generators': [134983133510400, 46036847792341, 26428580635, 25430664104, 1078133167, 112608921600, 2647090220036, 9360177523200], 'label': '20736.hv.16.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '16.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 165831694
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '9.a1'], 'contains': ['36.t1', '36.w1', '36.x1', '36.be1', '36.bg1', '36.bm1', '36.bn1', '36.dc1', '36.dd1', '36.de1', '36.df1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7398, -1, 5986, -1], 'generators': [25514092800, 26468500904, 1078117201, 2647090225052, 30235, 16687, 9360177523200, 1078121465, 112608921600], 'label': '20736.hv.18.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '20736.hv', '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': '1152.43028'}
  • id: 165831695
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '9.a1'], 'contains': ['36.u1', '36.v1', '36.x1', '36.bi1', '36.bj1', '36.bo1', '36.bp1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6087, -1, 6407, -1], 'generators': [25514092800, 26468500904, 1078117201, 30235, 16687, 9360177523200, 2628844618652, 1078121465, 112608921600], 'label': '20736.hv.18.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '20736.hv', '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': '1152.43028'}
  • id: 165831696
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '9.a1'], 'contains': ['36.z1', '36.bc1', '36.bd1', '36.bf1', '36.bk1', '36.bm1', '36.bp1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6646, -1, 6328, -1], 'generators': [16687, 1078121465, 25514092800, 25430664104, 1078117201, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.18.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.c1', 'projective_image': '20736.hv', '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': '1152.43028'}
  • id: 165831697
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '9.a1'], 'contains': ['36.ba1', '36.bb1', '36.bd1', '36.bh1', '36.bl1', '36.bn1', '36.bo1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5640, -1, 6306, -1], 'generators': [16687, 1078121465, 25514092800, 25430664104, 1078117201, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.18.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '20736.hv', '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': '1152.43028'}
  • id: 165831698
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.j1', '12.n1', '12.o1', '12.v1', '12.x1', '12.bd1', '12.be1', '12.cc1', '12.cd1', '12.ce1', '12.cf1', '18.a1', '54.c1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7246, -1, 5958, -1], 'generators': [25514092800, 26468500904, 1078117201, 2647090225052, 30235, 16687, 9360177523200, 134983133510400, 1078121465, 112608921600], 'label': '20736.hv.6.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '10000.ej'}
  • id: 165831699
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '9.a1'], 'contains': ['36.c1', '36.d1', '36.g1', '36.h1', '36.t1', '36.v1', '36.z1', '36.ba1', '36.br1', '36.bt1', '36.bu1', '36.cy1', '36.cz1', '36.da1', '36.db1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [8352, -1, 8448, -1], 'generators': [25514092800, 26468500904, 16687, 9360177523200, 1078116480, 2628844639618, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.18.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.e1', 'projective_image': '20736.hv', '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': '1152.43028'}
  • id: 165831700
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '9.a1'], 'contains': ['36.u1', '36.w1', '36.bb1', '36.bc1', '36.br1', '36.bw1', '36.bx1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5899, -1, 6736, -1], 'generators': [25514092800, 26468500904, 16687, 9360177523200, 2628844618652, 1078116480, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.18.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831701
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '9.a1'], 'contains': ['36.be1', '36.bf1', '36.bj1', '36.bl1', '36.bt1', '36.bv1', '36.bx1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5809, -1, 6541, -1], 'generators': [25514092800, 26468479846, 16687, 9360177523200, 2628844618652, 1078116480, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.18.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831702
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1', '9.a1'], 'contains': ['36.bg1', '36.bh1', '36.bi1', '36.bk1', '36.bu1', '36.bv1', '36.bw1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6786, -1, 6623, -1], 'generators': [25514092800, 26468479846, 16687, 9360177523200, 1078116480, 2628844639618, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.18.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831703
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1'], 'contains': ['36.i1', '36.k1', '36.q1', '36.r1', '36.bz1', '36.ca1', '36.cb1', '36.cc1', '36.ce1', '36.ch1', '36.ci1', '36.cr1', '36.cs1', '36.ct1', '36.cv1', '54.k1', '54.m1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3068, -1, 3011, -1], 'generators': [721, 16687, 4985, 126937858924800, 25514092800, 9683982604800, 133913559601052, 30235, 26468500904], 'label': '20736.hv.18.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '18.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831704
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '9.a1'], 'contains': ['36.t1', '36.u1', '36.bf1', '36.bh1', '36.by1', '36.cd1', '36.cj1', '36.cl1', '36.cm1', '36.cq1', '36.cw1', '54.m1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [4674, -1, 5414, -1], 'generators': [25514092800, 26468500904, 721, 30235, 16687, 9360177523200, 4985, 2628844618652, 112608921600], 'label': '20736.hv.18.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831705
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '9.a1'], 'contains': ['36.v1', '36.w1', '36.bk1', '36.bl1', '36.cj1', '36.cn1', '36.co1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6758, -1, 6666, -1], 'generators': [25514092800, 26468500904, 2647090225052, 721, 30235, 16687, 9360177523200, 4985, 112608921600], 'label': '20736.hv.18.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831706
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1', '9.a1'], 'contains': ['36.z1', '36.bb1', '36.be1', '36.bi1', '36.ck1', '36.cl1', '36.cn1'], 'core': '1296.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5700, -1, 6495, -1], 'generators': [721, 16687, 4985, 25514092800, 25430664104, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.18.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.l1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831707
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1', '9.a1'], 'contains': ['36.ba1', '36.bc1', '36.bg1', '36.bj1', '36.ck1', '36.cm1', '36.co1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6692, -1, 6518, -1], 'generators': [721, 16687, 4985, 25514092800, 25430664104, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.18.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.m1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831708
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.j1', '36.l1', '36.m1', '36.n1', '36.o1', '36.p1', '36.s1', '36.x1', '36.y1', '36.bd1', '36.bq1', '36.br1', '36.bs1', '36.bv1', '36.cf1', '36.cg1', '36.cj1', '36.ck1', '36.cp1', '54.q1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [3777, -1, 5432, -1], 'generators': [25514092800, 126937858924800, 26468500904, 1078117201, 16687, 4985, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.18.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.n1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831709
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.l1', '12.m1', '12.o1', '12.z1', '12.ba1', '12.bf1', '12.bg1', '18.b1', '54.d1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5664, -1, 6263, -1], 'generators': [25514092800, 26468500904, 1078117201, 30235, 16687, 9360177523200, 2628844618652, 134983133510400, 1078121465, 112608921600], 'label': '20736.hv.6.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '10000.dl'}
  • id: 165831710
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '9.a1'], 'contains': ['36.a1', '36.b1', '36.bm1', '36.bo1', '36.bt1', '36.bw1', '36.cl1', '36.co1', '36.cp1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5841, -1, 5815, -1], 'generators': [25514092800, 1078117201, 16687, 2646966474806, 9360177523200, 4985, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.18.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.o1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831711
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1', '9.a1'], 'contains': ['36.e1', '36.f1', '36.bn1', '36.bp1', '36.bu1', '36.bx1', '36.cm1', '36.cn1', '36.cp1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5485, -1, 5583, -1], 'generators': [25514092800, 1078117201, 16687, 9360177523200, 4985, 2628844618652, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.18.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.p1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831712
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.bp1', '12.bw1'], 'contains': ['48.a1', '48.fj1', '48.fp1', '72.hs1', '72.ht1', '72.hu1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1729, 9090, 2771, 763], 'generators': [134983133510400, 721, 16687, 4985, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.a1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['48.a1', '96.A'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '20736.hv', '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': '10000.da'}
  • id: 165831713
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '12.bh1', '12.ca1'], 'contains': ['48.b1', '48.do1', '48.ed1', '48.ft1', '48.fu1', '72.jg1'], 'core': '24.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6210, 3997, 8359, 8831], 'generators': [134983133510400, 16687, 25514092800, 1078116480, 112608921600, 1078146715, 26468500904, 9360177523200], 'label': '20736.hv.24.b1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['48.b1', '96.A'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '20736.hv', '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': '10000.da'}
  • id: 165831714
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1', '12.o1', '12.cf1'], 'contains': ['48.c1', '48.gm1', '48.gp1', '72.kk1'], 'core': '24.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5281, 6849, 5340, 2739], 'generators': [134983133510400, 26428555385, 16687, 1078117201, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.c1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['48.c1', '96.A'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '10000.da'}
  • id: 165831715
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1'], 'contains': ['48.g1', '48.d1', '48.h1', '48.k1', '48.l1', '48.n1', '48.bz1', '48.ck1', '48.cq1', '48.he1', '48.hf1', '48.hi1', '48.hl1', '48.hu1', '48.hz1', '48.ib1', '48.iq1', '48.it1', '48.iv1', '72.a1', '72.d1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1156, -1, 1072, -1], 'generators': [1078117201, 9360177523200, 4985, 134983133510400, 25514109487, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.24.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '24.d1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165831716
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.br1'], 'contains': ['48.m1', '48.o1', '48.cc1', '48.cf1', '48.cw1', '48.hv1', '48.ir1', '72.b1', '72.f1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4980, -1, 2933, -1], 'generators': [134983133510400, 721, 4985, 25514092800, 24460, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.24.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '24.e1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165831717
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.br1'], 'contains': ['48.m1', '48.p1', '48.ce1', '48.cf1', '48.cy1', '72.c1', '72.g1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4950, -1, 3324, -1], 'generators': [134983133510400, 721, 4985, 25514092800, 24460, 112608921600, 2646966489420, 9360177523200], 'label': '20736.hv.24.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '24.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165831718
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.c1', '12.bu1'], 'contains': ['48.m1', '48.ch1', '48.ci1', '48.hw1', '48.is1', '72.h1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5783, -1, 3083, -1], 'generators': [134983133510400, 721, 2628761162700, 4985, 25514092800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.24.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '24.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '864.4700'}
  • id: 165831719
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.b1', '12.c1'], 'contains': ['48.f1', '48.e1', '48.i1', '48.j1', '48.l1', '48.m1', '48.bz1', '48.cj1', '48.cl1', '48.he1', '48.hi1', '48.hj1', '48.hk1', '48.hx1', '48.hy1', '48.ia1', '48.iq1', '48.it1', '48.iu1', '72.e1', '72.i1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [3893, -1, 1432, -1], 'generators': [134983133510400, 1078121465, 25514092800, 1078133167, 1078117201, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.24.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '24.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
  • id: 165831720
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.p1', '12.t1', '12.u1', '12.w1', '12.bb1', '12.bd1', '12.bg1', '18.c1', '54.a1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6637, -1, 6237, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 25430664104, 1078117201, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.6.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831721
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1'], 'contains': ['48.n1', '48.o1', '48.p1', '48.cr1', '48.ct1', '48.cw1', '48.cy1', '72.j1', '72.k1', '72.l1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3728, -1, 3180, -1], 'generators': [134983133510400, 721, 4985, 25514109487, 24460, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.24.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.br1', 'old_label': '24.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165831722
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.j1'], 'contains': ['48.t1', '48.x1', '48.y1', '48.bg1', '48.bo1', '48.dd1', '48.dg1', '48.dr1', '48.dx1', '48.en1', '48.ez1', '72.m1', '72.q1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8820, -1, 8253, -1], 'generators': [134983133510400, 20063, 25514092800, 24460, 112608921600, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.24.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831723
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.j1'], 'contains': ['48.t1', '48.x1', '48.ba1', '48.bh1', '48.bp1', '48.de1', '48.dh1', '48.ds1', '48.dz1', '48.eo1', '48.fa1', '72.n1', '72.r1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9046, -1, 8212, -1], 'generators': [25514092800, 26468500904, 2628844644964, 24460, 9360177523200, 134983133510400, 20063, 112608921600], 'label': '20736.hv.24.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831724
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.e1', '12.m1'], 'contains': ['48.t1', '48.z1', '48.bd1', '48.di1', '48.di2', '48.ea1', '48.ea2', '72.s1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9420, -1, 9674, -1], 'generators': [25514092800, 26468500904, 24460, 9360177523200, 134983133510400, 20063, 2647090251364, 112608921600], 'label': '20736.hv.24.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.l1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831725
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.e1', '12.p1'], 'contains': ['48.u1', '48.x1', '48.z1', '48.dj1', '48.dm1', '48.dt1', '48.eb1', '72.t1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9176, -1, 9435, -1], 'generators': [134983133510400, 25430669871, 20063, 25514092800, 24460, 112608921600, 2647090251364, 9360177523200], 'label': '20736.hv.24.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.m1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165831726
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.r1'], 'contains': ['48.u1', '48.y1', '48.bd1', '48.dl1', '48.dy1', '72.u1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8349, -1, 9469, -1], 'generators': [134983133510400, 25430669871, 20063, 25514092800, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.24.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.n1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831727
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.r1'], 'contains': ['48.u1', '48.ba1', '48.bd1', '48.dn1', '48.ec1', '72.v1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8651, -1, 9352, -1], 'generators': [134983133510400, 25430669871, 20063, 25514092800, 24460, 112608921600, 2628844644964, 9360177523200], 'label': '20736.hv.24.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.o1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831728
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1'], 'contains': ['48.q1', '48.r1', '48.v1', '48.bf1', '48.bi1', '48.cz1', '48.db1', '48.do1', '48.dp1', '48.em1', '48.ep1', '72.o1', '72.p1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6615, -1, 8085, -1], 'generators': [134983133510400, 25514109487, 1078116480, 112608921600, 1078146715, 19342, 26468500904, 9360177523200], 'label': '20736.hv.24.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '24.p1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165831729
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.be1'], 'contains': ['48.y1', '48.bc1', '48.w1', '48.fb1', '48.eq1', '48.hm1', '48.hq1', '72.x1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1911, -1, 1768, -1], 'generators': [134983133510400, 1078135822, 25514092800, 1078117201, 24460, 112608921600, 2647090220514, 9360177523200], 'label': '20736.hv.24.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '24.q1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1', 'subgroup_fusion': None, 'weyl_group': '864.4701'}
  • id: 165831730
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.g1', '12.bg1'], 'contains': ['48.z1', '48.bb1', '48.w1', '48.hn1', '48.hr1', '72.y1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1413, -1, 1646, -1], 'generators': [1078135822, 25514092800, 1078117201, 24460, 9360177523200, 2628844618652, 134983133510400, 112608921600], 'label': '20736.hv.24.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '24.r1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1', 'subgroup_fusion': None, 'weyl_group': '864.4701'}
  • id: 165831731
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.r1', '12.s1', '12.u1', '12.y1', '12.bc1', '12.be1', '12.bf1', '18.d1', '54.b1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5457, -1, 6213, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 25430664104, 1078117201, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.6.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '20000.dn'}
  • id: 165831732
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.be1'], 'contains': ['48.ba1', '48.bc1', '48.w1', '48.fc1', '48.er1', '72.z1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2752, -1, 2826, -1], 'generators': [134983133510400, 1078135822, 25514092800, 1078117201, 24460, 112608921600, 2647090225052, 9360177523200], 'label': '20736.hv.24.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '24.s1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1', 'subgroup_fusion': None, 'weyl_group': '864.4701'}
  • id: 165831733
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.e1', '12.bh1'], 'contains': ['48.q1', '48.r1', '48.t1', '48.u1', '48.be1', '48.da1', '48.dc1', '48.df1', '48.dk1', '48.ed1', '48.eg1', '72.w1', '72.ba1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [8261, -1, 8542, -1], 'generators': [134983133510400, 25514092800, 1078116480, 112608921600, 1078146715, 19342, 26468500904, 9360177523200], 'label': '20736.hv.24.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.t1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165831734
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.e1', '12.bi1'], 'contains': ['48.x1', '48.bd1', '48.be1', '48.dq1', '48.dv1', '48.ee1', '48.eh1', '72.bb1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9216, -1, 9504, -1], 'generators': [134983133510400, 1078120744, 2646966471087, 25514092800, 1078133167, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.24.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.u1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165831735
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.f1', '12.bj1'], 'contains': ['48.y1', '48.z1', '48.be1', '48.du1', '48.ef1', '48.ho1', '48.hs1', '72.bc1'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [7272, -1, 7960, -1], 'generators': [134983133510400, 1078120744, 25514092800, 1078133167, 112608921600, 1078146715, 2628844639618, 9360177523200], 'label': '20736.hv.24.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.v1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165831736
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.g1', '12.bj1'], 'contains': ['48.z1', '48.ba1', '48.be1', '48.dw1', '48.ei1', '72.bd1'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [7382, -1, 8476, -1], 'generators': [134983133510400, 1078136543, 25514092800, 1078116480, 112608921600, 1078140940, 2628844644964, 9360177523200], 'label': '20736.hv.24.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.w1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165831737
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.g1', '12.bm1'], 'contains': ['48.bb1', '48.bc1', '48.be1', '48.hp1', '48.ht1', '72.be1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1355, -1, 1701, -1], 'generators': [134983133510400, 1078136543, 25514092800, 1078116480, 112608921600, 1078140940, 2628844618652, 9360177523200], 'label': '20736.hv.24.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '24.x1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1', 'subgroup_fusion': None, 'weyl_group': '864.4701'}
  • id: 165831738
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1'], 'contains': ['48.bf1', '48.bg1', '48.bh1', '48.bj1', '48.bk1', '48.bo1', '48.bp1', '48.ej1', '48.ek1', '48.el1', '48.el2', '48.es1', '48.eu1', '48.ey1', '48.ey2', '72.bf1', '72.bg1', '72.bh1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8159, -1, 6763, -1], 'generators': [134983133510400, 25514109487, 25514097064, 24460, 112608921600, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.24.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '24.y1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831739
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1'], 'contains': ['48.bi1', '48.bl1', '48.bm1', '72.bi1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6797, -1, 7000, -1], 'generators': [134983133510400, 25514109487, 25514097064, 24460, 112608921600, 123775784, 2628844618652, 9360177523200], 'label': '20736.hv.24.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '24.z1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1', 'subgroup_fusion': None, 'weyl_group': '864.4285'}
  • id: 165831740
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1'], 'contains': ['48.bn1', '48.bj1', '48.bm1', '48.ew1', '48.ex1', '48.et1', '48.ev1', '72.bj1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7477, -1, 5594, -1], 'generators': [7879101314486, 1078117201, 24460, 9360177523200, 134983133510400, 25514109487, 26428555385, 112608921600], 'label': '20736.hv.24.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '24.ba1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165831741
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1'], 'contains': ['48.f1', '48.e1', '48.h1', '48.k1', '48.s1', '48.v1', '48.bn1', '48.bs1', '48.bu1', '48.he1', '48.hj1', '48.hl1', '48.hu1', '48.hx1', '48.hy1', '48.ib1', '48.ic1', '48.if1', '48.ih1', '72.bk1', '72.bn1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1209, -1, 1177, -1], 'generators': [134983133510400, 25514109487, 1078117201, 1078116480, 112608921600, 1078146715, 19342, 9360177523200], 'label': '20736.hv.24.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '24.bb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165831742
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.d1', '12.e1', '12.h1', '12.i1', '12.j1', '12.m1', '12.p1', '12.r1', '12.bh1', '12.bi1', '12.bj1', '12.by1', '12.bz1', '12.ca1', '12.cb1', '18.e1', '54.e1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8113, -1, 8496, -1], 'generators': [25514092800, 26468500904, 16687, 9360177523200, 134983133510400, 1078116480, 2628844639618, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.6.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '50000.bt'}
  • id: 165831743
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.bs1'], 'contains': ['48.y1', '48.bb1', '48.bq1', '48.bt1', '48.bv1', '48.hg1', '48.id1', '72.bl1', '72.bp1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1440, -1, 1725, -1], 'generators': [134983133510400, 4985, 25514092800, 24460, 112608921600, 15966, 2628844618652, 9360177523200], 'label': '20736.hv.24.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '24.bc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1', 'subgroup_fusion': None, 'weyl_group': '864.4701'}
  • id: 165831744
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.g1', '12.bt1'], 'contains': ['48.z1', '48.bc1', '48.bt1', '48.hh1', '48.ie1', '72.bq1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1386, -1, 1677, -1], 'generators': [134983133510400, 4985, 25514092800, 24460, 112608921600, 2647090225052, 15966, 9360177523200], 'label': '20736.hv.24.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '24.bd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165831745
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.bs1'], 'contains': ['48.ba1', '48.bb1', '48.br1', '48.bt1', '48.bw1', '72.bm1', '72.br1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1534, -1, 1895, -1], 'generators': [134983133510400, 2628844614114, 4985, 25514092800, 24460, 112608921600, 15966, 9360177523200], 'label': '20736.hv.24.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '24.be1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1', 'subgroup_fusion': None, 'weyl_group': '864.4701'}
  • id: 165831746
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.f1', '12.g1'], 'contains': ['48.g1', '48.d1', '48.i1', '48.j1', '48.s1', '48.w1', '48.be1', '48.bs1', '48.bt1', '48.hf1', '48.hi1', '48.hk1', '48.hu1', '48.hy1', '48.hz1', '48.ia1', '48.ic1', '48.if1', '48.ig1', '72.bo1', '72.bs1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [903, -1, 1042, -1], 'generators': [134983133510400, 4985, 25514092800, 1078133167, 1078117201, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.24.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '24.bf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1', 'subgroup_fusion': None, 'weyl_group': '216.159'}
  • id: 165831747
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1'], 'contains': ['48.bk1', '48.bl1', '48.bq1', '48.br1', '48.bu1', '48.bv1', '48.bw1', '72.bt1', '72.bu1', '72.bv1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2025, -1, 2444, -1], 'generators': [24460, 25514093521, 9360177523200, 4985, 2628844618652, 134983133510400, 25514109487, 112608921600], 'label': '20736.hv.24.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bs1', 'old_label': '24.bg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1', 'subgroup_fusion': None, 'weyl_group': '432.769'}
  • id: 165831748
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.j1'], 'contains': ['48.ca1', '48.cc1', '48.cd1', '48.cn1', '48.cv1', '48.dd1', '48.de1', '48.dr1', '48.ds1', '48.ej1', '48.es1', '72.bw1', '72.ca1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9153, -1, 8272, -1], 'generators': [25514092800, 26468500904, 4264, 24460, 9360177523200, 134983133510400, 2628844639618, 112608921600], 'label': '20736.hv.24.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.bh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831749
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '12.j1'], 'contains': ['48.ca1', '48.cd1', '48.ce1', '48.co1', '48.cx1', '48.dg1', '48.dh1', '48.dx1', '48.dz1', '48.ek1', '48.eu1', '72.bx1', '72.cb1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8843, -1, 8233, -1], 'generators': [25514092800, 26468506671, 4264, 24460, 9360177523200, 134983133510400, 2628844639618, 112608921600], 'label': '20736.hv.24.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.bi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831750
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '12.i1', '12.m1'], 'contains': ['48.ca1', '48.cg1', '48.ch1', '48.di1', '48.di2', '48.ea1', '48.ea2', '72.cc1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9494, -1, 9693, -1], 'generators': [25514092800, 26468506671, 4264, 24460, 9360177523200, 134983133510400, 2647090251364, 112608921600], 'label': '20736.hv.24.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.bj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831751
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.p1'], 'contains': ['48.cb1', '48.cc1', '48.cg1', '48.dj1', '48.dt1', '72.cd1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8987, -1, 9393, -1], 'generators': [134983133510400, 25430669871, 25514092800, 24460, 112608921600, 4264, 2647090251364, 9360177523200], 'label': '20736.hv.24.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.bk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165831752
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '12.i1', '12.r1'], 'contains': ['48.cb1', '48.cd1', '48.ch1', '48.dl1', '48.dn1', '48.dy1', '48.ec1', '72.ce1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9291, -1, 9453, -1], 'generators': [134983133510400, 25514092800, 25430664104, 24460, 112608921600, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.24.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.bl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831753
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.l1', '12.n1', '12.s1', '12.t1', '12.bh1', '12.bl1', '12.bm1', '18.f1', '54.f1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5745, -1, 6658, -1], 'generators': [25514092800, 26468500904, 16687, 9360177523200, 2628844618652, 134983133510400, 1078116480, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.6.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '10000.bz'}
  • id: 165831754
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '12.p1'], 'contains': ['48.cb1', '48.ce1', '48.cg1', '48.dm1', '48.eb1', '72.cf1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8958, -1, 9372, -1], 'generators': [134983133510400, 25514092800, 25430664104, 24460, 112608921600, 4264, 2647090251364, 9360177523200], 'label': '20736.hv.24.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.bm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165831755
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1'], 'contains': ['48.bx1', '48.by1', '48.ck1', '48.cm1', '48.cp1', '48.da1', '48.dc1', '48.do1', '48.dp1', '48.em1', '48.ep1', '72.by1', '72.bz1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6380, -1, 7939, -1], 'generators': [26468500904, 9360177523200, 4985, 134983133510400, 25514109487, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.24.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '24.bn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165831756
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.bd1'], 'contains': ['48.cj1', '48.cc1', '48.ci1', '48.ew1', '48.et1', '48.ik1', '48.im1', '72.ch1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6553, -1, 4419, -1], 'generators': [1078132446, 134983133510400, 1078135822, 2628761162700, 25514092800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.24.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '24.bo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1', 'subgroup_fusion': None, 'weyl_group': '864.4700'}
  • id: 165831757
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.bd1'], 'contains': ['48.cj1', '48.ce1', '48.ci1', '48.ex1', '48.ev1', '72.ci1'], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7067, -1, 5285, -1], 'generators': [1078135822, 25514092800, 24460, 9360177523200, 134983133510400, 2628761148086, 1078132446, 112608921600], 'label': '20736.hv.24.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '24.bp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1', 'subgroup_fusion': None, 'weyl_group': '864.4700'}
  • id: 165831758
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.c1', '12.bf1'], 'contains': ['48.cj1', '48.cf1', '48.ch1', '48.il1', '48.in1', '72.cj1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5637, -1, 3504, -1], 'generators': [1078132446, 134983133510400, 1078135822, 25514092800, 24460, 112608921600, 2646966489420, 9360177523200], 'label': '20736.hv.24.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '24.bq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1', 'subgroup_fusion': None, 'weyl_group': '864.4700'}
  • id: 165831759
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '12.i1', '12.bh1'], 'contains': ['48.bx1', '48.by1', '48.ca1', '48.cb1', '48.cl1', '48.cz1', '48.db1', '48.df1', '48.dk1', '48.ed1', '48.eg1', '72.cg1', '72.ck1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [8934, -1, 8584, -1], 'generators': [134983133510400, 4985, 25514092800, 1078116480, 112608921600, 1078146715, 26468500904, 9360177523200], 'label': '20736.hv.24.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.br1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165831760
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.h1', '12.bi1'], 'contains': ['48.cc1', '48.ch1', '48.cl1', '48.dq1', '48.ee1', '48.ii1', '48.io1', '72.cl1'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [5971, -1, 8129, -1], 'generators': [134983133510400, 1078120744, 2646966471087, 25514092800, 1078116480, 112608921600, 1078140940, 9360177523200], 'label': '20736.hv.24.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165831761
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '12.i1', '12.bj1'], 'contains': ['48.cd1', '48.cg1', '48.cl1', '48.du1', '48.dw1', '48.ef1', '48.ei1', '72.cm1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9374, -1, 9414, -1], 'generators': [134983133510400, 1078120744, 25514092800, 1078116480, 112608921600, 1078140940, 2628844639618, 9360177523200], 'label': '20736.hv.24.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.bt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165831762
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.i1', '12.bi1'], 'contains': ['48.ce1', '48.ch1', '48.cl1', '48.dv1', '48.eh1', '72.cn1'], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [6577, -1, 8498, -1], 'generators': [134983133510400, 1078120744, 25514092800, 1078116480, 112608921600, 1078140940, 2646966487501, 9360177523200], 'label': '20736.hv.24.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165831763
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.c1', '12.bl1'], 'contains': ['48.cf1', '48.ci1', '48.cl1', '48.ij1', '48.ip1', '72.co1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5672, -1, 3526, -1], 'generators': [134983133510400, 1078120744, 25514092800, 1078116480, 112608921600, 2646966474806, 1078140940, 9360177523200], 'label': '20736.hv.24.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '24.bv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1', 'subgroup_fusion': None, 'weyl_group': '864.4700'}
  • id: 165831764
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.v1', '12.w1', '12.ba1', '12.bc1', '12.bi1', '12.bk1', '12.bm1', '18.g1', '54.g1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5590, -1, 6400, -1], 'generators': [25514092800, 26468479846, 16687, 9360177523200, 2628844618652, 134983133510400, 1078116480, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.6.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '4000.fh'}
  • id: 165831765
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1'], 'contains': ['48.cm1', '48.cn1', '48.co1', '48.cr1', '48.cs1', '48.cv1', '48.cx1', '48.en1', '48.eo1', '48.el1', '48.el2', '48.ez1', '48.fa1', '48.ey1', '48.ey2', '72.cp1', '72.cq1', '72.cr1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8089, -1, 6779, -1], 'generators': [134983133510400, 997953704, 25514109487, 24460, 112608921600, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.24.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '24.bw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831766
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1'], 'contains': ['48.cp1', '48.ct1', '48.cu1', '72.cs1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4790, -1, 6939, -1], 'generators': [134983133510400, 25514109487, 25430664104, 7865729194652, 24460, 112608921600, 4264, 9360177523200], 'label': '20736.hv.24.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '24.bx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1', 'subgroup_fusion': None, 'weyl_group': '288.880'}
  • id: 165831767
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1'], 'contains': ['48.cs1', '48.cu1', '48.cq1', '48.fb1', '48.fc1', '48.eq1', '48.er1', '72.ct1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4610, -1, 4687, -1], 'generators': [134983133510400, 26428555385, 25514109487, 26428551121, 7865729194652, 24460, 112608921600, 9360177523200], 'label': '20736.hv.24.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.be1', 'old_label': '24.by1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165831768
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.h1', '12.by1'], 'contains': ['48.dd1', '48.df1', '48.di1', '48.dq1', '48.dt1', '48.du1', '48.dy1', '72.cu1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9729, -1, 9795, -1], 'generators': [134983133510400, 1078120744, 25514092800, 24460, 112608921600, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.24.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.bz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831769
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.h1', '12.by1'], 'contains': ['48.de1', '48.df1', '48.di2', '48.dq1', '48.dt1', '48.dw1', '48.ec1', '72.cv1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9945, -1, 9637, -1], 'generators': [134983133510400, 1078120744, 25514092800, 24460, 112608921600, 26468506671, 2628844644964, 9360177523200], 'label': '20736.hv.24.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ca1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831770
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.i1', '12.by1'], 'contains': ['48.df1', '48.dg1', '48.di2', '48.du1', '48.dv1', '48.dy1', '48.eb1', '72.cw1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9687, -1, 9760, -1], 'generators': [134983133510400, 1078120744, 25514092800, 24460, 112608921600, 26468506671, 2628844639618, 9360177523200], 'label': '20736.hv.24.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.cb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831771
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.i1', '12.by1'], 'contains': ['48.df1', '48.dh1', '48.di1', '48.dv1', '48.dw1', '48.eb1', '48.ec1', '72.cx1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9920, -1, 9589, -1], 'generators': [25514092800, 26468500904, 2628844644964, 24460, 9360177523200, 134983133510400, 1078120744, 112608921600], 'label': '20736.hv.24.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.cc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831772
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.h1', '12.bz1'], 'contains': ['48.dj1', '48.dk1', '48.dl1', '48.dq1', '48.dr1', '48.du1', '48.ea1', '72.cy1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9335, -1, 9726, -1], 'generators': [134983133510400, 1078120744, 25514092800, 25430664104, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.24.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.cd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831773
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.h1', '12.bz1'], 'contains': ['48.dj1', '48.dk1', '48.dn1', '48.dq1', '48.ds1', '48.dw1', '48.ea2', '72.cz1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9819, -1, 9554, -1], 'generators': [134983133510400, 25430669871, 1078120744, 25514092800, 24460, 112608921600, 2628844644964, 9360177523200], 'label': '20736.hv.24.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ce1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831774
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.i1', '12.bz1'], 'contains': ['48.dk1', '48.dl1', '48.dm1', '48.du1', '48.dv1', '48.dx1', '48.ea2', '72.da1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9352, -1, 9711, -1], 'generators': [134983133510400, 25430669871, 1078120744, 25514092800, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.24.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.cf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831775
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.x1', '12.y1', '12.z1', '12.bb1', '12.bj1', '12.bk1', '12.bl1', '18.h1', '54.h1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5811, -1, 6486, -1], 'generators': [25514092800, 26468479846, 16687, 9360177523200, 134983133510400, 1078116480, 2628844639618, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.6.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831776
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.i1', '12.bz1'], 'contains': ['48.dk1', '48.dm1', '48.dn1', '48.dv1', '48.dw1', '48.dz1', '48.ea1', '72.db1'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9578, -1, 9539, -1], 'generators': [134983133510400, 1078120744, 25514092800, 25430664104, 24460, 112608921600, 2628844644964, 9360177523200], 'label': '20736.hv.24.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.cg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831777
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.h1', '12.ca1'], 'contains': ['48.dd1', '48.di2', '48.dj1', '48.dl1', '48.ed1', '48.ee1', '48.ef1', '48.iw1', '48.ix1', '72.dc1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9254, -1, 9606, -1], 'generators': [134983133510400, 25514092800, 25430664104, 1078133167, 112608921600, 1078146715, 2647090220036, 9360177523200], 'label': '20736.hv.24.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ch1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831778
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.h1', '12.ca1'], 'contains': ['48.de1', '48.di1', '48.dj1', '48.dn1', '48.ed1', '48.ee1', '48.ei1', '72.dd1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9848, -1, 9521, -1], 'generators': [134983133510400, 25514092800, 1078133167, 112608921600, 1078146715, 2628844613636, 26468500904, 9360177523200], 'label': '20736.hv.24.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ci1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831779
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.i1', '12.ca1'], 'contains': ['48.dg1', '48.di1', '48.dl1', '48.dm1', '48.ed1', '48.ef1', '48.eh1', '72.de1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9397, -1, 9571, -1], 'generators': [134983133510400, 25514092800, 1078133167, 112608921600, 1078146715, 2647090220036, 26468500904, 9360177523200], 'label': '20736.hv.24.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.cj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831780
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.i1', '12.ca1'], 'contains': ['48.dh1', '48.di2', '48.dm1', '48.dn1', '48.ed1', '48.eh1', '48.ei1', '72.df1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9519, -1, 9487, -1], 'generators': [134983133510400, 25514092800, 1078116480, 112608921600, 2647090220036, 1078140940, 26468506671, 9360177523200], 'label': '20736.hv.24.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ck1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831781
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.h1', '12.cb1'], 'contains': ['48.dr1', '48.dt1', '48.dy1', '48.ea2', '48.ee1', '48.ef1', '48.eg1', '72.dg1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9619, -1, 9777, -1], 'generators': [134983133510400, 25430643767, 25514092800, 1078116480, 112608921600, 2647090225530, 1078140940, 9360177523200], 'label': '20736.hv.24.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.cl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cl1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831782
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.h1', '12.cb1'], 'contains': ['48.ds1', '48.dt1', '48.ea1', '48.ec1', '48.ee1', '48.eg1', '48.ei1', '72.dh1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9752, -1, 9655, -1], 'generators': [25514092800, 1078140940, 2647090220036, 25430638000, 9360177523200, 134983133510400, 1078116480, 112608921600], 'label': '20736.hv.24.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.cm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cm1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831783
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.i1', '12.cb1'], 'contains': ['48.dx1', '48.dy1', '48.ea1', '48.eb1', '48.ef1', '48.eg1', '48.eh1', '72.di1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9472, -1, 9742, -1], 'generators': [25514092800, 2647090225530, 1078140940, 25430638000, 9360177523200, 134983133510400, 1078116480, 112608921600], 'label': '20736.hv.24.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.cn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831784
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.i1', '12.cb1'], 'contains': ['48.dz1', '48.ea2', '48.eb1', '48.ec1', '48.eg1', '48.eh1', '48.ei1', '72.dj1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9670, -1, 9622, -1], 'generators': [134983133510400, 25430643767, 25514092800, 1078116480, 112608921600, 2647090220036, 1078140940, 9360177523200], 'label': '20736.hv.24.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.co1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831785
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.l1', '12.m1', '12.n1', '12.o1', '12.bh1', '12.bp1'], 'contains': ['48.t1', '48.bf1', '48.ca1', '48.cm1', '48.fd1', '48.ff1', '48.fj1', '48.ft1', '48.ga1', '48.gg1', '48.gm1', '72.dk1', '72.dl1', '72.eh1'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6838, -1, 6622, -1], 'generators': [134983133510400, 26428580635, 16687, 4985, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831834
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1'], 'contains': ['48.fs1', '72.hx1', '72.ia1'], 'core': '1296.A', 'coset_action_label': None, 'count': 24, 'diagramx': [293, -1, 184, -1], 'generators': [154860865673341, 721, 16687, 4985, 132523584036480, 9683982604800, 30235, 2628844618652], 'label': '20736.hv.24.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.eg1', 'old_label': '24.eg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eg1', 'subgroup_fusion': None, 'weyl_group': '864.4017'}
  • id: 165831786
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.j1', '12.l1', '12.w1', '12.y1', '12.bn1', '12.bo1', '12.bp1', '12.br1', '12.bs1', '12.bv1', '12.bw1', '18.i1', '18.j1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3118, -1, 3863, -1], 'generators': [25514092800, 26468500904, 721, 30235, 16687, 9360177523200, 4985, 2628844618652, 134983133510400, 112608921600], 'label': '20736.hv.6.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831787
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.bh1', '12.bp1'], 'contains': ['48.q1', '48.bx1', '48.fe1', '48.fg1', '48.fj1', '48.ft1', '48.gb1', '48.gk1', '48.gy1', '72.dm1', '72.dn1', '72.do1', '72.ei1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2898, -1, 5085, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831788
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '12.r1', '12.s1', '12.t1', '12.u1', '12.bh1', '12.bq1'], 'contains': ['48.u1', '48.bi1', '48.cb1', '48.cp1', '48.fd1', '48.fg1', '48.fu1', '48.gc1', '48.gf1', '72.dp1', '72.ej1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6242, -1, 7698, -1], 'generators': [134983133510400, 26428580635, 16687, 4985, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831789
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '12.bh1', '12.bq1'], 'contains': ['48.r1', '48.by1', '48.fe1', '48.ff1', '48.fg1', '48.fu1', '48.fz1', '48.gi1', '48.gj1', '72.dq1', '72.dr1', '72.ek1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3912, -1, 6326, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831790
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.p1', '12.v1', '12.w1', '12.bd1', '12.bi1', '12.br1'], 'contains': ['48.x1', '48.bj1', '48.cc1', '48.ce1', '48.cr1', '48.fd1', '48.fi1', '48.fw1', '48.gl1', '72.ds1', '72.em1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6267, -1, 6645, -1], 'generators': [134983133510400, 16687, 2646966471087, 25514092800, 112608921600, 30235, 4264, 9360177523200], 'label': '20736.hv.24.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ct1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831791
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.k1', '12.q1'], 'contains': ['48.g1', '48.e1', '48.i1', '48.k1', '48.s1', '48.bz1', '48.fe1', '48.fh1', '48.fk1', '48.fv1', '48.fx1', '48.gn1', '48.hd1', '72.dt1', '72.ea1', '72.el1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1501, -1, 2409, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.cu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 165831792
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.r1', '12.x1', '12.y1', '12.be1', '12.bj1', '12.bs1'], 'contains': ['48.y1', '48.ba1', '48.bk1', '48.cd1', '48.cs1', '48.fd1', '48.fl1', '48.fy1', '48.go1', '72.du1', '72.en1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7157, -1, 6601, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.24.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165831793
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '12.v1', '12.x1', '12.z1', '12.ba1', '12.bk1', '12.bq1'], 'contains': ['48.fd1', '48.fm1', '48.fz1', '48.gp1', '48.gr1', '72.dy1', '72.eo1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5239, -1, 6203, -1], 'generators': [134983133510400, 26428580635, 16687, 4985, 112608921600, 30235, 25430669150, 9360177523200], 'label': '20736.hv.24.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cw1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831794
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '12.w1', '12.y1', '12.bb1', '12.bc1', '12.bk1', '12.bp1'], 'contains': ['48.fd1', '48.fn1', '48.fp1', '48.gb1', '48.gq1', '72.dv1', '72.dz1', '72.ep1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [3948, -1, 5406, -1], 'generators': [134983133510400, 26428580635, 16687, 4985, 112608921600, 26468505950, 30235, 9360177523200], 'label': '20736.hv.24.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831795
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.s1', '12.y1', '12.z1', '12.bf1', '12.bl1', '12.br1'], 'contains': ['48.cf1', '48.ct1', '48.fd1', '48.fo1', '72.dw1', '72.eq1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4927, -1, 6401, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 2646966474806, 30235, 4264, 9360177523200], 'label': '20736.hv.24.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831796
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.p1', '12.z1', '12.bb1', '12.bg1', '12.bj1', '12.bt1'], 'contains': ['48.z1', '48.cg1', '48.fd1', '48.gd1', '72.er1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7202, -1, 8409, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 2647090246018, 30235, 4264, 9360177523200], 'label': '20736.hv.24.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831797
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.a1', '8.b1', '8.d1', '8.h1', '8.j1', '54.n1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [252, 4993, 224, 3968], 'generators': [25514092800, 26468500904, 1078117201, 16687, 9360177523200, 4985, 134983133510400, 46036847791741, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.2.a1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '20000.dv'}
  • id: 165831798
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.m1', '12.n1', '12.bb1', '12.bc1', '12.bp1', '12.bt1', '12.bu1', '18.k1', '54.l1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6677, -1, 6585, -1], 'generators': [25514092800, 26468500904, 2647090225052, 721, 30235, 16687, 9360177523200, 4985, 134983133510400, 112608921600], 'label': '20736.hv.6.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831799
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.t1', '12.w1', '12.ba1', '12.bg1', '12.bm1', '12.bs1'], 'contains': ['48.bb1', '48.bl1', '48.fd1', '48.fq1', '72.dx1', '72.es1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5609, -1, 6363, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.24.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.da1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165831800
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '12.s1', '12.v1', '12.bc1', '12.be1', '12.bm1', '12.bt1'], 'contains': ['48.bc1', '48.cu1', '48.fd1', '48.gs1', '72.et1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5344, -1, 6477, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 2647090225052, 30235, 4264, 9360177523200], 'label': '20736.hv.24.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.db1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831851
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1', '12.by1', '12.cb1'], 'contains': ['48.dy1', '48.ec1', '48.fy1', '48.gc1', '48.ge1', '72.je1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8374, -1, 9309, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 25430638000, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.24.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ew1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ew1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831801
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.r1', '12.ba1', '12.bc1', '12.bf1', '12.bi1', '12.bu1'], 'contains': ['48.bd1', '48.ch1', '48.fd1', '48.ge1', '72.eu1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7129, -1, 8431, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 30235, 4264, 2628761144367, 9360177523200], 'label': '20736.hv.24.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dc1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165831802
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '12.t1', '12.x1', '12.bb1', '12.bd1', '12.bl1', '12.bu1'], 'contains': ['48.bm1', '48.ci1', '48.fd1', '48.gt1', '72.ev1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7331, -1, 6580, -1], 'generators': [134983133510400, 16687, 25514092800, 2628761148086, 112608921600, 30235, 4264, 9360177523200], 'label': '20736.hv.24.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dd1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165831803
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.o1', '12.u1', '12.bd1', '12.be1', '12.bf1', '12.bg1'], 'contains': ['48.c1', '48.f1', '48.d1', '48.w1', '48.bn1', '48.cj1', '48.cq1', '48.fd1', '48.fh1', '48.fv1', '48.gn1', '72.eb1', '72.ew1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5128, -1, 4367, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.de1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 165831804
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '12.bk1', '12.bp1'], 'contains': ['48.fe1', '48.fm1', '48.fp1', '48.ga1', '48.gb1', '48.ha1', '48.hb1', '72.ec1', '72.ee1', '72.ef1', '72.ex1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2681, -1, 4442, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 112608921600, 26468505950, 30235, 9360177523200], 'label': '20736.hv.24.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.df1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.df1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831805
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.bk1', '12.bq1'], 'contains': ['48.fe1', '48.fm1', '48.fn1', '48.fz1', '48.gc1', '48.gz1', '48.hc1', '72.ed1', '72.eg1', '72.ey1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3528, -1, 5495, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 112608921600, 30235, 25430669150, 9360177523200], 'label': '20736.hv.24.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dg1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831806
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.bh1', '12.bi1', '12.bj1', '12.bk1', '12.bl1', '12.bm1'], 'contains': ['48.b1', '48.h1', '48.j1', '48.v1', '48.be1', '48.ck1', '48.cl1', '48.fd1', '48.fe1', '48.fv1', '48.fx1', '72.ez1', '72.fa1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5314, -1, 6889, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.24.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dh1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 165831807
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '12.q1', '12.bq1'], 'contains': ['48.ff1', '48.fh1', '48.fm1', '48.gf1', '48.gi1', '48.gp1', '48.gz1', '72.fb1', '72.fj1', '72.fn1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3652, -1, 5122, -1], 'generators': [134983133510400, 16687, 4985, 1078117201, 112608921600, 123775784, 30235, 9360177523200], 'label': '20736.hv.24.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.di1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.di1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831808
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '12.u1', '12.bp1'], 'contains': ['48.fg1', '48.fh1', '48.fp1', '48.gg1', '48.gk1', '48.gq1', '48.hb1', '72.fd1', '72.fi1', '72.fk1', '72.fl1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2724, -1, 4402, -1], 'generators': [134983133510400, 16687, 4985, 25430664104, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dj1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831809
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.p1', '12.s1', '12.v1', '12.z1', '12.bq1', '12.br1', '12.bt1', '18.l1', '54.i1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5515, -1, 6352, -1], 'generators': [134983133510400, 721, 16687, 4985, 25514092800, 25430664104, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.6.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.l1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831810
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.u1', '12.bq1'], 'contains': ['48.fg1', '48.fh1', '48.fn1', '48.gf1', '48.gj1', '48.gr1', '48.hc1', '72.fc1', '72.fm1', '72.fo1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3601, -1, 5323, -1], 'generators': [134983133510400, 997953704, 16687, 4985, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dk1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831811
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.bn1', '12.bv1'], 'contains': ['48.bg1', '48.bh1', '48.cn1', '48.co1', '48.ff1', '48.fi1', '48.fl1', '48.gh1', '48.gv1', '72.fe1', '72.fp1', '72.fq1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6744, -1, 6035, -1], 'generators': [134983133510400, 997953704, 16687, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.24.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.dl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dl1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831812
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.q1', '12.bq1'], 'contains': ['48.fg1', '48.fk1', '48.fm1', '48.gi1', '48.gj1', '48.gz1', '48.hc1', '72.ff1', '72.fs1', '72.fu1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2245, -1, 4640, -1], 'generators': [134983133510400, 997953704, 16687, 4985, 26428551121, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dm1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831813
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '12.bn1', '12.bp1'], 'contains': ['48.ff1', '48.fk1', '48.fp1', '48.gk1', '48.ha1', '72.fg1', '72.fr1', '72.ft1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1787, -1, 3600, -1], 'generators': [134983133510400, 16687, 4985, 26428551121, 112608921600, 123775784, 30235, 9360177523200], 'label': '20736.hv.24.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dn1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831814
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.bn1', '12.bv1'], 'contains': ['48.ff1', '48.fo1', '48.fq1', '72.fh1', '72.fv1', '72.fw1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2977, -1, 3167, -1], 'generators': [134983133510400, 997953704, 16687, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.24.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.do1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.do1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831815
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.o1', '12.bp1'], 'contains': ['48.fh1', '48.fj1', '48.fm1', '48.gm1', '48.gq1', '48.gy1', '48.ha1', '72.fx1', '72.fy1', '72.fz1', '72.ga1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2701, -1, 4224, -1], 'generators': [134983133510400, 16687, 4985, 1078117201, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.dp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dp1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831816
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1', '12.bo1', '12.br1'], 'contains': ['48.cw1', '48.cy1', '48.fi1', '48.fk1', '48.fo1', '72.gc1', '72.gi1', '72.gj1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3298, -1, 3061, -1], 'generators': [134983133510400, 16687, 112608921600, 2646966474806, 30235, 25514093521, 25514097785, 9360177523200], 'label': '20736.hv.24.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.dq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dr1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165831817
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.bo1', '12.bw1'], 'contains': ['48.bo1', '48.bp1', '48.cv1', '48.cx1', '48.fi1', '48.fj1', '48.fl1', '48.gu1', '48.gw1', '72.gb1', '72.gf1', '72.gg1', '72.gh1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4686, -1, 4655, -1], 'generators': [134983133510400, 16687, 112608921600, 30235, 2628844639618, 4264, 26468500904, 9360177523200], 'label': '20736.hv.24.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.dr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dq1', 'subgroup_fusion': None, 'weyl_group': '1728.39000'}
  • id: 165831818
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '12.bo1', '12.bv1'], 'contains': ['48.fi1', '48.fn1', '48.fq1', '72.gd1', '72.gk1', '72.gm1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3341, -1, 3142, -1], 'generators': [134983133510400, 16687, 997932646, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.24.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.ds1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ds1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831819
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '12.bn1', '12.bw1'], 'contains': ['48.fi1', '48.fp1', '48.fq1', '72.ge1', '72.gl1', '72.gn1', '72.go1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2181, -1, 2915, -1], 'generators': [134983133510400, 26468479846, 16687, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.24.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.dt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dt1', 'subgroup_fusion': None, 'weyl_group': '1728.39000'}
  • id: 165831820
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.r1', '12.t1', '12.x1', '12.ba1', '12.bq1', '12.bs1', '12.bu1', '18.m1', '54.j1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6607, -1, 6432, -1], 'generators': [134983133510400, 721, 16687, 4985, 25514092800, 25430664104, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.6.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.m1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831821
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.bo1', '12.bp1'], 'contains': ['48.fk1', '48.fj1', '48.fn1', '48.gy1', '48.hb1', '72.gp1', '72.gq1', '72.gr1'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [2007, -1, 3629, -1], 'generators': [134983133510400, 16687, 4985, 26428551121, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.du1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.du1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831822
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1', '12.bo1', '12.bs1'], 'contains': ['48.bq1', '48.br1', '48.fk1', '48.fl1', '48.fq1', '72.gw1', '72.gx1', '72.gy1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2220, -1, 2756, -1], 'generators': [134983133510400, 16687, 112608921600, 30235, 25514093521, 2628844618652, 25514097785, 9360177523200], 'label': '20736.hv.24.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.dv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dw1', 'subgroup_fusion': None, 'weyl_group': '864.4407'}
  • id: 165831823
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.bo1', '12.bw1'], 'contains': ['48.fj1', '48.fo1', '48.fq1', '72.gs1', '72.gt1', '72.gu1', '72.gv1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3085, -1, 2863, -1], 'generators': [134983133510400, 16687, 112608921600, 30235, 4264, 26468500904, 2628844618652, 9360177523200], 'label': '20736.hv.24.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.dw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dv1', 'subgroup_fusion': None, 'weyl_group': '1728.39000'}
  • id: 165831824
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1', '12.bo1', '12.bv1'], 'contains': ['48.fl1', '48.fn1', '48.fo1', '72.gz1', '72.hb1', '72.he1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3169, -1, 3155, -1], 'generators': [134983133510400, 16687, 997932646, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.24.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.dx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dx1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831825
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1', '12.bn1', '12.bw1'], 'contains': ['48.fl1', '48.fo1', '48.fp1', '72.ha1', '72.hc1', '72.hd1', '72.hf1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2197, -1, 3024, -1], 'generators': [134983133510400, 26468479846, 16687, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.24.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.dy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dy1', 'subgroup_fusion': None, 'weyl_group': '1728.39000'}
  • id: 165831826
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.bp1', '12.bq1', '12.br1', '12.bs1', '12.bt1', '12.bu1'], 'contains': ['48.a1', '48.l1', '48.m1', '48.n1', '48.bs1', '48.bt1', '48.bu1', '48.fd1', '48.fe1', '48.fh1', '48.fk1', '72.hg1', '72.hh1', '72.hi1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3424, -1, 2803, -1], 'generators': [134983133510400, 721, 16687, 4985, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dz1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165831827
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '12.bq1', '12.bv1'], 'contains': ['48.a1', '48.ff1', '48.fg1', '48.fm1', '48.fn1', '72.hj1', '72.hk1', '72.hl1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2812, -1, 4730, -1], 'generators': [134983133510400, 997953704, 721, 16687, 4985, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ea1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ea1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165831828
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.br1', '12.bv1', '12.bw1'], 'contains': ['48.a1', '48.o1', '48.p1', '48.fi1', '48.fo1', '72.hm1', '72.hn1', '72.ho1', '72.hp1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3107, -1, 2784, -1], 'generators': [134983133510400, 721, 16687, 4985, 112608921600, 2646966474806, 30235, 9360177523200], 'label': '20736.hv.24.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.eb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eb1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165831829
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.bx1'], 'contains': ['48.fr1', '72.hp1', '72.hq1'], 'core': '1296.A', 'coset_action_label': None, 'count': 4, 'diagramx': [694, -1, 330, -1], 'generators': [132523584036480, 9683982604800, 721, 30235, 16687, 4985, 46036847791741, 86575308386486], 'label': '20736.hv.24.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '24.ec1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ec1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
  • id: 165831830
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.bx1'], 'contains': ['48.fr1', '72.hr1', '72.hu1'], 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [372, -1, 297, -1], 'generators': [721, 16687, 4985, 132523584036480, 9683982604800, 46036847791741, 30235, 26468500904], 'label': '20736.hv.24.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bx1', 'old_label': '24.ed1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ed1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
  • id: 165831831
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.c1', '12.bd1', '12.bf1', '12.bi1', '12.bl1', '12.br1', '12.bu1', '18.o1', '54.r1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5645, -1, 5815, -1], 'generators': [25514092800, 1078117201, 16687, 2646966474806, 9360177523200, 4985, 134983133510400, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.6.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.n1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165831832
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '12.bs1', '12.bv1', '12.bw1'], 'contains': ['48.a1', '48.bv1', '48.bw1', '48.fl1', '48.fq1', '72.hv1', '72.hw1', '72.hx1', '72.hy1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1745, -1, 2310, -1], 'generators': [134983133510400, 721, 16687, 4985, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.24.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.ee1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ee1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165831833
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '12.bx1'], 'contains': ['48.fr1', '72.hx1', '72.hz1'], 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [351, -1, 278, -1], 'generators': [721, 16687, 4985, 132523584036480, 9683982604800, 46036847791741, 30235, 2628844618652], 'label': '20736.hv.24.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bx1', 'old_label': '24.ef1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ef1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
  • id: 165831835
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.o1', '12.bh1'], 'contains': ['48.da1', '48.cz1', '48.ft1', '48.fv1', '48.fz1', '48.gf1', '48.gi1', '48.gm1', '48.gy1', '72.ib1', '72.ic1', '72.ip1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5168, -1, 5743, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.eh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eh1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831836
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.by1', '12.ca1'], 'contains': ['48.dd1', '48.de1', '48.dg1', '48.dh1', '48.el1', '48.el2', '48.ft1', '48.fw1', '48.fy1', '48.gh1', '48.gu1', '72.id1', '72.iq1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8112, -1, 8292, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 2628844613636, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ei1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ei1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831837
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.bh1', '12.by1'], 'contains': ['48.df1', '48.em1', '48.ft1', '48.fx1', '48.gc1', '48.gj1', '48.gy1', '72.ie1', '72.ir1'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6154, -1, 7677, -1], 'generators': [134983133510400, 26428580635, 16687, 1078121465, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ej1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ej1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831838
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.by1', '12.ca1'], 'contains': ['48.di1', '48.di2', '48.ft1', '48.gd1', '48.ge1', '72.is1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7853, -1, 9288, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 2647090220036, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ek1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ek1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831839
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '12.u1', '12.bh1'], 'contains': ['48.dc1', '48.db1', '48.fu1', '48.fv1', '48.gb1', '48.gf1', '48.gg1', '48.gj1', '48.gk1', '72.if1', '72.ig1', '72.it1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4727, -1, 6112, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.el1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.el1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831840
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '12.bz1', '12.ca1'], 'contains': ['48.dj1', '48.dm1', '48.fu1', '48.fw1', '48.gd1', '72.iu1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7951, -1, 9174, -1], 'generators': [134983133510400, 16687, 25514092800, 25430664104, 112608921600, 2647090220036, 30235, 9360177523200], 'label': '20736.hv.24.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.em1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.em1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165831841
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '12.bh1', '12.bz1'], 'contains': ['48.dk1', '48.ep1', '48.fu1', '48.fx1', '48.ga1', '48.gi1', '48.gk1', '72.ih1', '72.iv1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6297, -1, 7655, -1], 'generators': [134983133510400, 26428580635, 16687, 1078121465, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.en1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.en1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831842
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '12.f1', '12.g1', '12.be1', '12.bg1', '12.bj1', '12.bm1', '12.bs1', '12.bt1', '18.p1', '54.s1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5289, -1, 5583, -1], 'generators': [25514092800, 1078117201, 16687, 9360177523200, 4985, 2628844618652, 134983133510400, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.6.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.o1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165831843
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1', '12.bz1', '12.ca1'], 'contains': ['48.dl1', '48.dn1', '48.fu1', '48.fy1', '48.ge1', '72.iw1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7912, -1, 9208, -1], 'generators': [134983133510400, 16687, 25514092800, 25430664104, 112608921600, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.24.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.eo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eo1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831844
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '12.q1', '12.bk1'], 'contains': ['48.fv1', '48.fz1', '48.ga1', '48.gp1', '48.gq1', '48.gz1', '48.ha1', '72.ii1', '72.ik1', '72.ix1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4829, -1, 5306, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 112608921600, 30235, 25430669150, 9360177523200], 'label': '20736.hv.24.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ep1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ep1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831845
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.u1', '12.bk1'], 'contains': ['48.fv1', '48.gb1', '48.gc1', '48.gq1', '48.gr1', '48.hb1', '48.hc1', '72.ij1', '72.il1', '72.iy1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4497, -1, 5474, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 112608921600, 26468505950, 30235, 9360177523200], 'label': '20736.hv.24.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.eq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eq1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831846
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1', '12.by1', '12.bz1'], 'contains': ['48.dq1', '48.dv1', '48.fw1', '48.fx1', '48.ge1', '72.iz1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8306, -1, 9247, -1], 'generators': [134983133510400, 1078120744, 16687, 2646966471087, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.er1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.er1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165831847
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.bz1', '12.cb1'], 'contains': ['48.dr1', '48.ds1', '48.dx1', '48.dz1', '48.ey1', '48.ey2', '48.fw1', '48.fy1', '48.ga1', '48.gv1', '48.gw1', '72.im1', '72.ja1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8398, -1, 8338, -1], 'generators': [134983133510400, 16687, 25514092800, 26468474800, 112608921600, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.24.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.es1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.es1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831848
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '12.by1', '12.cb1'], 'contains': ['48.dt1', '48.eb1', '48.fw1', '48.gc1', '48.gd1', '72.jb1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8426, -1, 9265, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 25430638000, 2647090220036, 30235, 9360177523200], 'label': '20736.hv.24.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.et1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.et1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165831849
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1', '12.by1', '12.bz1'], 'contains': ['48.du1', '48.dw1', '48.fx1', '48.fy1', '48.gd1', '72.jc1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8328, -1, 9227, -1], 'generators': [134983133510400, 1078120744, 16687, 25514092800, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.24.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.eu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eu1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165831850
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.q1', '12.bk1'], 'contains': ['48.fx1', '48.fz1', '48.gb1', '48.gz1', '48.ha1', '48.hb1', '48.hc1', '72.in1', '72.io1', '72.jd1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2639, -1, 4753, -1], 'generators': [134983133510400, 26428580635, 16687, 1078121465, 112608921600, 30235, 25430669150, 9360177523200], 'label': '20736.hv.24.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.ev1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ev1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831852
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.bz1', '12.cb1'], 'contains': ['48.ea1', '48.ea2', '48.ga1', '48.gd1', '48.ge1', '72.jf1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8284, -1, 9331, -1], 'generators': [134983133510400, 16687, 25514092800, 26468474800, 112608921600, 2647090220036, 30235, 9360177523200], 'label': '20736.hv.24.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ex1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ex1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165831853
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '4.b1'], 'contains': ['16.a1', '24.eb1', '24.ec1', '32.a1', '32.e1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [361, -1, 320, -1], 'generators': [134983133510400, 721, 16687, 4985, 112608921600, 2646966474806, 46036847791741, 30235, 9360177523200], 'label': '20736.hv.8.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '8.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
  • id: 165831854
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '12.bi1', '12.ca1', '12.cb1'], 'contains': ['48.b1', '48.ee1', '48.eh1', '48.fw1', '48.ge1', '72.jh1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7786, -1, 9192, -1], 'generators': [134983133510400, 16687, 25514092800, 2628761147486, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.24.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ey1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ey1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165831855
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '12.bj1', '12.ca1', '12.cb1'], 'contains': ['48.b1', '48.ef1', '48.ei1', '48.fy1', '48.gd1', '72.ji1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7761, -1, 9153, -1], 'generators': [134983133510400, 16687, 25514092800, 1078116480, 112608921600, 1078146715, 2647090220036, 9360177523200], 'label': '20736.hv.24.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '24.ez1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ez1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165831856
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '12.bk1', '12.cb1'], 'contains': ['48.b1', '48.dp1', '48.eg1', '48.fz1', '48.ga1', '48.gb1', '48.gc1', '72.jj1', '72.jk1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6183, -1, 7758, -1], 'generators': [134983133510400, 26468479846, 16687, 25514092800, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.24.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.fa1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fa1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831857
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.cc1', '12.cd1'], 'contains': ['48.en1', '48.eo1', '48.ej1', '48.ek1', '48.gg1', '48.gh1', '48.gl1', '48.go1', '48.gw1', '72.jm1', '72.jr1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8240, -1, 6221, -1], 'generators': [134983133510400, 997953704, 16687, 25514097064, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.24.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fb1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165831858
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '12.q1', '12.cc1'], 'contains': ['48.gg1', '48.gi1', '48.gn1', '48.gp1', '48.ha1', '72.jn1', '72.js1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5218, -1, 5046, -1], 'generators': [134983133510400, 16687, 25430664104, 1078117201, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.24.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.fc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fc1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831859
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.q1', '12.u1'], 'contains': ['48.gf1', '48.gj1', '48.gk1', '48.gn1', '48.gq1', '48.hb1', '48.hc1', '72.jl1', '72.jt1', '72.ju1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2659, -1, 4626, -1], 'generators': [997953704, 1078117201, 30235, 16687, 9360177523200, 25514097785, 134983133510400, 112608921600], 'label': '20736.hv.24.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.fd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fd1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831860
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '12.cc1', '12.cd1'], 'contains': ['48.gg1', '48.gs1', '48.gt1', '72.jo1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7628, -1, 5928, -1], 'generators': [134983133510400, 997953704, 16687, 25514097064, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.24.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fe1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fe1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165831861
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '12.u1', '12.cd1'], 'contains': ['48.c1', '48.gf1', '48.gg1', '48.gq1', '48.gr1', '72.jp1', '72.jv1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5260, -1, 5545, -1], 'generators': [134983133510400, 26428555385, 997953704, 16687, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ff1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ff1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831862
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.q1'], 'contains': ['48.gi1', '48.gj1', '48.gk1', '48.gz1', '48.ha1', '48.hb1', '48.hd1', '72.jq1', '72.jw1', '72.jx1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1815, -1, 4389, -1], 'generators': [134983133510400, 997953704, 16687, 26428551121, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.24.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.fg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fg1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165831863
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '12.cc1', '12.ce1'], 'contains': ['48.et1', '48.ev1', '48.gl1', '48.gn1', '48.gt1', '72.kb1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7609, -1, 5724, -1], 'generators': [134983133510400, 16687, 1078121465, 26428551121, 2628761148086, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fi1', 'subgroup_fusion': None, 'weyl_group': '864.4080'}
  • id: 165831864
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '4.b1'], 'contains': ['16.a1', '24.a1', '24.ed1', '32.b1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [335, -1, 272, -1], 'generators': [134983133510400, 721, 16687, 4985, 112608921600, 46036847791741, 30235, 26468500904, 9360177523200], 'label': '20736.hv.8.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '8.b1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831865
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.ce1', '12.cf1'], 'contains': ['48.ez1', '48.fa1', '48.es1', '48.eu1', '48.gl1', '48.gm1', '48.go1', '48.gu1', '48.gv1', '72.jy1', '72.ka1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8222, -1, 6131, -1], 'generators': [134983133510400, 16687, 25514097064, 112608921600, 30235, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.24.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fh1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165831866
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '12.cc1', '12.cf1'], 'contains': ['48.gl1', '48.gp1', '48.gs1', '72.kc1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7238, -1, 5850, -1], 'generators': [134983133510400, 16687, 123754726, 25514097064, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.24.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fj1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831867
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '12.cd1', '12.ce1'], 'contains': ['48.gl1', '48.gr1', '48.gs1', '72.kd1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7656, -1, 5908, -1], 'generators': [134983133510400, 25430643046, 16687, 25514097064, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.24.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fk1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831868
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.o1', '12.ce1'], 'contains': ['48.gn1', '48.gm1', '48.gr1', '48.gy1', '48.gz1', '72.jz1', '72.ke1'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6515, -1, 5063, -1], 'generators': [26468500904, 1078117201, 30235, 16687, 9360177523200, 25514097785, 134983133510400, 112608921600], 'label': '20736.hv.24.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.fl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fl1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165831869
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1', '12.cc1', '12.ce1'], 'contains': ['48.fb1', '48.fc1', '48.gn1', '48.go1', '48.gs1', '72.kg1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7411, -1, 5427, -1], 'generators': [134983133510400, 16687, 1078121465, 26428551121, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.24.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fn1', 'subgroup_fusion': None, 'weyl_group': '864.4080'}
  • id: 165831870
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '12.ce1', '12.cf1'], 'contains': ['48.gm1', '48.gs1', '48.gt1', '72.kf1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7523, -1, 5887, -1], 'generators': [134983133510400, 16687, 25514097064, 112608921600, 2647090225052, 30235, 26468500904, 9360177523200], 'label': '20736.hv.24.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fm1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165831871
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1', '12.cc1', '12.cf1'], 'contains': ['48.go1', '48.gp1', '48.gt1', '72.kh1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7504, -1, 5870, -1], 'generators': [134983133510400, 16687, 123754726, 25514097064, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.24.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fo1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165831872
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1', '12.cd1', '12.ce1'], 'contains': ['48.go1', '48.gr1', '48.gt1', '72.ki1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7683, -1, 5945, -1], 'generators': [134983133510400, 25430643046, 16687, 25514097064, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.24.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fp1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165831873
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '12.bd1', '12.cd1', '12.cf1'], 'contains': ['48.c1', '48.ew1', '48.ex1', '48.gl1', '48.gt1', '72.kj1'], 'core': '48.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [7353, -1, 5669, -1], 'generators': [134983133510400, 26428555385, 16687, 2628761148086, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.24.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fq1', 'subgroup_fusion': None, 'weyl_group': '864.4080'}
  • id: 165831874
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1', '12.be1', '12.cd1', '12.cf1'], 'contains': ['48.c1', '48.eq1', '48.er1', '48.go1', '48.gs1', '72.kl1'], 'core': '48.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [5372, -1, 5362, -1], 'generators': [134983133510400, 26428555385, 16687, 1078117201, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.24.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.fr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fr1', 'subgroup_fusion': None, 'weyl_group': '864.4080'}
  • id: 165831875
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '4.b1'], 'contains': ['16.a1', '24.ee1', '24.ef1', '24.eg1', '32.c1', '32.d1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [280, -1, 206, -1], 'generators': [134983133510400, 721, 16687, 4985, 112608921600, 46036847791741, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.8.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '8.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831876
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1', '12.k1'], 'contains': ['48.gy1', '48.hc1', '48.hd1', '72.km1'], 'core': '96.A', 'coset_action_label': None, 'count': 2, 'diagramx': [1476, -1, 3815, -1], 'generators': [134983133510400, 16687, 26428551121, 112608921600, 30235, 26468500904, 25514097785, 9360177523200], 'label': '20736.hv.24.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.fs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fs1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831877
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1'], 'contains': ['48.hg1', '48.hh1', '48.hf1', '48.ho1', '48.hp1', '48.hq1', '48.hr1', '72.kn1'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [575, -1, 632, -1], 'generators': [134983133510400, 721, 1078121465, 7865729194652, 112608921600, 1078146715, 26428567087, 9360177523200], 'label': '20736.hv.24.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '24.ft1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ft1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165831878
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1'], 'contains': ['48.hg1', '48.hh1', '48.hk1', '48.hm1', '48.hn1', '48.hs1', '48.ht1', '72.ko1'], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [617, -1, 654, -1], 'generators': [134983133510400, 2628844614114, 25514092800, 1078142574, 1078117201, 1078116480, 112608921600, 9360177523200], 'label': '20736.hv.24.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '24.fu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fu1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165831879
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1'], 'contains': ['48.hv1', '48.hw1', '48.hx1', '48.ii1', '48.ij1', '48.im1', '48.in1', '72.kp1'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5858, -1, 2197, -1], 'generators': [26428567087, 25514093521, 2646966474806, 9360177523200, 25514097785, 134983133510400, 1078146715, 112608921600], 'label': '20736.hv.24.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '24.fv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fv1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165831880
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1'], 'contains': ['48.hv1', '48.hw1', '48.ia1', '48.ik1', '48.il1', '48.io1', '48.ip1', '72.kq1'], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [5746, -1, 2156, -1], 'generators': [134983133510400, 29514, 25514092800, 1078116480, 112608921600, 2646966489420, 19342, 9360177523200], 'label': '20736.hv.24.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '24.fw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fw1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165831881
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1'], 'contains': ['48.hm1', '48.hn1', '48.ho1', '48.hp1', '48.ic1', '48.id1', '48.ie1', '72.kr1'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [550, -1, 545, -1], 'generators': [1078132446, 134983133510400, 1078121465, 25514092800, 112608921600, 1078140940, 2628844618652, 9360177523200], 'label': '20736.hv.24.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '24.fx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fx1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165831882
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.k1', '12.f1'], 'contains': ['48.hq1', '48.hr1', '48.hs1', '48.ht1', '48.id1', '48.ie1', '48.ig1', '72.ks1'], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [490, -1, 460, -1], 'generators': [134983133510400, 26428580635, 1078121465, 1078133167, 112608921600, 2647090225052, 25514093521, 9360177523200], 'label': '20736.hv.24.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '24.fy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fy1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165831883
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1'], 'contains': ['48.ik1', '48.il1', '48.ii1', '48.ij1', '48.iq1', '48.ir1', '48.is1', '72.kt1'], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5837, -1, 2181, -1], 'generators': [134983133510400, 1078121465, 26428551121, 112608921600, 1078146715, 7879101314486, 26428567087, 9360177523200], 'label': '20736.hv.24.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '24.fz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.fz1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165831884
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '24.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.l1', '12.b1'], 'contains': ['48.im1', '48.in1', '48.io1', '48.ip1', '48.ir1', '48.is1', '48.iu1', '72.ku1'], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [5460, -1, 2011, -1], 'generators': [134983133510400, 4985, 25514092800, 1078117201, 1078116480, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.24.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '24.ga1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ga1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165831885
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['54.n1', '54.o1', '54.p1', '81.a1'], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [122, -1, 179, -1], 'generators': [25514092800, 41876802358141, 26468500904, 1078117201, 16687, 4985, 1078116480, 1078146715, 1321086788252], 'label': '20736.hv.27.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 165831886
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '4.c1'], 'contains': ['16.b1', '24.b1', '32.b1', '32.f1', '32.i1'], 'core': '24.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [87, -1, 86, -1], 'generators': [25514092800, 26468500904, 16687, 9360177523200, 134983133510400, 46036847791741, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.8.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.d1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 165831887
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['54.a1', '54.b1', '54.c1', '54.d1', '54.e1', '54.f1', '54.g1', '54.h1', '54.i1', '54.j1', '54.k1', '54.l1', '54.q1', '54.r1', '54.s1', '81.a1'], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [4096, -1, 6245, -1], 'generators': [25514092800, 26468500904, 126937858924800, 1078117201, 16687, 4985, 1078116480, 1078146715, 1321086788252], 'label': '20736.hv.27.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '27.b1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165831888
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.e1', '8.g1', '16.d1'], 'contains': ['64.a1'], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [253, -1, 227, -1], 'generators': [134983133510400, 46036847792341, 16687, 2646966474206, 112608921600, 30235, 9360177523200], 'label': '20736.hv.32.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '32.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 165831889
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.d1', '8.h1', '8.j1', '16.d1'], 'contains': ['64.a1', '96.A'], 'core': '96.A', 'coset_action_label': None, 'count': 16, 'diagramx': [238, -1, 198, -1], 'generators': [134983133510400, 16687, 112608921600, 46036847791741, 30235, 26468500904, 9360177523200], 'label': '20736.hv.32.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '32.b1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '1296.1790'}
  • id: 165831890
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.f1', '8.i1', '16.d1'], 'contains': ['64.a1'], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [209, -1, 173, -1], 'generators': [134983133510400, 46036847792341, 16687, 112608921600, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.32.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '32.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '1296.1790'}
  • id: 165831891
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.k1'], 'contains': ['64.b1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [156, -1, 79, -1], 'generators': [29514, 46036847797335, 9360177523200, 2628844618652, 134983133510400, 21769, 112608921600], 'label': '20736.hv.32.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '32.d1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '648.281'}
  • id: 165831892
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.l1'], 'contains': ['64.c1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [331, -1, 687, -1], 'generators': [134983133510400, 26094, 112608921600, 2646966489420, 46036847791741, 15966, 9360177523200], 'label': '20736.hv.32.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.e1', 'old_label': '32.e1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
  • id: 165831893
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '16.j1'], 'contains': ['64.d1'], 'core': '192.B', 'coset_action_label': None, 'count': 32, 'diagramx': [20, -1, 6, -1], 'generators': [134983133510400, 26428580635, 997953704, 1078133167, 112608921600, 46036847791741, 9360177523200], 'label': '20736.hv.32.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '32.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 165831894
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.l1', '16.j1'], 'contains': ['64.d1'], 'core': '192.B', 'coset_action_label': None, 'count': 32, 'diagramx': [55, -1, 48, -1], 'generators': [134983133510400, 26428580635, 2646966474206, 1078133167, 112608921600, 48913735030741, 9360177523200], 'label': '20736.hv.32.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '32.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 165831895
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '8.k1', '16.j1'], 'contains': ['64.d1'], 'core': '192.B', 'coset_action_label': None, 'count': 32, 'diagramx': [5, -1, 34, -1], 'generators': [134983133510400, 25514092800, 1078116480, 112608921600, 2647090225530, 48913735030741, 9360177523200], 'label': '20736.hv.32.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '32.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 165831896
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1'], 'contains': ['64.f1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [36, -1, 21, -1], 'generators': [134983133510400, 25430664104, 112608921600, 46036847791741, 1078140940, 26428567087, 9360177523200], 'label': '20736.hv.32.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.i1', 'old_label': '32.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1', 'subgroup_fusion': None, 'weyl_group': '648.705'}
  • id: 165831897
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '4.c1'], 'contains': ['16.b1', '24.ey1', '32.a1', '32.g1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [107, -1, 123, -1], 'generators': [134983133510400, 16687, 25514092800, 2628761147486, 1078116480, 112608921600, 1078146715, 48913735030741, 9360177523200], 'label': '20736.hv.8.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.e1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '3456.hx'}
  • id: 165831898
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1', '8.k1'], 'contains': ['64.g1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [83, -1, 99, -1], 'generators': [48913735006760, 134983133510400, 2647090245299, 26428569742, 112608921600, 1078141661, 9360177523200], 'label': '20736.hv.32.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.k1', 'old_label': '32.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1', 'subgroup_fusion': None, 'weyl_group': '648.703'}
  • id: 165831899
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '8.l1'], 'contains': ['64.e1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [313, -1, 1260, -1], 'generators': [134983133510400, 26428555385, 48913735023170, 1078117201, 112608921600, 2628761165811, 9360177523200], 'label': '20736.hv.32.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.j1', 'old_label': '32.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1', 'subgroup_fusion': None, 'weyl_group': '648.704'}
  • id: 165831900
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '18.o1'], 'contains': ['72.f1', '72.h1', '72.i1', '72.ch1', '72.cj1', '72.cl1', '72.co1', '72.kp1', '72.kq1', '72.kt1', '72.ku1'], 'core': '20736.a1', 'coset_action_label': '36T11999', 'count': 36, 'diagramx': [5740, -1, 3548, -1], 'generators': [721, 4985, 25514092800, 1078133167, 112608921600, 2646966474806, 1078146715, 9360177523200], 'label': '20736.hv.36.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.a1', 'projective_image': '20736.hv', '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': '288.1031'}
  • id: 165831901
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '18.o1'], 'contains': ['72.g1', '72.h1', '72.i1', '72.ci1', '72.cj1', '72.cn1', '72.co1'], 'core': '20736.a1', 'coset_action_label': '36T11998', 'count': 36, 'diagramx': [6070, -1, 4717, -1], 'generators': [4985, 25514092800, 1078117201, 1078116480, 112608921600, 2646966489420, 1078140940, 9360177523200], 'label': '20736.hv.36.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.b1', 'projective_image': '20736.hv', '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': '288.1031'}
  • id: 165831902
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '18.e1'], 'contains': ['72.q1', '72.s1', '72.t1', '72.u1', '72.ba1', '72.bb1', '72.bc1', '72.cu1', '72.cw1', '72.cy1', '72.da1', '72.dc1', '72.de1', '72.dg1', '72.di1'], 'core': '20736.a1', 'coset_action_label': '36T12207', 'count': 36, 'diagramx': [8876, -1, 9136, -1], 'generators': [1078120744, 25514092800, 1078133167, 112608921600, 1078146715, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.36.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.c1', 'projective_image': '20736.hv', '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': '576.8666'}
  • id: 165831903
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '18.e1'], 'contains': ['72.r1', '72.s1', '72.t1', '72.v1', '72.ba1', '72.bb1', '72.bd1', '72.cv1', '72.cx1', '72.cz1', '72.db1', '72.dd1', '72.df1', '72.dh1', '72.dj1'], 'core': '20736.a1', 'coset_action_label': '36T12215', 'count': 36, 'diagramx': [9012, -1, 9082, -1], 'generators': [1078120744, 25514092800, 1078133167, 112608921600, 2647090246018, 1078146715, 26468500904, 9360177523200], 'label': '20736.hv.36.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.d1', 'projective_image': '20736.hv', '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': '576.8666'}
  • id: 165831904
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '18.p1'], 'contains': ['72.x1', '72.y1', '72.bc1', '72.be1', '72.bp1', '72.bq1', '72.bs1', '72.kn1', '72.ko1', '72.kr1', '72.ks1'], 'core': '20736.a1', 'coset_action_label': '36T11985', 'count': 36, 'diagramx': [1401, -1, 1415, -1], 'generators': [4985, 25514092800, 1078133167, 1078117201, 112608921600, 1078146715, 2628844618652, 9360177523200], 'label': '20736.hv.36.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.e1', 'projective_image': '20736.hv', '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': '288.1031'}
  • id: 165831905
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.g1', '18.p1'], 'contains': ['72.y1', '72.z1', '72.bd1', '72.be1', '72.bq1', '72.br1', '72.bs1'], 'core': '20736.a1', 'coset_action_label': '36T11984', 'count': 36, 'diagramx': [1479, -1, 1856, -1], 'generators': [4985, 25514092800, 1078133167, 1078117201, 112608921600, 1078146715, 2647090225052, 9360177523200], 'label': '20736.hv.36.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.f1', 'projective_image': '20736.hv', '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': '288.1031'}
  • id: 165831906
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '18.e1'], 'contains': ['72.ca1', '72.cc1', '72.cd1', '72.ce1', '72.ck1', '72.cl1', '72.cm1', '72.cu1', '72.cv1', '72.cy1', '72.cz1', '72.dc1', '72.dd1', '72.dg1', '72.dh1'], 'core': '20736.a1', 'coset_action_label': '36T12205', 'count': 36, 'diagramx': [9140, -1, 9123, -1], 'generators': [25514092800, 1078133167, 112608921600, 1078146715, 2628844639618, 4264, 26468500904, 9360177523200], 'label': '20736.hv.36.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.g1', 'projective_image': '20736.hv', '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': '576.8666'}
  • id: 165831907
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.i1', '18.e1'], 'contains': ['72.cb1', '72.cc1', '72.ce1', '72.cf1', '72.ck1', '72.cm1', '72.cn1', '72.cw1', '72.cx1', '72.da1', '72.db1', '72.de1', '72.df1', '72.di1', '72.dj1'], 'core': '20736.a1', 'coset_action_label': '36T12206', 'count': 36, 'diagramx': [8997, -1, 9109, -1], 'generators': [25514092800, 25430664104, 1078133167, 112608921600, 1078146715, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.36.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.h1', 'projective_image': '20736.hv', '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': '576.8666'}
  • id: 165831908
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.n1', '8.a1', '8.e1', '8.g1', '8.l1', '54.o1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [314, 2951, 295, 7568], 'generators': [25514092800, 1078117201, 2646966474806, 16687, 9360177523200, 4985, 46036847791741, 134983133510400, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.2.b1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '20000.dv'}
  • id: 165831909
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '4.c1'], 'contains': ['16.b1', '24.ez1', '32.c1', '32.h1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [68, -1, 107, -1], 'generators': [134983133510400, 16687, 25514092800, 1078116480, 112608921600, 1078146715, 2647090220036, 48913735030741, 9360177523200], 'label': '20736.hv.8.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831910
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '18.i1'], 'contains': ['72.m1', '72.n1', '72.bg1', '72.bh1', '72.bw1', '72.bx1', '72.cq1', '72.cr1', '72.dk1', '72.ds1', '72.du1', '72.fp1', '72.fq1', '72.gb1', '72.gf1', '72.id1', '72.im1', '72.jr1', '72.jy1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7210, -1, 6015, -1], 'generators': [16687, 126937858924800, 25514092800, 9683982604800, 133913559622018, 30235, 4264, 26468500904], 'label': '20736.hv.36.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831911
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '18.n1'], 'contains': ['72.do1', '72.dt1', '72.eg1', '72.fm1', '72.fu1', '72.fz1', '72.gr1', '72.ib1', '72.ie1', '72.ij1', '72.io1', '72.jt1', '72.jx1', '72.jz1', '72.km1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2945, -1, 4527, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078117201, 112608921600, 30235, 26468500904], 'label': '20736.hv.36.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831912
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '18.i1'], 'contains': ['72.dk1', '72.dw1', '72.dx1', '72.fv1', '72.fw1', '72.gs1', '72.gt1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3133, -1, 3124, -1], 'generators': [16687, 126937858924800, 25514092800, 9683982604800, 133913559601052, 30235, 4264, 26468500904], 'label': '20736.hv.36.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831913
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '18.n1'], 'contains': ['72.dn1', '72.ea1', '72.ed1', '72.fo1', '72.fs1', '72.ga1', '72.gq1', '72.ic1', '72.ie1', '72.il1', '72.in1', '72.ju1', '72.jw1', '72.ke1', '72.km1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2768, -1, 4598, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078117201, 5324705527680, 30235, 26468500904], 'label': '20736.hv.36.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.l1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831914
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '18.n1'], 'contains': ['72.dl1', '72.dy1', '72.eb1', '72.fj1', '72.fn1', '72.fy1', '72.ga1', '72.ib1', '72.ic1', '72.ii1', '72.ik1', '72.js1', '72.jv1', '72.jz1', '72.kk1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4674, -1, 5032, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 1078117201, 112608921600, 30235, 26468500904], 'label': '20736.hv.36.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.m1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831915
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '18.n1'], 'contains': ['72.dq1', '72.dt1', '72.ef1', '72.fb1', '72.fg1', '72.fl1', '72.fu1', '72.if1', '72.ih1', '72.ii1', '72.in1', '72.jl1', '72.jq1', '72.js1', '72.jw1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2691, -1, 4459, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 25430664104, 1078117201, 112608921600, 30235], 'label': '20736.hv.36.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.n1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831916
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '18.n1'], 'contains': ['72.dr1', '72.ea1', '72.ee1', '72.fd1', '72.ff1', '72.fn1', '72.ft1', '72.ig1', '72.ih1', '72.ik1', '72.io1', '72.jn1', '72.jq1', '72.ju1', '72.jx1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2637, -1, 4585, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 25430664104, 1078117201, 5324705527680, 30235], 'label': '20736.hv.36.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.o1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831917
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '18.n1'], 'contains': ['72.dp1', '72.dz1', '72.eb1', '72.fc1', '72.fd1', '72.fk1', '72.fo1', '72.if1', '72.ig1', '72.ij1', '72.il1', '72.jl1', '72.jp1', '72.jt1', '72.jv1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4234, -1, 5268, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 25430664104, 1078117201, 112608921600, 30235], 'label': '20736.hv.36.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.p1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831918
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '18.i1'], 'contains': ['72.ds1', '72.dv1', '72.dx1', '72.gd1', '72.ge1', '72.gk1', '72.gl1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3363, -1, 3040, -1], 'generators': [26468479846, 16687, 126937858924800, 25514092800, 9683982604800, 133913559601052, 30235, 4264], 'label': '20736.hv.36.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.q1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831919
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1', '18.i1'], 'contains': ['72.du1', '72.dv1', '72.dw1', '72.gz1', '72.ha1', '72.he1', '72.hf1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3235, -1, 3104, -1], 'generators': [26468479846, 16687, 126937858924800, 25514092800, 9683982604800, 133913559622018, 30235, 4264], 'label': '20736.hv.36.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.r1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831920
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '4.d1'], 'contains': ['16.c1', '24.fq1', '32.a1', '32.j1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [297, -1, 363, -1], 'generators': [1078117201, 30235, 16687, 9360177523200, 134983133510400, 2628761148086, 26428555385, 112608921600, 48913735030141], 'label': '20736.hv.8.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '8.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165831921
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '18.n1'], 'contains': ['72.ei1', '72.el1', '72.ey1', '72.fc1', '72.ff1', '72.fy1', '72.gq1', '72.ip1', '72.ir1', '72.iy1', '72.jd1', '72.jl1', '72.jq1', '72.jz1', '72.km1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2652, -1, 4611, -1], 'generators': [16687, 4985, 25514092800, 1078117201, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.36.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.s1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831922
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '18.a1', '18.e1', '18.j1'], 'contains': ['72.q1', '72.r1', '72.bf1', '72.ca1', '72.cb1', '72.cp1', '72.eh1', '72.em1', '72.en1', '72.fe1', '72.gg1', '72.iq1', '72.ja1', '72.jm1', '72.ka1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7891, -1, 6797, -1], 'generators': [16687, 25514092800, 112608921600, 30235, 2628844639618, 4264, 26468500904, 9360177523200], 'label': '20736.hv.36.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.t1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831923
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '18.b1', '18.f1', '18.j1'], 'contains': ['72.eh1', '72.eq1', '72.es1', '72.fh1', '72.gu1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6013, -1, 6439, -1], 'generators': [16687, 25514092800, 112608921600, 30235, 4264, 26468500904, 2628844618652, 9360177523200], 'label': '20736.hv.36.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.u1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831924
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '18.b1', '18.e1', '18.k1'], 'contains': ['72.s1', '72.cc1', '72.eh1', '72.er1', '72.eu1', '72.is1', '72.jf1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7686, -1, 8453, -1], 'generators': [16687, 25514092800, 112608921600, 2647090246018, 30235, 4264, 26468500904, 9360177523200], 'label': '20736.hv.36.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.v1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831925
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '18.a1', '18.f1', '18.k1'], 'contains': ['72.eh1', '72.et1', '72.ev1', '72.jo1', '72.kf1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7478, -1, 6689, -1], 'generators': [16687, 25514092800, 112608921600, 2647090225052, 30235, 4264, 26468500904, 9360177523200], 'label': '20736.hv.36.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.w1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831926
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '18.a1', '18.b1', '18.n1'], 'contains': ['72.eh1', '72.eo1', '72.ew1', '72.fb1', '72.fz1', '72.ip1', '72.ix1', '72.jn1', '72.jp1', '72.ke1', '72.kk1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6033, -1, 5562, -1], 'generators': [16687, 1078121465, 25514092800, 1078117201, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.36.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.x1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831927
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '18.n1'], 'contains': ['72.ek1', '72.el1', '72.ex1', '72.fj1', '72.fk1', '72.fs1', '72.ft1', '72.it1', '72.iv1', '72.ix1', '72.jd1', '72.js1', '72.jt1', '72.jw1', '72.jx1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2676, -1, 4540, -1], 'generators': [16687, 4985, 25514092800, 25430664104, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.36.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.y1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831928
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '18.c1', '18.e1', '18.l1'], 'contains': ['72.t1', '72.cd1', '72.cf1', '72.ej1', '72.em1', '72.er1', '72.iu1', '72.jb1'], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [8462, -1, 8377, -1], 'generators': [16687, 25514092800, 25430664104, 112608921600, 2647090246018, 30235, 4264, 9360177523200], 'label': '20736.hv.36.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.z1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831929
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1', '18.d1', '18.e1', '18.m1'], 'contains': ['72.u1', '72.v1', '72.ce1', '72.ej1', '72.en1', '72.eu1', '72.iw1', '72.je1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7521, -1, 8391, -1], 'generators': [16687, 25514092800, 25430664104, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.36.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.ba1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831930
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '18.d1', '18.f1', '18.l1'], 'contains': ['72.cs1', '72.ej1', '72.eq1', '72.et1'], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5600, -1, 6960, -1], 'generators': [16687, 25514092800, 25430664104, 112608921600, 2647090225052, 30235, 4264, 9360177523200], 'label': '20736.hv.36.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.bb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831931
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '4.d1'], 'contains': ['16.c1', '24.c1', '32.b1'], 'core': '24.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [256, -1, 344, -1], 'generators': [134983133510400, 26428555385, 16687, 1078117201, 112608921600, 46036847791741, 30235, 26468500904, 9360177523200], 'label': '20736.hv.8.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '8.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 165831932
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1', '18.c1', '18.f1', '18.m1'], 'contains': ['72.bi1', '72.ej1', '72.es1', '72.ev1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6721, -1, 6980, -1], 'generators': [16687, 25514092800, 25430664104, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.36.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831933
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '18.c1', '18.d1', '18.n1'], 'contains': ['72.ej1', '72.ep1', '72.ew1', '72.fl1', '72.fm1', '72.it1', '72.iy1', '72.ju1', '72.jv1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [4651, -1, 5696, -1], 'generators': [16687, 1078121465, 25514092800, 25430664104, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.36.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831934
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '18.a1', '18.g1', '18.l1'], 'contains': ['72.em1', '72.eo1', '72.et1', '72.kc1', '72.kd1'], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6223, -1, 6521, -1], 'generators': [25430643046, 16687, 25514092800, 112608921600, 2647090225052, 30235, 4264, 9360177523200], 'label': '20736.hv.36.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.be1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831935
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '18.c1', '18.g1', '18.j1'], 'contains': ['72.em1', '72.ep1', '72.es1', '72.gm1', '72.gn1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5295, -1, 6057, -1], 'generators': [26468479846, 16687, 25514092800, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.36.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831936
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1', '18.a1', '18.h1', '18.m1'], 'contains': ['72.en1', '72.eo1', '72.ev1', '72.kh1', '72.ki1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7449, -1, 6544, -1], 'generators': [25430643046, 16687, 25514092800, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.36.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831937
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1', '18.d1', '18.h1', '18.j1'], 'contains': ['72.en1', '72.ep1', '72.eq1', '72.hb1', '72.hc1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5319, -1, 6078, -1], 'generators': [26468479846, 16687, 25514092800, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.36.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831938
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1', '18.b1', '18.h1', '18.l1'], 'contains': ['72.eo1', '72.eq1', '72.er1'], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6810, -1, 6711, -1], 'generators': [25430643046, 16687, 25514092800, 112608921600, 2647090246018, 30235, 4264, 9360177523200], 'label': '20736.hv.36.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.bi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831939
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1', '18.b1', '18.g1', '18.m1'], 'contains': ['72.eo1', '72.es1', '72.eu1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6745, -1, 6668, -1], 'generators': [25430643046, 16687, 25514092800, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.36.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831940
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1', '18.c1', '18.h1', '18.k1'], 'contains': ['72.ep1', '72.er1', '72.ev1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7249, -1, 6923, -1], 'generators': [26468479846, 16687, 25514092800, 112608921600, 2647090246018, 30235, 4264, 9360177523200], 'label': '20736.hv.36.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831941
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1', '18.d1', '18.g1', '18.k1'], 'contains': ['72.ep1', '72.et1', '72.eu1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5496, -1, 6910, -1], 'generators': [26468479846, 16687, 25514092800, 112608921600, 2647090225052, 30235, 4264, 9360177523200], 'label': '20736.hv.36.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165831942
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '4.d1'], 'contains': ['16.c1', '24.fr1', '32.c1', '32.k1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [188, -1, 254, -1], 'generators': [1078117201, 2647090225052, 30235, 16687, 9360177523200, 134983133510400, 26428555385, 112608921600, 48913735030141], 'label': '20736.hv.8.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '8.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '50000.bq'}
  • id: 165831943
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '18.a1', '18.c1', '18.o1'], 'contains': ['72.bj1', '72.ch1', '72.ci1', '72.em1', '72.ev1', '72.ew1', '72.kb1', '72.kj1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7366, -1, 5811, -1], 'generators': [16687, 1078121465, 25514092800, 2628761148086, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.36.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831944
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1', '18.a1', '18.d1', '18.p1'], 'contains': ['72.x1', '72.z1', '72.ct1', '72.en1', '72.et1', '72.ew1', '72.kg1', '72.kl1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5581, -1, 5683, -1], 'generators': [16687, 1078121465, 25514092800, 1078117201, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.36.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831945
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1', '18.b1', '18.d1', '18.o1'], 'contains': ['72.cj1', '72.eq1', '72.eu1', '72.ew1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5990, -1, 6266, -1], 'generators': [16687, 1078121465, 25514092800, 1078117201, 112608921600, 2646966474806, 30235, 9360177523200], 'label': '20736.hv.36.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831946
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1', '18.b1', '18.c1', '18.p1'], 'contains': ['72.y1', '72.er1', '72.es1', '72.ew1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6052, -1, 6253, -1], 'generators': [16687, 1078121465, 25514092800, 1078117201, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.36.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831947
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '18.n1'], 'contains': ['72.p1', '72.w1', '72.bz1', '72.cg1', '72.dl1', '72.dn1', '72.dp1', '72.dr1', '72.ei1', '72.ek1', '72.ez1', '72.ib1', '72.ie1', '72.if1', '72.ih1', '72.ip1', '72.it1', '72.jg1', '72.jk1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4895, -1, 6305, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078116480, 1078146715, 5324705527680, 26468500904], 'label': '20736.hv.36.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.bq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831948
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '18.e1', '18.f1', '18.n1'], 'contains': ['72.o1', '72.ba1', '72.by1', '72.ck1', '72.do1', '72.dq1', '72.eh1', '72.ej1', '72.fa1', '72.ic1', '72.ig1', '72.ir1', '72.iv1', '72.jg1', '72.jj1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6428, -1, 7633, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078116480, 112608921600, 1078146715, 26468500904], 'label': '20736.hv.36.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.br1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831949
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1', '18.n1'], 'contains': ['72.dy1', '72.dz1', '72.ed1', '72.ee1', '72.ex1', '72.ey1', '72.ez1', '72.ii1', '72.ij1', '72.in1', '72.io1', '72.ix1', '72.iy1', '72.jj1', '72.jk1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4473, -1, 5457, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078116480, 1078146715, 5324705527680, 25430669150], 'label': '20736.hv.36.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.bs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831950
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1', '18.e1', '18.g1', '18.o1'], 'contains': ['72.bb1', '72.cl1', '72.cn1', '72.em1', '72.eu1', '72.fa1', '72.iz1', '72.jh1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7096, -1, 8321, -1], 'generators': [1078120744, 16687, 2646966471087, 25514092800, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.36.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831951
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1', '18.e1', '18.h1', '18.p1'], 'contains': ['72.bc1', '72.bd1', '72.cm1', '72.en1', '72.er1', '72.fa1', '72.jc1', '72.ji1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7314, -1, 8308, -1], 'generators': [1078120744, 16687, 25514092800, 1078116480, 112608921600, 1078146715, 2628844639618, 9360177523200], 'label': '20736.hv.36.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831952
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1', '18.g1', '18.h1', '18.n1'], 'contains': ['72.ef1', '72.eg1', '72.eo1', '72.ep1', '72.fa1', '72.ik1', '72.il1', '72.jd1', '72.jk1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [4964, -1, 6095, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078116480, 112608921600, 1078146715, 25430669150], 'label': '20736.hv.36.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831953
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['16.e1', '24.fs1', '32.b1'], 'core': '96.A', 'coset_action_label': None, 'count': 8, 'diagramx': [218, -1, 235, -1], 'generators': [134983133510400, 16687, 26428551121, 112608921600, 46036847791741, 30235, 26468500904, 25514097785, 9360177523200], 'label': '20736.hv.8.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.j1', 'old_label': '8.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '200000.p'}
  • id: 165831954
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1', '18.f1', '18.h1', '18.o1'], 'contains': ['72.co1', '72.eq1', '72.ev1', '72.fa1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6136, -1, 6732, -1], 'generators': [25514092800, 16687, 2646966474806, 9360177523200, 1078116480, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.36.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831955
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1', '18.f1', '18.g1', '18.p1'], 'contains': ['72.be1', '72.es1', '72.et1', '72.fa1'], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5975, -1, 6562, -1], 'generators': [25514092800, 16687, 9360177523200, 2628844618652, 1078116480, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.36.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bx1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831956
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1', '18.j1'], 'contains': ['72.fe1', '72.fg1', '72.fh1', '72.gj1', '72.gn1', '72.gy1', '72.hc1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3899, -1, 4065, -1], 'generators': [997953704, 30235, 25514093521, 16687, 9360177523200, 2628844618652, 25514097785, 112608921600], 'label': '20736.hv.36.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '36.by1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.by1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
  • id: 165831957
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1', '18.i1'], 'contains': ['72.fp1', '72.fr1', '72.fw1', '72.gc1', '72.ge1', '72.gw1', '72.ha1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2381, -1, 2954, -1], 'generators': [134983133510400, 997953704, 16687, 1321086788252, 30235, 25514093521, 25514097785, 9360177523200], 'label': '20736.hv.36.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.bz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bz1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831958
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1', '18.i1'], 'contains': ['72.fq1', '72.fr1', '72.fv1', '72.gi1', '72.gl1', '72.gx1', '72.hf1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2355, -1, 2899, -1], 'generators': [89377906464721, 997953704, 16687, 126937858924800, 9683982604800, 89377906468985, 30235, 2628844618652], 'label': '20736.hv.36.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.ca1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ca1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831959
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1', '18.i1'], 'contains': ['72.gc1', '72.gb1', '72.gd1', '72.gp1', '72.gx1', '72.gt1', '72.he1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3111, -1, 2879, -1], 'generators': [16687, 126937858924800, 9683982604800, 133913559601052, 30235, 25514093521, 26468500904, 25514097785], 'label': '20736.hv.36.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.cb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cb1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831960
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1', '18.i1'], 'contains': ['72.gi1', '72.gf1', '72.gk1', '72.gp1', '72.gw1', '72.gs1', '72.gz1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3192, -1, 2847, -1], 'generators': [134983133510400, 16687, 1321086788252, 30235, 25514093521, 26468500904, 25514097785, 9360177523200], 'label': '20736.hv.36.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.cc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cc1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831961
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1', '18.j1'], 'contains': ['72.gj1', '72.gg1', '72.gm1', '72.gr1', '72.gy1', '72.gu1', '72.hb1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4166, -1, 4094, -1], 'generators': [26468500904, 30235, 25514093521, 16687, 9360177523200, 2628844618652, 25514097785, 112608921600], 'label': '20736.hv.36.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '36.cd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cd1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
  • id: 165831962
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '18.i1'], 'contains': ['72.dk1', '72.dm1', '72.dv1', '72.ec1', '72.fi1', '72.fr1', '72.fx1', '72.gp1', '72.hg1', '72.hk1', '72.hs1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2120, -1, 3307, -1], 'generators': [721, 16687, 4985, 126937858924800, 25514092800, 9683982604800, 30235, 26468500904], 'label': '20736.hv.36.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.ce1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ce1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165831963
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '18.n1'], 'contains': ['72.dl1', '72.dn1', '72.do1', '72.dz1', '72.ee1', '72.ef1', '72.fk1', '72.fl1', '72.ft1', '72.fy1', '72.fz1', '72.gq1', '72.hh1', '72.hl1', '72.ht1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2719, -1, 4110, -1], 'generators': [721, 16687, 4985, 126937858924800, 25514092800, 112608921600, 30235, 26468500904], 'label': '20736.hv.36.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.cf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cf1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165831964
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['16.f1', '24.fy1', '32.d1', '32.h1', '32.k1'], 'core': '192.B', 'coset_action_label': None, 'count': 16, 'diagramx': [130, -1, 143, -1], 'generators': [26428551121, 1078133167, 9360177523200, 2628844618652, 25514097785, 134983133510400, 26428580635, 112608921600, 48913735030141], 'label': '20736.hv.8.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.k1', 'old_label': '8.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 165831965
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '18.n1'], 'contains': ['72.dp1', '72.dq1', '72.dr1', '72.dy1', '72.ed1', '72.eg1', '72.fb1', '72.fc1', '72.ff1', '72.fj1', '72.fm1', '72.fs1', '72.hh1', '72.hj1', '72.hl1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3852, -1, 5445, -1], 'generators': [721, 16687, 4985, 126937858924800, 25514092800, 25430664104, 112608921600, 30235], 'label': '20736.hv.36.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '36.cg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cg1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165831966
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '18.i1'], 'contains': ['72.b1', '72.c1', '72.j1', '72.k1', '72.ds1', '72.dw1', '72.gc1', '72.gi1', '72.hg1', '72.hm1', '72.hn1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3504, -1, 3011, -1], 'generators': [133937077482806, 721, 16687, 4985, 126937858924800, 25514092800, 9683982604800, 30235], 'label': '20736.hv.36.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.ch1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ch1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165831967
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '18.i1'], 'contains': ['72.bl1', '72.bm1', '72.bt1', '72.bu1', '72.du1', '72.dx1', '72.gw1', '72.gx1', '72.hg1', '72.hv1', '72.hy1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1681, -1, 2457, -1], 'generators': [126937858924800, 9683982604800, 89377906464000, 721, 30235, 16687, 4985, 2628844618652], 'label': '20736.hv.36.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.ci1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ci1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165831968
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '18.j1', '18.k1', '18.n1'], 'contains': ['72.eh1', '72.ei1', '72.ep1', '72.ex1', '72.fd1', '72.fg1', '72.ga1', '72.gr1', '72.hi1', '72.hj1', '72.ht1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [3387, -1, 4669, -1], 'generators': [721, 16687, 4985, 25514092800, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.36.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cj1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831969
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '18.l1', '18.m1', '18.n1'], 'contains': ['72.ej1', '72.ek1', '72.eo1', '72.ey1', '72.fn1', '72.fo1', '72.fu1', '72.hi1', '72.hl1'], 'core': '1296.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4624, -1, 5709, -1], 'generators': [721, 16687, 4985, 25514092800, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.36.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.ck1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ck1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831970
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '18.j1', '18.l1', '18.o1'], 'contains': ['72.f1', '72.g1', '72.l1', '72.em1', '72.eq1', '72.gj1', '72.hi1', '72.ho1'], 'core': '1296.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5267, -1, 4704, -1], 'generators': [721, 16687, 4985, 25514092800, 112608921600, 2646966474806, 30235, 9360177523200], 'label': '20736.hv.36.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.cl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cl1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831971
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '18.j1', '18.m1', '18.p1'], 'contains': ['72.bp1', '72.br1', '72.bv1', '72.en1', '72.es1', '72.gy1', '72.hi1', '72.hw1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [3690, -1, 3396, -1], 'generators': [721, 16687, 4985, 25514092800, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.36.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cm1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831972
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1', '18.k1', '18.l1', '18.p1'], 'contains': ['72.bq1', '72.er1', '72.et1', '72.hi1'], 'core': '1296.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5347, -1, 6499, -1], 'generators': [721, 16687, 4985, 25514092800, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.36.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.cn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cn1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831973
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '18.k1', '18.m1', '18.o1'], 'contains': ['72.h1', '72.eu1', '72.ev1', '72.hi1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6784, -1, 6283, -1], 'generators': [721, 16687, 4985, 25514092800, 2628761148086, 112608921600, 30235, 9360177523200], 'label': '20736.hv.36.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.co1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.co1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165831974
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '18.n1', '18.o1', '18.p1'], 'contains': ['72.a1', '72.d1', '72.e1', '72.i1', '72.bk1', '72.bn1', '72.bo1', '72.bs1', '72.dt1', '72.ea1', '72.eb1', '72.el1', '72.ew1', '72.ez1', '72.fa1', '72.hh1', '72.hi1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [2187, -1, 2429, -1], 'generators': [25514092800, 126937858924800, 1078117201, 16687, 4985, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.36.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cp1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165831975
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['16.h1', '24.ga1', '32.e1', '32.g1', '32.j1'], 'core': '192.B', 'coset_action_label': None, 'count': 16, 'diagramx': [315, -1, 694, -1], 'generators': [134983133510400, 48913735030141, 26428580635, 721, 4985, 1078133167, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.8.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.l1', 'old_label': '8.l1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': '4374.r'}
  • id: 165831976
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '18.j1'], 'contains': ['72.fe1', '72.fh1', '72.gm1', '72.hb1', '72.hj1', '72.ho1', '72.hw1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4135, -1, 4342, -1], 'generators': [997953704, 721, 30235, 16687, 9360177523200, 4985, 2628844618652, 112608921600], 'label': '20736.hv.36.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '36.cq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cq1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165831977
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '18.i1'], 'contains': ['72.fp1', '72.fv1', '72.gd1', '72.gz1', '72.hk1', '72.hm1', '72.hv1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2968, -1, 2994, -1], 'generators': [126937858924800, 997953704, 9683982604800, 721, 30235, 16687, 4985, 2628844618652], 'label': '20736.hv.36.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.cr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cr1', 'subgroup_fusion': None, 'weyl_group': '192.1358'}
  • id: 165831978
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '18.i1'], 'contains': ['72.fq1', '72.fw1', '72.gk1', '72.he1', '72.hk1', '72.hn1', '72.hy1'], 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2995, -1, 2974, -1], 'generators': [134983133510400, 997953704, 721, 16687, 4985, 1321086788252, 30235, 9360177523200], 'label': '20736.hv.36.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '36.cs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cs1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831979
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '18.i1'], 'contains': ['72.gb1', '72.ge1', '72.gs1', '72.hf1', '72.hm1', '72.hs1', '72.hy1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2167, -1, 2503, -1], 'generators': [134983133510400, 721, 16687, 4985, 1321086788252, 30235, 26468500904, 9360177523200], 'label': '20736.hv.36.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.ct1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ct1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831980
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1'], 'contains': ['72.hq1', '72.hr1', '72.hz1'], 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [651, -1, 313, -1], 'generators': [41876802358141, 26468500904, 132523584036480, 721, 30235, 16687, 4985, 1321086788252], 'label': '20736.hv.36.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1', 'old_label': '36.cu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cu1', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
  • id: 165831981
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '18.i1'], 'contains': ['72.gf1', '72.gl1', '72.gt1', '72.ha1', '72.hn1', '72.hs1', '72.hv1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2217, -1, 2484, -1], 'generators': [721, 16687, 4985, 126937858924800, 9683982604800, 133913559601052, 30235, 26468500904], 'label': '20736.hv.36.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.cv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cv1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165831982
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '18.j1'], 'contains': ['72.gg1', '72.gn1', '72.gu1', '72.hc1', '72.ho1', '72.ht1', '72.hw1'], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3457, -1, 3645, -1], 'generators': [26468500904, 721, 30235, 16687, 9360177523200, 4985, 2628844618652, 112608921600], 'label': '20736.hv.36.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '36.cw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cw1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
  • id: 165831983
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '12.bx1'], 'contains': ['72.gh1', '72.go1', '72.gv1', '72.hd1', '72.hp1', '72.hu1', '72.hx1'], 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1353, -1, 1748, -1], 'generators': [134983133510400, 721, 16687, 4985, 9683982604800, 8371035965852, 30235, 26468500904], 'label': '20736.hv.36.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cx1', 'old_label': '36.cx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cx1', 'subgroup_fusion': None, 'weyl_group': '288.631'}
  • id: 165831984
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1', '18.e1'], 'contains': ['72.cu1', '72.cv1', '72.cw1', '72.cx1', '72.iq1', '72.ir1', '72.is1', '72.iz1', '72.jb1', '72.jc1', '72.je1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8667, -1, 8924, -1], 'generators': [1078120744, 16687, 25514092800, 112608921600, 30235, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.36.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.cy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cy1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165831985
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1', '18.e1'], 'contains': ['72.cy1', '72.cz1', '72.da1', '72.db1', '72.iu1', '72.iv1', '72.iw1', '72.iz1', '72.ja1', '72.jc1', '72.jf1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8487, -1, 8781, -1], 'generators': [1078120744, 16687, 25514092800, 25430664104, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.36.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.cz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cz1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165831986
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.a1', '18.b1', '18.c1', '18.d1', '18.e1', '18.f1', '18.g1', '18.h1', '18.j1', '18.k1', '18.l1', '18.m1', '18.n1', '18.o1', '18.p1', '81.a1'], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5831, -1, 6328, -1], 'generators': [25514092800, 26468500904, 1078117201, 16687, 9360177523200, 4985, 2628844618652, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.9.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '20736.hv', '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': '1152.43028'}
  • id: 165831987
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1', '18.e1'], 'contains': ['72.dc1', '72.dd1', '72.de1', '72.df1', '72.iq1', '72.is1', '72.iu1', '72.iw1', '72.jg1', '72.jh1', '72.ji1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7752, -1, 8751, -1], 'generators': [16687, 25514092800, 1078116480, 112608921600, 1078146715, 2647090220036, 26468500904, 9360177523200], 'label': '20736.hv.36.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.da1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.da1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165831988
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1', '18.e1'], 'contains': ['72.dg1', '72.dh1', '72.di1', '72.dj1', '72.ja1', '72.jb1', '72.je1', '72.jf1', '72.jh1', '72.ji1', '72.jj1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8647, -1, 8945, -1], 'generators': [16687, 25514092800, 1078116480, 112608921600, 1078146715, 25430638000, 2647090220036, 9360177523200], 'label': '20736.hv.36.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.db1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.db1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165831989
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1', '18.a1'], 'contains': ['72.jm1', '72.jn1', '72.jo1', '72.kb1', '72.kc1', '72.kg1', '72.kh1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8003, -1, 5973, -1], 'generators': [997953704, 16687, 1078121465, 26428551121, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.36.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.dc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dc1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831990
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1', '18.a1'], 'contains': ['72.jm1', '72.jo1', '72.jp1', '72.kd1', '72.ki1', '72.kj1', '72.kl1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8017, -1, 5999, -1], 'generators': [997953704, 1078117201, 2647090225052, 30235, 16687, 9360177523200, 26428555385, 112608921600], 'label': '20736.hv.36.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.dd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dd1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831991
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1', '18.a1'], 'contains': ['72.kb1', '72.ka1', '72.kd1', '72.ke1', '72.kg1', '72.kf1', '72.ki1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7988, -1, 5986, -1], 'generators': [16687, 1078121465, 26428551121, 112608921600, 2647090225052, 30235, 26468500904, 9360177523200], 'label': '20736.hv.36.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.de1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.de1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831992
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '36.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1', '18.a1'], 'contains': ['72.ka1', '72.kc1', '72.kf1', '72.kh1', '72.kj1', '72.kk1', '72.kl1'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7506, -1, 5960, -1], 'generators': [26468500904, 1078117201, 2647090225052, 30235, 16687, 9360177523200, 26428555385, 112608921600], 'label': '20736.hv.36.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.df1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.df1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165831993
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.dz1', '24.ea1', '24.eb1', '24.ee1'], 'contains': [], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1900, 9090, 2310, 763], 'generators': [134983133510400, 721, 16687, 4985, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.a1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': ['12.a1', '24.a1'], 'normal_contains': ['192.A', '1296.A'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 165831994
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.b1', '24.dh1', '24.ey1', '24.ez1', '24.fa1'], 'contains': [], 'core': '48.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5479, 2390, 8372, 7711], 'generators': [134983133510400, 16687, 25514092800, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.48.b1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': ['12.a1', '24.b1'], 'normal_contains': ['192.A', '192.B'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 165831995
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '24.c1', '24.de1', '24.ff1', '24.fq1', '24.fr1'], 'contains': [], 'core': '48.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5196, 5255, 4893, 5187], 'generators': [134983133510400, 26428555385, 16687, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.c1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': ['12.a1', '24.c1'], 'normal_contains': ['192.A'], 'normalizer': '1.a1', 'old_label': '48.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 165831996
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.bb1', '24.de1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5004, -1, 1514, -1], 'generators': [1078117201, 24460, 9360177523200, 134983133510400, 26428580635, 26428555385, 112608921600], 'label': '20736.hv.48.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.d1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165831997
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1', '6.n1', '6.o1'], 'contains': ['24.d1', '24.h1', '24.bb1', '24.bf1', '24.cu1', '24.de1', '24.dh1', '24.dz1', '36.cp1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2133, 2765, 2140, 5768], 'generators': [134983133510400, 16687, 4985, 25514092800, 1078117201, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.12.a1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['48.a1', '48.b1', '48.c1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '20736.hv', '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': '1296.3490'}
  • id: 165831998
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.bf1', '24.cu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [848, -1, 890, -1], 'generators': [134983133510400, 1078135822, 721, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.e1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165831999
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.bf1', '24.de1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [923, -1, 913, -1], 'generators': [134983133510400, 26428580635, 4985, 1078117201, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832000
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.bb1', '24.cu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1233, -1, 1432, -1], 'generators': [134983133510400, 721, 1078121465, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832001
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.bb1', '24.dh1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1129, -1, 1244, -1], 'generators': [134983133510400, 4985, 25514109487, 1078116480, 112608921600, 1078140940, 9360177523200], 'label': '20736.hv.48.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832002
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.bf1', '24.cu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1258, -1, 1090, -1], 'generators': [134983133510400, 25514092800, 1078117201, 24460, 112608921600, 19342, 9360177523200], 'label': '20736.hv.48.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832003
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.bf1', '24.dh1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [5029, -1, 1410, -1], 'generators': [134983133510400, 4985, 25514092800, 1078133167, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.48.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832004
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.bb1', '24.cu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1104, -1, 1068, -1], 'generators': [1078117201, 24460, 9360177523200, 4985, 134983133510400, 25514109487, 112608921600], 'label': '20736.hv.48.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832005
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.h1', '24.dz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3598, -1, 1456, -1], 'generators': [134983133510400, 26428555385, 26428580635, 26428551121, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.l1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 165832006
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.f1', '24.g1', '24.h1', '24.dz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4792, -1, 2544, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 15966, 19342, 9360177523200], 'label': '20736.hv.48.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '48.m1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 165832007
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.i1', '24.dz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3569, -1, 2350, -1], 'generators': [134983133510400, 25514109487, 24460, 112608921600, 25514093521, 25514097785, 9360177523200], 'label': '20736.hv.48.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '48.n1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 165832008
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.n1'], 'contains': ['24.e1', '24.g1', '24.h1', '24.bo1', '24.bq1', '24.bs1', '24.bv1', '24.fv1', '24.fw1', '24.fz1', '24.ga1', '36.a1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5744, -1, 2995, -1], 'generators': [134983133510400, 721, 4985, 25514092800, 1078133167, 112608921600, 2646966474806, 1078146715, 9360177523200], 'label': '20736.hv.12.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '12.b1', 'projective_image': '20736.hv', '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': '864.4700'}
  • id: 165832009
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.i1', '24.eb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3771, -1, 2678, -1], 'generators': [134983133510400, 721, 4985, 24460, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.48.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.br1', 'old_label': '48.o1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 165832010
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '24.i1', '24.eb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3817, -1, 2949, -1], 'generators': [134983133510400, 721, 4985, 2646966496929, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.br1', 'old_label': '48.p1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 165832011
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '24.t1', '24.cq1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6720, -1, 8212, -1], 'generators': [134983133510400, 25514092800, 112608921600, 30235, 19342, 26468500904, 9360177523200], 'label': '20736.hv.48.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.q1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832012
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '24.t1', '24.cs1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6700, -1, 8284, -1], 'generators': [134983133510400, 25514109487, 25430664104, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.r1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832013
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bb1', '24.bf1', '24.cu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1053, -1, 1046, -1], 'generators': [1078117201, 24460, 9360177523200, 25514097785, 134983133510400, 26428580635, 112608921600], 'label': '20736.hv.48.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.s1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832014
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.k1', '24.l1', '24.t1', '24.cp1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9164, -1, 8476, -1], 'generators': [134983133510400, 26428580635, 112608921600, 30235, 19342, 26468500904, 9360177523200], 'label': '20736.hv.48.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.t1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832015
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '24.n1', '24.o1', '24.t1', '24.cr1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8405, -1, 9468, -1], 'generators': [134983133510400, 26428580635, 997953704, 112608921600, 30235, 19342, 9360177523200], 'label': '20736.hv.48.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.u1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832016
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.k1', '24.m1', '24.u1', '24.ct1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9193, -1, 8531, -1], 'generators': [134983133510400, 2646966471087, 20063, 25514092800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.v1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832017
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.n1', '24.q1', '24.v1', '24.bc1', '24.cv1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7111, -1, 7480, -1], 'generators': [134983133510400, 20063, 25514092800, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.48.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.w1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165832018
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.l1', '24.m1', '24.r1', '24.v1', '24.w1', '24.bd1', '24.cz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7351, -1, 8412, -1], 'generators': [134983133510400, 20063, 25514092800, 24460, 112608921600, 2647090246018, 9360177523200], 'label': '20736.hv.48.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.x1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832019
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.o1', '8.c1', '8.f1', '8.i1', '8.k1', '54.p1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [153, 910, 181, 5768], 'generators': [25514092800, 1078117201, 16687, 9360177523200, 4985, 2628844618652, 134983133510400, 46036847791741, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.2.c1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165832020
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.n1'], 'contains': ['24.f1', '24.g1', '24.h1', '24.bp1', '24.bq1', '24.bu1', '24.bv1', '36.b1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5777, -1, 3526, -1], 'generators': [134983133510400, 4985, 25514092800, 1078117201, 1078116480, 112608921600, 2646966489420, 1078140940, 9360177523200], 'label': '20736.hv.12.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '12.c1', 'projective_image': '20736.hv', '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': '864.4700'}
  • id: 165832021
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.o1', '24.s1', '24.w1', '24.be1', '24.cv1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7140, -1, 7534, -1], 'generators': [134983133510400, 20063, 25514092800, 24460, 112608921600, 2628844644964, 9360177523200], 'label': '20736.hv.48.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.y1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165832022
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1', '24.x1', '24.bc1', '24.be1', '24.da1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1284, -1, 1718, -1], 'generators': [134983133510400, 20063, 25514092800, 24460, 112608921600, 2628844618652, 9360177523200], 'label': '20736.hv.48.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '48.z1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1', 'subgroup_fusion': None, 'weyl_group': '864.4701'}
  • id: 165832023
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '24.s1', '24.x1', '24.bd1', '24.db1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1764, -1, 1742, -1], 'generators': [134983133510400, 20063, 25514092800, 24460, 112608921600, 2647090220514, 9360177523200], 'label': '20736.hv.48.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '48.ba1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832024
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '24.n1', '24.o1', '24.u1', '24.dc1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8423, -1, 9535, -1], 'generators': [134983133510400, 20063, 25514092800, 24460, 112608921600, 2628761160781, 9360177523200], 'label': '20736.hv.48.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.bb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832025
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '24.r1', '24.s1', '24.bf1', '24.de1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1792, -1, 1595, -1], 'generators': [134983133510400, 1078135822, 25514092800, 1078117201, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '48.bc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1', 'subgroup_fusion': None, 'weyl_group': '216.159'}
  • id: 165832026
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '24.bb1', '24.dh1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5365, -1, 7458, -1], 'generators': [134983133510400, 25514109487, 1078116480, 112608921600, 1078146715, 19342, 9360177523200], 'label': '20736.hv.48.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.bd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 165832027
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '24.u1', '24.v1', '24.w1', '24.x1', '24.bf1', '24.dh1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [7411, -1, 7918, -1], 'generators': [134983133510400, 1078121465, 25514109487, 1078133167, 112608921600, 1078140940, 9360177523200], 'label': '20736.hv.48.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.be1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 165832028
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '24.y1', '24.cp1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7086, -1, 7555, -1], 'generators': [134983133510400, 26428555385, 112608921600, 30235, 26428574860, 26468500904, 9360177523200], 'label': '20736.hv.48.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.bf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832029
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.y1', '24.dl1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8274, -1, 6992, -1], 'generators': [134983133510400, 997953704, 24460, 112608921600, 26815, 2628844639618, 9360177523200], 'label': '20736.hv.48.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.bg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832030
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.y1', '24.dl1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8347, -1, 6725, -1], 'generators': [134983133510400, 24460, 112608921600, 26815, 2628844617933, 997931543, 9360177523200], 'label': '20736.hv.48.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.bh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832031
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.f1'], 'contains': ['24.j1', '24.l1', '24.m1', '24.n1', '24.t1', '24.u1', '24.v1', '24.bz1', '24.cb1', '24.cd1', '24.cf1', '24.ch1', '24.cj1', '24.cl1', '24.cn1', '36.c1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9091, -1, 9571, -1], 'generators': [134983133510400, 1078136543, 25514092800, 1078116480, 112608921600, 1078140940, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.12.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.d1', 'projective_image': '20736.hv', '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': '1728.47887'}
  • id: 165832032
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '24.z1', '24.cr1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6880, -1, 7829, -1], 'generators': [134983133510400, 26428555385, 25430664104, 112608921600, 30235, 26428574860, 9360177523200], 'label': '20736.hv.48.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '48.bi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1', 'subgroup_fusion': None, 'weyl_group': '288.880'}
  • id: 165832033
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '24.bb1', '24.de1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5150, -1, 4152, -1], 'generators': [134983133510400, 26428555385, 25514109487, 1078117201, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '48.bj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
  • id: 165832034
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.ba1', '24.ct1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7597, -1, 6607, -1], 'generators': [134983133510400, 2646966471087, 25514109487, 25514097064, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832035
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.bg1', '24.cv1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7021, -1, 6511, -1], 'generators': [134983133510400, 25514109487, 25514097064, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.48.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '48.bl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1', 'subgroup_fusion': None, 'weyl_group': '864.4407'}
  • id: 165832036
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1', '24.bg1', '24.da1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5765, -1, 6450, -1], 'generators': [134983133510400, 25514109487, 25514097064, 24460, 112608921600, 2628844618652, 9360177523200], 'label': '20736.hv.48.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1', 'old_label': '48.bm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1', 'subgroup_fusion': None, 'weyl_group': '864.4297'}
  • id: 165832037
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1', '24.ba1', '24.dd1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7436, -1, 6977, -1], 'generators': [134983133510400, 25514109487, 25514097064, 24460, 112608921600, 7879101314486, 9360177523200], 'label': '20736.hv.48.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.bn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1', 'subgroup_fusion': None, 'weyl_group': '864.4084'}
  • id: 165832038
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.y1', '24.dq1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8295, -1, 6782, -1], 'generators': [134983133510400, 24460, 112608921600, 26815, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.48.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.bo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832039
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.y1', '24.dq1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8367, -1, 6660, -1], 'generators': [134983133510400, 24460, 112608921600, 26468478743, 26815, 2628844617933, 9360177523200], 'label': '20736.hv.48.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.bp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832040
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '24.bg1', '24.dw1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1871, -1, 1913, -1], 'generators': [25514122314, 24460, 9360177523200, 2628844618652, 25514097785, 134983133510400, 112608921600], 'label': '20736.hv.48.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bs1', 'old_label': '48.bq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1', 'subgroup_fusion': None, 'weyl_group': '432.769'}
  • id: 165832041
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1', '24.bg1', '24.dw1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1850, -1, 1932, -1], 'generators': [25514122314, 24460, 2628844638899, 9360177523200, 25514097785, 134983133510400, 112608921600], 'label': '20736.hv.48.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bs1', 'old_label': '48.br1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1', 'subgroup_fusion': None, 'weyl_group': '432.769'}
  • id: 165832042
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.f1'], 'contains': ['24.k1', '24.l1', '24.m1', '24.o1', '24.t1', '24.u1', '24.w1', '24.ca1', '24.cc1', '24.ce1', '24.cg1', '24.ci1', '24.ck1', '24.cm1', '24.co1', '36.d1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9311, -1, 9487, -1], 'generators': [134983133510400, 1078120744, 25514092800, 1078133167, 112608921600, 2647090246018, 1078146715, 26468500904, 9360177523200], 'label': '20736.hv.12.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.e1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832043
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bb1', '24.bf1', '24.dz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1026, -1, 1168, -1], 'generators': [134983133510400, 721, 25514092800, 112608921600, 30235, 19342, 9360177523200], 'label': '20736.hv.48.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.bs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 165832044
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '24.bd1', '24.be1', '24.bf1', '24.dz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1155, -1, 1555, -1], 'generators': [134983133510400, 4985, 25514092800, 24460, 112608921600, 15966, 9360177523200], 'label': '20736.hv.48.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '48.bt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 165832045
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1', '24.bg1', '24.dz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1827, -1, 1953, -1], 'generators': [134983133510400, 4985, 25514109487, 24460, 112608921600, 25514093521, 9360177523200], 'label': '20736.hv.48.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '48.bu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 165832046
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '24.bg1', '24.ee1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1694, -1, 1764, -1], 'generators': [29514, 24460, 9360177523200, 4985, 2628844618652, 134983133510400, 112608921600], 'label': '20736.hv.48.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bs1', 'old_label': '48.bv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832047
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1', '24.bg1', '24.ee1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1716, -1, 1876, -1], 'generators': [29514, 24460, 2628844638899, 9360177523200, 4985, 134983133510400, 112608921600], 'label': '20736.hv.48.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bs1', 'old_label': '48.bw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832048
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bn1', '24.br1', '24.cq1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6479, -1, 7938, -1], 'generators': [134983133510400, 4985, 25514109487, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.48.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.bx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832049
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bn1', '24.br1', '24.cs1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6459, -1, 8229, -1], 'generators': [134983133510400, 4985, 25514109487, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.by1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832050
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.h1', '24.cu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1207, -1, 1388, -1], 'generators': [134983133510400, 4985, 25514092800, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.bz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832051
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1', '24.bi1', '24.bj1', '24.br1', '24.cp1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9331, -1, 8549, -1], 'generators': [134983133510400, 26428580635, 4985, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.48.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ca1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832052
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '24.bl1', '24.bm1', '24.br1', '24.cr1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8932, -1, 9484, -1], 'generators': [134983133510400, 26428580635, 997953704, 4985, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.cb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832053
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.o1'], 'contains': ['24.q1', '24.r1', '24.v1', '24.x1', '24.bc1', '24.bd1', '24.bf1', '24.ft1', '24.fu1', '24.fx1', '24.fy1', '36.e1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1376, -1, 1646, -1], 'generators': [134983133510400, 4985, 25514092800, 1078133167, 1078117201, 112608921600, 1078146715, 2628844618652, 9360177523200], 'label': '20736.hv.12.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '12.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '864.4701'}
  • id: 165832054
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '24.bo1', '24.bp1', '24.bq1', '24.de1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5407, -1, 3579, -1], 'generators': [134983133510400, 1078121465, 25514092800, 1078117201, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '48.cc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
  • id: 165832055
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.bn1', '24.dh1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5221, -1, 7401, -1], 'generators': [134983133510400, 4985, 25514109487, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.48.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.cd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 165832056
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.bh1', '24.bk1', '24.bo1', '24.bs1', '24.ct1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6217, -1, 7614, -1], 'generators': [134983133510400, 2646966471087, 25514092800, 24460, 112608921600, 4264, 9360177523200], 'label': '20736.hv.48.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ce1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832057
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1', '24.bi1', '24.bl1', '24.bt1', '24.cv1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9396, -1, 8514, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.48.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.cf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832058
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '24.bi1', '24.bm1', '24.bp1', '24.bu1', '24.ct1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6500, -1, 7758, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 4264, 2646966487501, 9360177523200], 'label': '20736.hv.48.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832059
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.f1', '24.bq1', '24.bv1', '24.cy1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4907, -1, 3324, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 2646966474806, 4264, 9360177523200], 'label': '20736.hv.48.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '48.ch1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832060
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1', '24.bk1', '24.bm1', '24.bt1', '24.cz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8997, -1, 9503, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 4264, 2647090251364, 9360177523200], 'label': '20736.hv.48.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ci1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832061
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.g1', '24.bj1', '24.bl1', '24.bq1', '24.bs1', '24.bu1', '24.dc1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5683, -1, 8455, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 4264, 2628761144367, 9360177523200], 'label': '20736.hv.48.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165832062
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '24.bo1', '24.bp1', '24.bv1', '24.dd1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6804, -1, 4269, -1], 'generators': [134983133510400, 2628761162700, 25514092800, 24460, 112608921600, 4264, 9360177523200], 'label': '20736.hv.48.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '48.ck1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1', 'subgroup_fusion': None, 'weyl_group': '864.4700'}
  • id: 165832063
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.br1', '24.bs1', '24.bt1', '24.bu1', '24.bv1', '24.dh1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [5649, -1, 7983, -1], 'generators': [134983133510400, 4985, 25514092800, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.48.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 165832064
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.o1'], 'contains': ['24.r1', '24.s1', '24.w1', '24.x1', '24.bd1', '24.be1', '24.bf1', '36.f1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1462, -1, 2164, -1], 'generators': [134983133510400, 4985, 25514092800, 1078133167, 1078117201, 112608921600, 1078146715, 2647090225052, 9360177523200], 'label': '20736.hv.12.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '12.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '864.4701'}
  • id: 165832065
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1', '24.bw1', '24.cp1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7065, -1, 7437, -1], 'generators': [134983133510400, 4985, 112608921600, 30235, 26428574860, 26468500904, 9360177523200], 'label': '20736.hv.48.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.cm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832066
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1', '24.bw1', '24.dl1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8210, -1, 7230, -1], 'generators': [4264, 24460, 997931543, 9360177523200, 134983133510400, 2628844617933, 112608921600], 'label': '20736.hv.48.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.cn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832067
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1', '24.bw1', '24.dl1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8166, -1, 7130, -1], 'generators': [134983133510400, 997953704, 24460, 112608921600, 2628844617933, 4264, 9360177523200], 'label': '20736.hv.48.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.co1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832068
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1', '24.bx1', '24.cr1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6284, -1, 7775, -1], 'generators': [134983133510400, 4985, 25430664104, 112608921600, 30235, 26428574860, 9360177523200], 'label': '20736.hv.48.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '48.cp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1', 'subgroup_fusion': None, 'weyl_group': '288.880'}
  • id: 165832069
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '24.bw1', '24.ct1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5601, -1, 6551, -1], 'generators': [134983133510400, 2646966471087, 25514109487, 24460, 112608921600, 4264, 9360177523200], 'label': '20736.hv.48.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '48.cq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832070
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '24.by1', '24.cv1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7043, -1, 6590, -1], 'generators': [134983133510400, 25514109487, 24460, 112608921600, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.48.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cs1', 'subgroup_fusion': None, 'weyl_group': '864.4080'}
  • id: 165832071
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '24.bx1', '24.cy1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4394, -1, 6532, -1], 'generators': [134983133510400, 25514109487, 24460, 112608921600, 2646966474806, 4264, 9360177523200], 'label': '20736.hv.48.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ct1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832072
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1', '24.by1', '24.db1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4546, -1, 6879, -1], 'generators': [134983133510400, 25514109487, 7865729194652, 24460, 112608921600, 4264, 9360177523200], 'label': '20736.hv.48.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '48.ct1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cu1', 'subgroup_fusion': None, 'weyl_group': '288.878'}
  • id: 165832073
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.by1', '24.de1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4292, -1, 3474, -1], 'generators': [1078117201, 24460, 9360177523200, 134983133510400, 25514109487, 1078121465, 112608921600], 'label': '20736.hv.48.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '48.cu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cq1', 'subgroup_fusion': None, 'weyl_group': '216.159'}
  • id: 165832074
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.i1', '24.dr1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3747, -1, 3061, -1], 'generators': [134983133510400, 24460, 112608921600, 2646966474806, 25514093521, 25514097785, 9360177523200], 'label': '20736.hv.48.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.br1', 'old_label': '48.cv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cw1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832075
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.f1'], 'contains': ['24.bh1', '24.bj1', '24.bk1', '24.bl1', '24.br1', '24.bs1', '24.bt1', '24.bz1', '24.ca1', '24.cd1', '24.ce1', '24.ch1', '24.ci1', '24.cl1', '24.cm1', '36.g1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9208, -1, 9521, -1], 'generators': [134983133510400, 1078120744, 25514092800, 1078116480, 112608921600, 1078140940, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.12.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832076
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1', '24.bw1', '24.dq1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8188, -1, 7053, -1], 'generators': [134983133510400, 24460, 112608921600, 26468478743, 2628844617933, 4264, 9360177523200], 'label': '20736.hv.48.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.cw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cv1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832077
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '24.i1', '24.dr1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3795, -1, 3234, -1], 'generators': [24460, 25514093521, 9360177523200, 2646966496929, 25514097785, 134983133510400, 112608921600], 'label': '20736.hv.48.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.br1', 'old_label': '48.cx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cy1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832078
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1', '24.bw1', '24.dq1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8145, -1, 6744, -1], 'generators': [26468500904, 4264, 24460, 9360177523200, 134983133510400, 2628844617933, 112608921600], 'label': '20736.hv.48.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.cy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cx1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832079
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '24.bn1', '24.eh1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6394, -1, 8022, -1], 'generators': [134983133510400, 1078121465, 25514109487, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.48.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.cz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.da1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832080
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '24.br1', '24.eh1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6858, -1, 8247, -1], 'generators': [134983133510400, 1078121465, 25514092800, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.48.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.da1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cz1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832081
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '24.bn1', '24.el1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6372, -1, 8041, -1], 'generators': [134983133510400, 1078121465, 25514109487, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.db1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dc1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832082
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '24.br1', '24.el1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6837, -1, 8267, -1], 'generators': [134983133510400, 1078121465, 25514092800, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.dc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.db1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832083
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.bh1', '24.bz1', '24.ch1', '24.ei1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9351, -1, 8691, -1], 'generators': [134983133510400, 2628844619130, 25514092800, 24460, 112608921600, 26468506671, 9360177523200], 'label': '20736.hv.48.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dd1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832084
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.bh1', '24.ca1', '24.ci1', '24.ei1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9747, -1, 8654, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 2628844613636, 26468500904, 9360177523200], 'label': '20736.hv.48.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.de1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.de1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832085
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '24.br1', '24.bz1', '24.ca1', '24.cb1', '24.cc1', '24.ej1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9976, -1, 9688, -1], 'generators': [134983133510400, 26428580635, 112608921600, 30235, 26468500904, 25514112142, 9360177523200], 'label': '20736.hv.48.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.df1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.df1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832086
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.f1'], 'contains': ['24.bi1', '24.bj1', '24.bl1', '24.bm1', '24.br1', '24.bt1', '24.bu1', '24.cb1', '24.cc1', '24.cf1', '24.cg1', '24.cj1', '24.ck1', '24.cn1', '24.co1', '36.h1'], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9187, -1, 9506, -1], 'generators': [134983133510400, 1078120744, 25514092800, 1078116480, 112608921600, 1078140940, 26468506671, 2628844639618, 9360177523200], 'label': '20736.hv.12.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832087
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.bi1', '24.cb1', '24.cj1', '24.ei1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8975, -1, 8674, -1], 'generators': [134983133510400, 2628844619130, 25514092800, 24460, 112608921600, 26468500904, 9360177523200], 'label': '20736.hv.48.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dg1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832088
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.bi1', '24.cc1', '24.ck1', '24.ei1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9228, -1, 8636, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 2628844613636, 26468506671, 9360177523200], 'label': '20736.hv.48.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dh1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832089
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.l1', '24.bj1', '24.bz1', '24.cc1', '24.ci1', '24.cj1', '24.ek1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9933, -1, 9860, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 2647090225530, 26468500904, 9360177523200], 'label': '20736.hv.48.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.di1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.di1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832090
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.di2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.l1', '24.bj1', '24.ca1', '24.cb1', '24.ch1', '24.ck1', '24.ek1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9852, -1, 9902, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 2647090220036, 26468506671, 9360177523200], 'label': '20736.hv.48.di2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.di2', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.di2', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832091
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.m1', '24.bk1', '24.cd1', '24.ce1', '24.ch1', '24.ci1', '24.em1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9486, -1, 9638, -1], 'generators': [134983133510400, 25430669871, 25514092800, 24460, 112608921600, 2647090225530, 9360177523200], 'label': '20736.hv.48.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dj1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832092
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '24.br1', '24.cd1', '24.ce1', '24.cf1', '24.cg1', '24.en1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9464, -1, 9584, -1], 'generators': [134983133510400, 26428580635, 997953704, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dk1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832093
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.n1', '24.bl1', '24.cd1', '24.cf1', '24.ch1', '24.cj1', '24.eo1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9442, -1, 9783, -1], 'generators': [134983133510400, 25430669871, 2628844619130, 25514092800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dl1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832094
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.m1', '24.bm1', '24.cf1', '24.cg1', '24.cj1', '24.ck1', '24.em1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9559, -1, 9617, -1], 'generators': [134983133510400, 25430669871, 25514092800, 24460, 112608921600, 2647090220036, 9360177523200], 'label': '20736.hv.48.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dm1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832095
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.o1', '24.bl1', '24.ce1', '24.cg1', '24.ci1', '24.ck1', '24.eo1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9876, -1, 9566, -1], 'generators': [134983133510400, 25514092800, 25430664104, 24460, 112608921600, 2628844613636, 9360177523200], 'label': '20736.hv.48.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dn1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832096
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.p1', '24.bn1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6331, -1, 8391, -1], 'generators': [134983133510400, 25514109487, 1078116480, 112608921600, 1078146715, 26468500904, 9360177523200], 'label': '20736.hv.48.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.do1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.do1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832097
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.f1', '6.j1'], 'contains': ['24.j1', '24.k1', '24.y1', '24.bh1', '24.bi1', '24.bw1', '24.cp1', '24.ct1', '24.cv1', '24.dl1', '24.dq1', '24.ei1', '24.es1', '24.fb1', '24.fh1', '36.i1', '36.t1'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7829, -1, 6563, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 30235, 2628844639618, 4264, 26468500904, 9360177523200], 'label': '20736.hv.12.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165832098
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '24.bn1', '24.fa1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6351, -1, 8192, -1], 'generators': [134983133510400, 26468479846, 25514109487, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.48.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.dp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dp1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832099
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '24.bs1', '24.bz1', '24.ca1', '24.cd1', '24.ce1', '24.er1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9827, -1, 9801, -1], 'generators': [134983133510400, 1078120744, 2646966471087, 25514092800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dq1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832100
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.bh1', '24.cd1', '24.cl1', '24.es1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9370, -1, 8884, -1], 'generators': [134983133510400, 2628844619130, 26468480567, 25514092800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dr1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832101
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.bh1', '24.ce1', '24.cm1', '24.es1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9725, -1, 8846, -1], 'generators': [134983133510400, 25514092800, 26468474800, 24460, 112608921600, 2628844613636, 9360177523200], 'label': '20736.hv.48.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ds1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ds1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832102
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.m1', '24.bk1', '24.bz1', '24.ca1', '24.cl1', '24.cm1', '24.et1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9914, -1, 9843, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 25430638000, 2647090220036, 9360177523200], 'label': '20736.hv.48.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dt1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832103
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '24.bt1', '24.bz1', '24.cb1', '24.cd1', '24.cf1', '24.eu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9600, -1, 9974, -1], 'generators': [134983133510400, 1078136543, 25514092800, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.48.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.du1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.du1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832104
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '24.bu1', '24.cb1', '24.cc1', '24.cf1', '24.cg1', '24.er1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9666, -1, 9671, -1], 'generators': [134983133510400, 1078120744, 25514092800, 24460, 112608921600, 2628761160781, 9360177523200], 'label': '20736.hv.48.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dv1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832105
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.w1', '24.bt1', '24.ca1', '24.cc1', '24.ce1', '24.cg1', '24.eu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9995, -1, 9601, -1], 'generators': [134983133510400, 1078136543, 25514092800, 24460, 112608921600, 2647090251364, 9360177523200], 'label': '20736.hv.48.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dw1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832106
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.bi1', '24.cf1', '24.cn1', '24.es1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8952, -1, 8865, -1], 'generators': [134983133510400, 2628844619130, 25514092800, 26468474800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dx1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832107
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.n1', '24.bl1', '24.bz1', '24.cb1', '24.cl1', '24.cn1', '24.ew1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9707, -1, 9994, -1], 'generators': [134983133510400, 25430643767, 2628844619130, 25514092800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dy1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832108
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1'], 'contains': ['24.cq1', '24.cu1', '24.dg1', '24.dk1', '24.dm1', '24.dp1', '24.du1', '24.eh1', '24.ej1', '24.eq1', '24.ev1', '24.fd1', '24.fg1', '24.fl1', '24.fs1', '36.j1', '36.l1', '36.s1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2948, -1, 4642, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 1078117201, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.12.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832109
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.bi1', '24.cg1', '24.co1', '24.es1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9210, -1, 8830, -1], 'generators': [134983133510400, 26468480567, 25514092800, 24460, 112608921600, 2628844613636, 9360177523200], 'label': '20736.hv.48.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.dz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dz1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832110
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.l1', '24.bj1', '24.cd1', '24.cg1', '24.cm1', '24.cn1', '24.ex1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9686, -1, 9950, -1], 'generators': [134983133510400, 25514092800, 26468474800, 24460, 112608921600, 2647090220036, 9360177523200], 'label': '20736.hv.48.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ea1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ea1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832111
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ea2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.l1', '24.bj1', '24.ce1', '24.cf1', '24.cl1', '24.co1', '24.ex1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9775, -1, 9927, -1], 'generators': [134983133510400, 26468480567, 25514092800, 24460, 112608921600, 2647090225530, 9360177523200], 'label': '20736.hv.48.ea2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ea2', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ea2', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832112
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.m1', '24.bm1', '24.cb1', '24.cc1', '24.cn1', '24.co1', '24.et1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9802, -1, 9823, -1], 'generators': [134983133510400, 25514092800, 24460, 112608921600, 25430638000, 2647090225530, 9360177523200], 'label': '20736.hv.48.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.eb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eb1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832113
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.o1', '24.bl1', '24.ca1', '24.cc1', '24.cm1', '24.co1', '24.ew1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9953, -1, 9748, -1], 'generators': [134983133510400, 25430643767, 25514092800, 24460, 112608921600, 2628844613636, 9360177523200], 'label': '20736.hv.48.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ec1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ec1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832114
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.t1', '24.br1', '24.ch1', '24.ci1', '24.cj1', '24.ck1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9540, -1, 9519, -1], 'generators': [134983133510400, 25514092800, 1078116480, 112608921600, 1078146715, 26468500904, 9360177523200], 'label': '20736.hv.48.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ed1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ed1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832115
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '24.bs1', '24.ch1', '24.ci1', '24.cl1', '24.cm1', '24.ey1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9646, -1, 9732, -1], 'generators': [134983133510400, 25514092800, 2628761147486, 1078116480, 112608921600, 1078140940, 9360177523200], 'label': '20736.hv.48.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ee1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ee1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832116
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '24.bt1', '24.ch1', '24.cj1', '24.cl1', '24.cn1', '24.ez1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9517, -1, 9711, -1], 'generators': [134983133510400, 25514092800, 1078116480, 112608921600, 2647090225530, 1078140940, 9360177523200], 'label': '20736.hv.48.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ef1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ef1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832117
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '24.br1', '24.cl1', '24.cm1', '24.cn1', '24.co1', '24.fa1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9625, -1, 9764, -1], 'generators': [134983133510400, 26468479846, 25514109487, 1078133167, 112608921600, 1078140940, 9360177523200], 'label': '20736.hv.48.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.eg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eg1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832118
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '24.bu1', '24.cj1', '24.ck1', '24.cn1', '24.co1', '24.ey1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9578, -1, 9656, -1], 'generators': [134983133510400, 25514092800, 1078116480, 112608921600, 1078140940, 2628761163300, 9360177523200], 'label': '20736.hv.48.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.eh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eh1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832119
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.g1', '6.j1'], 'contains': ['24.cp1', '24.cy1', '24.da1', '24.do1', '24.dv1', '36.k1', '36.u1'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5224, -1, 6263, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 30235, 4264, 26468500904, 2628844618652, 9360177523200], 'label': '20736.hv.12.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.l1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165832120
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.w1', '24.bt1', '24.ci1', '24.ck1', '24.cm1', '24.co1', '24.ez1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [9896, -1, 9549, -1], 'generators': [134983133510400, 25514092800, 1078116480, 112608921600, 2647090220036, 1078140940, 9360177523200], 'label': '20736.hv.48.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ei1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ei1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832121
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.bw1', '24.fb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8764, -1, 7267, -1], 'generators': [134983133510400, 24460, 112608921600, 25514119615, 2628844639618, 997931543, 9360177523200], 'label': '20736.hv.48.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.ej1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.en1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832122
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.bw1', '24.fb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8800, -1, 7209, -1], 'generators': [134983133510400, 997953704, 24460, 112608921600, 25514119615, 2628844617933, 9360177523200], 'label': '20736.hv.48.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.ek1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eo1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832123
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.bh1', '24.fb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8819, -1, 7250, -1], 'generators': [134983133510400, 997953704, 25514097064, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.48.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.el1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ej1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832124
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.bi1', '24.fb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8782, -1, 7037, -1], 'generators': [134983133510400, 25514097064, 24460, 112608921600, 2628844639618, 997931543, 9360177523200], 'label': '20736.hv.48.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.em1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ek1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832125
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.bw1', '24.ei1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8250, -1, 7320, -1], 'generators': [26468500904, 24460, 7879141234436, 9360177523200, 134983133510400, 25514109487, 112608921600], 'label': '20736.hv.48.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.en1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.el1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832126
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.el2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.bw1', '24.ei1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8232, -1, 7336, -1], 'generators': [134983133510400, 997953704, 25514109487, 24460, 112608921600, 7879141234436, 9360177523200], 'label': '20736.hv.48.el2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.en2', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.el2', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832127
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '24.bn1', '24.ej1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6417, -1, 8174, -1], 'generators': [134983133510400, 1078121465, 112608921600, 30235, 26428574860, 26468500904, 9360177523200], 'label': '20736.hv.48.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.eo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.em1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832128
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '24.bn1', '24.en1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6676, -1, 8060, -1], 'generators': [134983133510400, 1078121465, 25430664104, 112608921600, 30235, 26428574860, 9360177523200], 'label': '20736.hv.48.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bh1', 'old_label': '48.ep1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ep1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 165832129
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '24.bo1', '24.fq1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7291, -1, 5170, -1], 'generators': [134983133510400, 26428576494, 1078145994, 24460, 112608921600, 2628761170209, 9360177523200], 'label': '20736.hv.48.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '48.eq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ew1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832130
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '6.d1', '6.e1', '6.f1', '6.g1', '6.h1', '6.i1', '6.j1', '6.k1', '6.l1', '6.m1', '6.n1', '6.o1', '9.a1', '27.b1'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5655, -1, 6257, -1], 'generators': [25514092800, 26468500904, 1078117201, 16687, 9360177523200, 4985, 2628844618652, 134983133510400, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.3.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165832131
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.f1', '6.k1'], 'contains': ['24.l1', '24.bj1', '24.cp1', '24.cz1', '24.dc1', '24.ek1', '24.ex1', '36.v1'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7853, -1, 8506, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 2647090246018, 30235, 4264, 26468500904, 9360177523200], 'label': '20736.hv.12.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.m1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '100000.bt'}
  • id: 165832132
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '24.bp1', '24.fq1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7273, -1, 5579, -1], 'generators': [24460, 9360177523200, 26428576494, 134983133510400, 2628761148086, 1078145994, 112608921600], 'label': '20736.hv.48.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '48.er1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ex1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832133
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '24.bw1', '24.fh1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8552, -1, 7191, -1], 'generators': [134983133510400, 24460, 112608921600, 26468478743, 25514119615, 2628844639618, 9360177523200], 'label': '20736.hv.48.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.es1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ez1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832134
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.bw1', '24.fh1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8589, -1, 7008, -1], 'generators': [134983133510400, 24460, 112608921600, 25514119615, 2628844617933, 26468500904, 9360177523200], 'label': '20736.hv.48.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.et1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fa1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832135
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '24.by1', '24.fn1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4365, -1, 3985, -1], 'generators': [134983133510400, 26428551121, 2647090245299, 1078142574, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.be1', 'old_label': '48.eu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fb1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832136
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1', '24.by1', '24.fn1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4501, -1, 4005, -1], 'generators': [134983133510400, 26428551121, 1078142574, 24460, 112608921600, 2647090225052, 9360177523200], 'label': '20736.hv.48.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.be1', 'old_label': '48.ev1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fc1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832137
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '24.by1', '24.fr1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4320, -1, 3945, -1], 'generators': [134983133510400, 26428576494, 2647090245299, 1078117201, 24460, 112608921600, 9360177523200], 'label': '20736.hv.48.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.be1', 'old_label': '48.ew1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eq1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832138
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1', '24.by1', '24.fr1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4342, -1, 3965, -1], 'generators': [134983133510400, 26428576494, 1078117201, 24460, 112608921600, 2647090225052, 9360177523200], 'label': '20736.hv.48.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.be1', 'old_label': '48.ex1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.er1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832139
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '24.bo1', '24.fi1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7633, -1, 5485, -1], 'generators': [26428579914, 134983133510400, 1078142574, 24460, 112608921600, 2628761170209, 9360177523200], 'label': '20736.hv.48.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '48.ey1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.et1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832140
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.bh1', '24.fh1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8607, -1, 7172, -1], 'generators': [134983133510400, 25514097064, 24460, 112608921600, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.48.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.ez1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.es1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832141
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '24.bp1', '24.fi1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7614, -1, 5594, -1], 'generators': [24460, 9360177523200, 134983133510400, 2628761148086, 1078142574, 26428579914, 112608921600], 'label': '20736.hv.48.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '48.fa1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ev1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832142
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.g1', '6.k1'], 'contains': ['24.cp1', '24.db1', '24.dd1', '24.fe1', '24.fm1', '36.w1'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7266, -1, 6472, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 2647090225052, 30235, 4264, 26468500904, 9360177523200], 'label': '20736.hv.12.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.n1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1', 'subgroup_fusion': None, 'weyl_group': '20000.fw'}
  • id: 165832143
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.bi1', '24.fh1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8571, -1, 7023, -1], 'generators': [134983133510400, 25514097064, 24460, 112608921600, 26468478743, 2628844639618, 9360177523200], 'label': '20736.hv.48.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.fb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eu1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832144
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.bw1', '24.es1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8328, -1, 7350, -1], 'generators': [24460, 7879141234436, 9360177523200, 134983133510400, 25514109487, 26468474800, 112608921600], 'label': '20736.hv.48.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.fc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ey1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832145
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ey2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.bw1', '24.es1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8313, -1, 7364, -1], 'generators': [24460, 7879141234436, 9360177523200, 134983133510400, 25514109487, 997927600, 112608921600], 'label': '20736.hv.48.ey2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.fc2', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ey2', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832146
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '24.cr1', '24.ct1', '24.cv1', '24.cw1', '24.cx1', '24.cy1', '24.cz1', '24.da1', '24.db1', '24.dc1', '24.dd1', '24.de1', '24.dh1', '24.dz1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5811, -1, 6937, -1], 'generators': [134983133510400, 26428580635, 16687, 4985, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fd1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832147
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '24.cs1', '24.cu1', '24.df1', '24.dg1', '24.dh1', '24.dz1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3487, -1, 4940, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fe1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fe1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 165832148
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '24.cs1', '24.di1', '24.dl1', '24.dn1', '24.do1', '24.ea1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [3073, -1, 5223, -1], 'generators': [134983133510400, 16687, 4985, 112608921600, 123775784, 30235, 9360177523200], 'label': '20736.hv.48.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ff1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ff1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832149
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '24.cr1', '24.cs1', '24.dj1', '24.dk1', '24.dm1', '24.ea1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2423, -1, 5314, -1], 'generators': [134983133510400, 997953704, 16687, 4985, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fg1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832150
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '24.de1', '24.di1', '24.dj1', '24.dk1', '24.dp1', '24.dz1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3628, -1, 3622, -1], 'generators': [134983133510400, 16687, 4985, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 165832151
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '24.dl1', '24.dr1', '24.dq1', '24.ds1', '24.dt1', '24.eb1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3307, -1, 3437, -1], 'generators': [134983133510400, 16687, 2646966471087, 112608921600, 30235, 4264, 9360177523200], 'label': '20736.hv.48.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '48.fi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fi1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832152
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '24.dm1', '24.dn1', '24.dr1', '24.du1', '24.dw1', '24.dz1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1550, -1, 2971, -1], 'generators': [134983133510400, 16687, 4985, 26428551121, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fk1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832153
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.b1', '6.c1'], 'contains': ['24.c1', '24.cp1', '24.cw1', '24.de1', '24.di1', '24.dp1', '24.eh1', '24.ep1', '24.fc1', '24.ff1', '24.fl1', '36.m1', '36.x1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5285, -1, 5446, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 1078117201, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.12.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.o1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832154
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.cp1', '24.cq1', '24.dp1', '24.dq1', '24.du1', '24.dv1'], 'contains': ['96.A'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [2001, -1, 3399, -1], 'generators': [134983133510400, 16687, 4985, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.48.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fj1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832155
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '24.dl1', '24.dq1', '24.dw1', '24.dx1', '24.dy1', '24.ee1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3049, -1, 3215, -1], 'generators': [134983133510400, 16687, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.48.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '48.fl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fl1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832156
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '24.df1', '24.dg1', '24.di1', '24.dm1', '24.dp1', '24.ea1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2321, -1, 4791, -1], 'generators': [134983133510400, 16687, 4985, 112608921600, 30235, 25430669150, 9360177523200], 'label': '20736.hv.48.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fm1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832157
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1', '24.dg1', '24.dk1', '24.ds1', '24.du1', '24.dx1', '24.ea1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [3284, -1, 4326, -1], 'generators': [134983133510400, 16687, 123780830, 4985, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fn1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832158
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1', '24.do1', '24.dr1', '24.dv1', '24.dx1', '24.dy1', '24.eb1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3159, -1, 3015, -1], 'generators': [134983133510400, 16687, 112608921600, 2646966474806, 30235, 4264, 9360177523200], 'label': '20736.hv.48.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '48.fo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fo1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832159
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.cx1', '24.df1', '24.dj1', '24.dn1', '24.dt1', '24.dy1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1922, -1, 3290, -1], 'generators': [134983133510400, 16687, 4985, 112608921600, 26468505950, 30235, 9360177523200], 'label': '20736.hv.48.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fp1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832160
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1', '24.do1', '24.ds1', '24.dt1', '24.dw1', '24.dv1', '24.ee1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2877, -1, 2656, -1], 'generators': [134983133510400, 16687, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.48.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '48.fq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fq1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832161
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.ec1', '24.ed1', '24.ef1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 4, 'diagramx': [286, -1, 242, -1], 'generators': [721, 16687, 4985, 132523584036480, 9683982604800, 46036847791741, 30235], 'label': '20736.hv.48.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '48.fr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fr1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
  • id: 165832162
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.eg1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 8, 'diagramx': [248, -1, 159, -1], 'generators': [154860865673341, 721, 16687, 4985, 132523584036480, 9683982604800, 30235], 'label': '20736.hv.48.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.fs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fs1', 'subgroup_fusion': None, 'weyl_group': '864.4022'}
  • id: 165832163
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.cp1', '24.cq1', '24.eh1', '24.ei1', '24.ej1', '24.ek1'], 'contains': ['96.A'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6186, -1, 7737, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.48.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ft1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ft1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832164
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.f1', '6.l1'], 'contains': ['24.m1', '24.bk1', '24.bm1', '24.cr1', '24.ct1', '24.cz1', '24.em1', '24.et1', '36.z1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [8102, -1, 8466, -1], 'generators': [134983133510400, 16687, 25514092800, 25430664104, 112608921600, 2647090246018, 30235, 4264, 9360177523200], 'label': '20736.hv.12.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.p1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165832165
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.cr1', '24.cs1', '24.el1', '24.em1', '24.en1', '24.eo1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6306, -1, 8152, -1], 'generators': [134983133510400, 16687, 25514092800, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fu1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832166
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '24.de1', '24.dh1', '24.eh1', '24.el1', '24.ep1', '24.eq1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4731, -1, 5612, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fv1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 165832167
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '24.ei1', '24.em1', '24.er1', '24.es1', '24.et1', '24.ey1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7977, -1, 8815, -1], 'generators': [134983133510400, 16687, 2646966474206, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.fw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fw1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832168
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '24.dh1', '24.ej1', '24.en1', '24.er1', '24.eu1', '24.ev1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6154, -1, 7687, -1], 'generators': [134983133510400, 26428580635, 16687, 1078121465, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fx1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 165832169
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '24.ei1', '24.eo1', '24.es1', '24.eu1', '24.ew1', '24.ez1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7957, -1, 8798, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.48.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.fy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fy1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832170
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '24.cw1', '24.dg1', '24.eh1', '24.ep1', '24.ev1', '24.fa1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4754, -1, 6203, -1], 'generators': [134983133510400, 25430643046, 16687, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.fz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.fz1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832171
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '24.df1', '24.en1', '24.ep1', '24.es1', '24.ex1', '24.fa1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6745, -1, 7710, -1], 'generators': [134983133510400, 26428580635, 26468479846, 16687, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ga1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ga1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832172
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '24.cx1', '24.df1', '24.el1', '24.eq1', '24.ev1', '24.fa1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4005, -1, 5846, -1], 'generators': [134983133510400, 26468479846, 16687, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gb1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832173
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '24.dg1', '24.ej1', '24.eq1', '24.et1', '24.ew1', '24.fa1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6261, -1, 8003, -1], 'generators': [134983133510400, 25430643046, 26428580635, 16687, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gc1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832174
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cz1', '24.ek1', '24.em1', '24.et1', '24.eu1', '24.ex1', '24.ez1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7834, -1, 9436, -1], 'generators': [134983133510400, 16687, 25514092800, 112608921600, 2647090220036, 30235, 9360177523200], 'label': '20736.hv.48.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.gd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gd1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832175
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1'], 'contains': ['24.cs1', '24.cu1', '24.df1', '24.di1', '24.dj1', '24.dm1', '24.dn1', '24.el1', '24.en1', '24.ep1', '24.ev1', '24.fc1', '24.fd1', '24.fg1', '36.n1', '36.o1', '36.y1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3000, -1, 4626, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 25430664104, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.12.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.q1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832176
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1', '24.ek1', '24.eo1', '24.er1', '24.ew1', '24.ex1', '24.ey1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7811, -1, 9453, -1], 'generators': [134983133510400, 16687, 25514092800, 2628761147486, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '48.ge1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ge1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 165832177
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '24.di1', '24.dk1', '24.eh1', '24.el1', '24.fd1', '24.ff1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4091, -1, 5722, -1], 'generators': [134983133510400, 26428555385, 997953704, 16687, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gf1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832178
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '24.dj1', '24.el1', '24.fb1', '24.fc1', '24.fe1', '24.ff1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6645, -1, 6004, -1], 'generators': [134983133510400, 26428555385, 16687, 112608921600, 123775784, 30235, 9360177523200], 'label': '20736.hv.48.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gg1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832179
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1', '24.ei1', '24.fb1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7933, -1, 6818, -1], 'generators': [134983133510400, 997953704, 16687, 112608921600, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.48.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.gh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gh1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832180
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '24.di1', '24.dm1', '24.eh1', '24.en1', '24.fc1', '24.fg1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3839, -1, 5526, -1], 'generators': [134983133510400, 16687, 25430664104, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gi1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832181
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '24.dk1', '24.dm1', '24.ej1', '24.el1', '24.fd1', '24.fg1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3665, -1, 5824, -1], 'generators': [134983133510400, 16687, 112608921600, 123775784, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gj1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832182
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '24.dj1', '24.dn1', '24.el1', '24.en1', '24.fd1', '24.fg1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1948, -1, 4439, -1], 'generators': [134983133510400, 997953704, 16687, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gk1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832183
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '24.fb1', '24.fi1', '24.fh1', '24.fj1', '24.fk1', '24.fq1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8113, -1, 6240, -1], 'generators': [134983133510400, 16687, 2646966471087, 25514097064, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.gl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gl1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832184
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '24.de1', '24.fc1', '24.fd1', '24.fi1', '24.fl1', '24.fn1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6593, -1, 4629, -1], 'generators': [134983133510400, 16687, 1078117201, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gn1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 165832185
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.cp1', '24.dp1', '24.eh1', '24.fh1', '24.fl1', '24.fm1'], 'contains': ['96.A'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6777, -1, 5743, -1], 'generators': [134983133510400, 26428555385, 16687, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.48.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gm1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832186
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.f1', '6.m1'], 'contains': ['24.n1', '24.o1', '24.bl1', '24.cr1', '24.cv1', '24.dc1', '24.eo1', '24.ew1', '36.ba1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7554, -1, 8485, -1], 'generators': [134983133510400, 16687, 25514092800, 25430664104, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.12.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.r1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1', 'subgroup_fusion': None, 'weyl_group': '4000.fk'}
  • id: 165832187
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '24.fb1', '24.fh1', '24.fn1', '24.fo1', '24.fp1', '24.fr1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8089, -1, 6110, -1], 'generators': [134983133510400, 16687, 25514097064, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.48.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.go1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.go1', 'subgroup_fusion': None, 'weyl_group': '864.4080'}
  • id: 165832188
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.cw1', '24.di1', '24.ep1', '24.fc1', '24.fj1', '24.fo1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4929, -1, 5653, -1], 'generators': [134983133510400, 26428555385, 16687, 112608921600, 30235, 25430669150, 9360177523200], 'label': '20736.hv.48.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gp1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832189
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1', '24.dj1', '24.dp1', '24.ep1', '24.eq1', '24.fd1', '24.ff1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4033, -1, 4870, -1], 'generators': [134983133510400, 26428555385, 16687, 123780830, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gq1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832190
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '24.dk1', '24.eq1', '24.ff1', '24.fk1', '24.fl1', '24.fp1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6622, -1, 5764, -1], 'generators': [134983133510400, 26428555385, 16687, 112608921600, 997958750, 30235, 9360177523200], 'label': '20736.hv.48.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gr1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832191
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.db1', '24.fe1', '24.fj1', '24.fk1', '24.fn1', '24.fm1', '24.fr1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7577, -1, 5955, -1], 'generators': [134983133510400, 16687, 25514097064, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.48.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.gs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gs1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832192
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1', '24.fe1', '24.fi1', '24.fm1', '24.fo1', '24.fp1', '24.fq1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7660, -1, 6045, -1], 'generators': [134983133510400, 16687, 25514097064, 2628761148086, 112608921600, 30235, 9360177523200], 'label': '20736.hv.48.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.gt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gt1', 'subgroup_fusion': None, 'weyl_group': '864.4080'}
  • id: 165832193
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '24.dq1', '24.ei1', '24.fh1'], 'contains': ['96.A'], 'core': '96.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6439, -1, 5633, -1], 'generators': [134983133510400, 16687, 112608921600, 2628844613636, 30235, 26468500904, 9360177523200], 'label': '20736.hv.48.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.gu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gu1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832194
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1', '24.es1', '24.fh1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8530, -1, 6839, -1], 'generators': [134983133510400, 16687, 997927600, 112608921600, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.48.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.gv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gv1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832195
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1', '24.es1', '24.fb1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8742, -1, 6570, -1], 'generators': [134983133510400, 16687, 26468474800, 112608921600, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.48.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '48.gw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gw1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832196
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1', '16.d1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 48, 'diagramx': [690, -1, 214, -1], 'generators': [46036847792341, 16687, 132523584036480, 9683982604800, 30235, 86599221818756, 26468500904], 'label': '20736.hv.48.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.gx1', 'old_label': '48.gx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gx1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 165832197
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.g1', '6.l1'], 'contains': ['24.bx1', '24.cr1', '24.cy1', '24.db1', '36.bb1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5494, -1, 6712, -1], 'generators': [134983133510400, 16687, 25514092800, 25430664104, 112608921600, 2647090225052, 30235, 4264, 9360177523200], 'label': '20736.hv.12.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.s1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165832198
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '24.dp1', '24.du1', '24.eh1', '24.ej1', '24.fl1', '24.fs1'], 'contains': ['96.A'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1972, -1, 4708, -1], 'generators': [134983133510400, 16687, 112608921600, 30235, 26468500904, 25514097785, 9360177523200], 'label': '20736.hv.48.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gy1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832199
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dg1', '24.di1', '24.dm1', '24.ep1', '24.ev1', '24.fg1', '24.fl1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3424, -1, 4811, -1], 'generators': [134983133510400, 16687, 112608921600, 30235, 25430669150, 25514097785, 9360177523200], 'label': '20736.hv.48.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.gz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.gz1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832200
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1', '24.dn1', '24.dp1', '24.ep1', '24.ev1', '24.fc1', '24.fg1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1609, -1, 3799, -1], 'generators': [134983133510400, 16687, 112608921600, 26468505950, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.ha1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ha1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832201
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1', '24.dj1', '24.du1', '24.eq1', '24.ev1', '24.fd1', '24.fg1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1577, -1, 3823, -1], 'generators': [134983133510400, 16687, 112608921600, 997958750, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.hb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hb1', 'subgroup_fusion': None, 'weyl_group': '864.4704'}
  • id: 165832202
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dg1', '24.dk1', '24.dm1', '24.eq1', '24.ev1', '24.fd1', '24.fs1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1444, -1, 4772, -1], 'generators': [134983133510400, 16687, 123780830, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.hc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hc1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832203
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '24.cu1', '24.fg1', '24.fs1'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 2, 'diagramx': [1182, -1, 2105, -1], 'generators': [134983133510400, 16687, 26428551121, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.48.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '48.hd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hd1', 'subgroup_fusion': None, 'weyl_group': '648.705'}
  • id: 165832204
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.h1', '24.bb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1079, -1, 1001, -1], 'generators': [134983133510400, 25514109487, 1078142574, 1078117201, 1078116480, 112608921600, 9360177523200], 'label': '20736.hv.48.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.he1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.he1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832205
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bc1', '24.ft1', '24.fu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [540, -1, 671, -1], 'generators': [134983133510400, 4985, 25514092800, 112608921600, 15966, 2628844618652, 9360177523200], 'label': '20736.hv.48.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.hf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hg1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832206
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bd1', '24.ft1', '24.fu1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [561, -1, 652, -1], 'generators': [2647090248245, 134983133510400, 4985, 25514092800, 112608921600, 15966, 9360177523200], 'label': '20736.hv.48.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.hg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hh1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832207
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.bf1', '24.ft1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [747, -1, 742, -1], 'generators': [134983133510400, 29514, 25514109487, 1078142574, 1078116480, 112608921600, 9360177523200], 'label': '20736.hv.48.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '48.hh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hf1', 'subgroup_fusion': None, 'weyl_group': '216.159'}
  • id: 165832208
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.g1', '6.m1'], 'contains': ['24.z1', '24.cr1', '24.da1', '24.dd1', '36.bc1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6653, -1, 6760, -1], 'generators': [134983133510400, 16687, 25514092800, 25430664104, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.12.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.t1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165832209
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.h1', '24.bf1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [873, -1, 868, -1], 'generators': [134983133510400, 1078138249, 29514, 25514092800, 1078133167, 112608921600, 9360177523200], 'label': '20736.hv.48.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.hi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hi1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832210
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '24.bb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2853, -1, 1277, -1], 'generators': [134983133510400, 25514092800, 1078133167, 1078117201, 112608921600, 19342, 9360177523200], 'label': '20736.hv.48.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.hj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hj1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832211
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.bf1', '24.fu1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [772, -1, 779, -1], 'generators': [134983133510400, 26428580635, 4985, 1078133167, 1078117201, 112608921600, 9360177523200], 'label': '20736.hv.48.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '48.hk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hk1', 'subgroup_fusion': None, 'weyl_group': '216.159'}
  • id: 165832212
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.bb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [949, -1, 935, -1], 'generators': [134983133510400, 4985, 1078117201, 112608921600, 1078140940, 26428567087, 9360177523200], 'label': '20736.hv.48.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.hl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hl1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832213
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.q1', '24.fu1', '24.fx1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [587, -1, 565, -1], 'generators': [2647090248245, 1078132446, 134983133510400, 1078121465, 25514092800, 112608921600, 9360177523200], 'label': '20736.hv.48.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.hm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hm1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832214
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '24.fu1', '24.fx1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [521, -1, 545, -1], 'generators': [1078132446, 134983133510400, 1078121465, 25514092800, 112608921600, 2628844618652, 9360177523200], 'label': '20736.hv.48.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.hn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hn1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832215
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '24.ft1', '24.fx1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [498, -1, 590, -1], 'generators': [134983133510400, 1078136543, 25514092800, 112608921600, 1078140940, 2628844639618, 9360177523200], 'label': '20736.hv.48.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.ho1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ho1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832216
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.x1', '24.ft1', '24.fx1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [431, -1, 490, -1], 'generators': [134983133510400, 1078120744, 7865729194652, 112608921600, 1078146715, 26428567087, 9360177523200], 'label': '20736.hv.48.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.hp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hp1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832217
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.q1', '24.ft1', '24.fy1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [453, -1, 525, -1], 'generators': [134983133510400, 1078135822, 25514092800, 2647090245299, 112608921600, 1078141661, 9360177523200], 'label': '20736.hv.48.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.hq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hq1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832218
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '24.ft1', '24.fy1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [476, -1, 476, -1], 'generators': [134983133510400, 2628844614114, 1078135822, 25514092800, 112608921600, 1078141661, 9360177523200], 'label': '20736.hv.48.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.hr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hr1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832219
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.d1', '6.e1'], 'contains': ['24.cr1', '24.cx1', '24.de1', '24.dj1', '24.dk1', '24.el1', '24.eq1', '24.fd1', '24.ff1', '36.p1', '36.bd1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4772, -1, 5468, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 25430664104, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.12.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.u1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832220
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '24.fu1', '24.fy1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [615, -1, 615, -1], 'generators': [134983133510400, 26428580635, 1078120744, 1078133167, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.48.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.hs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hs1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832221
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.x1', '24.fu1', '24.fy1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [638, -1, 505, -1], 'generators': [134983133510400, 26428580635, 1078120744, 1078133167, 112608921600, 2628844618652, 9360177523200], 'label': '20736.hv.48.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.ht1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ht1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832222
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.bb1', '24.bf1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [898, -1, 824, -1], 'generators': [29514, 9360177523200, 4985, 134983133510400, 25514109487, 1078116480, 112608921600], 'label': '20736.hv.48.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.hu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hu1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832223
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '24.fv1', '24.fw1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5788, -1, 2173, -1], 'generators': [134983133510400, 29514, 25514092800, 112608921600, 2646966489420, 19342, 9360177523200], 'label': '20736.hv.48.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.hv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hv1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832224
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.g1', '24.fv1', '24.fw1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5876, -1, 2049, -1], 'generators': [134983133510400, 29514, 25514092800, 112608921600, 2628761170209, 19342, 9360177523200], 'label': '20736.hv.48.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.hw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hw1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832225
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.bb1', '24.fv1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5104, -1, 1365, -1], 'generators': [134983133510400, 26428555385, 1078133167, 1078117201, 112608921600, 26428574860, 9360177523200], 'label': '20736.hv.48.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '48.hx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hx1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
  • id: 165832226
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.bb1', '24.bf1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [999, -1, 979, -1], 'generators': [134983133510400, 25514092800, 1078142574, 1078133167, 1078117201, 112608921600, 9360177523200], 'label': '20736.hv.48.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.hy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hy1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832227
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.bf1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [797, -1, 801, -1], 'generators': [134983133510400, 4985, 29514, 25514092800, 1078133167, 112608921600, 9360177523200], 'label': '20736.hv.48.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.hz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.hz1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832228
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.bf1', '24.fw1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5054, -1, 1321, -1], 'generators': [134983133510400, 26428580635, 1078133167, 1078117201, 112608921600, 25514097785, 9360177523200], 'label': '20736.hv.48.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '48.ia1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ia1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
  • id: 165832229
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.bb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [974, -1, 957, -1], 'generators': [1078140940, 1078117201, 26428567087, 9360177523200, 25514097785, 134983133510400, 112608921600], 'label': '20736.hv.48.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.ib1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ib1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832230
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.h1', '6.l1'], 'contains': ['24.ct1', '24.cw1', '24.db1', '24.fj1', '24.fk1', '36.be1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6577, -1, 6282, -1], 'generators': [134983133510400, 25430643046, 16687, 25514092800, 112608921600, 2647090225052, 30235, 4264, 9360177523200], 'label': '20736.hv.12.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.v1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165832231
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bb1', '24.bf1', '24.fx1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [722, -1, 720, -1], 'generators': [134983133510400, 26428555385, 1078133167, 112608921600, 26428574860, 25514093521, 9360177523200], 'label': '20736.hv.48.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '48.ic1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ic1', 'subgroup_fusion': None, 'weyl_group': '216.159'}
  • id: 165832232
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bc1', '24.fx1', '24.fy1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [390, -1, 444, -1], 'generators': [25181, 134983133510400, 2628844614114, 25514092800, 112608921600, 19342, 9360177523200], 'label': '20736.hv.48.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.id1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.id1', 'subgroup_fusion': None, 'weyl_group': '432.756'}
  • id: 165832233
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bd1', '24.fx1', '24.fy1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [412, -1, 425, -1], 'generators': [25181, 134983133510400, 25514092800, 2647090245299, 112608921600, 19342, 9360177523200], 'label': '20736.hv.48.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '48.ie1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ie1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832234
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1', '24.bf1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [823, -1, 846, -1], 'generators': [134983133510400, 29514, 25514092800, 1078142574, 1078133167, 112608921600, 9360177523200], 'label': '20736.hv.48.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.if1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.if1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832235
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '24.bf1', '24.fy1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 4, 'diagramx': [311, -1, 327, -1], 'generators': [134983133510400, 1078138249, 29514, 25514092800, 1078116480, 112608921600, 9360177523200], 'label': '20736.hv.48.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.ig1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ig1', 'subgroup_fusion': None, 'weyl_group': '648.703'}
  • id: 165832236
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '24.bb1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 4, 'diagramx': [363, -1, 371, -1], 'generators': [134983133510400, 26428555385, 1078117201, 112608921600, 1078140940, 26428567087, 9360177523200], 'label': '20736.hv.48.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '48.ih1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ih1', 'subgroup_fusion': None, 'weyl_group': '324.160'}
  • id: 165832237
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bo1', '24.fw1', '24.fz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5912, -1, 2190, -1], 'generators': [134983133510400, 1078135822, 25514092800, 1078145994, 112608921600, 2628761170209, 9360177523200], 'label': '20736.hv.48.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.ii1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ik1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832238
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bq1', '24.fw1', '24.fz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5859, -1, 2034, -1], 'generators': [134983133510400, 1078135822, 25514092800, 1078145994, 112608921600, 2646966489420, 9360177523200], 'label': '20736.hv.48.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.ij1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.il1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832239
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bs1', '24.fv1', '24.fz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5933, -1, 2223, -1], 'generators': [134983133510400, 2646966471087, 25514097064, 112608921600, 1078146715, 26428567087, 9360177523200], 'label': '20736.hv.48.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.ik1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ii1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832240
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bv1', '24.fv1', '24.fz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5893, -1, 2206, -1], 'generators': [134983133510400, 25514097064, 112608921600, 1078146715, 7879101314486, 26428567087, 9360177523200], 'label': '20736.hv.48.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.il1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ij1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832241
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['12.a1', '16.a1', '16.b1', '16.c1', '16.e1', '16.f1', '16.g1', '16.h1', '16.i1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [170, 2927, 194, 5768], 'generators': [25514092800, 1078117201, 16687, 9360177523200, 4985, 134983133510400, 46036847791741, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.4.a1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '20736.hv', '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': '20000.dy'}
  • id: 165832242
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.h1', '6.j1'], 'contains': ['24.ct1', '24.cx1', '24.da1', '24.ds1', '24.dt1', '36.q1', '36.bf1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4755, -1, 5384, -1], 'generators': [134983133510400, 26468479846, 16687, 25514092800, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.12.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.w1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165832243
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bo1', '24.fv1', '24.ga1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5953, -1, 2066, -1], 'generators': [134983133510400, 1078121465, 25514092800, 1078117201, 112608921600, 2628761165811, 9360177523200], 'label': '20736.hv.48.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.im1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.im1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832244
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bq1', '24.fv1', '24.ga1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5428, -1, 2019, -1], 'generators': [134983133510400, 1078121465, 25514092800, 1078117201, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.48.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.in1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.in1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832245
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bs1', '24.fw1', '24.ga1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [5552, -1, 2156, -1], 'generators': [134983133510400, 1078120744, 2646966471087, 25514092800, 1078116480, 112608921600, 9360177523200], 'label': '20736.hv.48.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.io1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.io1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832246
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bv1', '24.fw1', '24.ga1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [5457, -1, 2004, -1], 'generators': [134983133510400, 26428580635, 1078133167, 112608921600, 2646966474806, 4264, 9360177523200], 'label': '20736.hv.48.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.ip1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ip1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832247
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.h1', '24.fz1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5079, -1, 1343, -1], 'generators': [1078117201, 9360177523200, 4985, 134983133510400, 25514109487, 1078116480, 112608921600], 'label': '20736.hv.48.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '48.iq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.iq1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
  • id: 165832248
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '24.fz1', '24.ga1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5244, -1, 1973, -1], 'generators': [134983133510400, 721, 4985, 25514092800, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.48.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.ir1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ir1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832249
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.g1', '24.fz1', '24.ga1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5842, -1, 1989, -1], 'generators': [134983133510400, 721, 4985, 25514092800, 112608921600, 2628761165811, 9360177523200], 'label': '20736.hv.48.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '48.is1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.is1', 'subgroup_fusion': None, 'weyl_group': '432.755'}
  • id: 165832250
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.h1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2282, -1, 1024, -1], 'generators': [134983133510400, 1078138249, 25514092800, 1078133167, 1078117201, 112608921600, 9360177523200], 'label': '20736.hv.48.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.it1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.it1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 165832251
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.h1', '24.h1', '24.ga1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 4, 'diagramx': [4059, -1, 1299, -1], 'generators': [134983133510400, 26428555385, 26428580635, 1078133167, 1078117201, 112608921600, 9360177523200], 'label': '20736.hv.48.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '48.iu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.iu1', 'subgroup_fusion': None, 'weyl_group': '648.704'}
  • id: 165832252
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1', '24.d1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 4, 'diagramx': [337, -1, 349, -1], 'generators': [134983133510400, 26428551121, 112608921600, 1078140940, 25514097785, 26428567087, 9360177523200], 'label': '20736.hv.48.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '48.iv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.iv1', 'subgroup_fusion': None, 'weyl_group': '324.160'}
  • id: 165832253
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.i1', '6.m1'], 'contains': ['24.cv1', '24.cw1', '24.dd1', '24.fo1', '24.fp1', '36.bg1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7238, -1, 6383, -1], 'generators': [134983133510400, 25430643046, 16687, 25514092800, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.12.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.x1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1', 'subgroup_fusion': None, 'weyl_group': '10000.en'}
  • id: 165832254
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ch1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 48, 'diagramx': [9420, -1, 9878, -1], 'generators': [134983133510400, 112608921600, 1078146715, 123775784, 2647090220036, 26428567087, 9360177523200], 'label': '20736.hv.48.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ch1', 'old_label': '48.iw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.iw1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 165832255
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '48.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.j1', '24.ch1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 48, 'diagramx': [5624, -1, 1659, -1], 'generators': [134983133510400, 25514092800, 25430641943, 1078116480, 112608921600, 2647090225530, 9360177523200], 'label': '20736.hv.48.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ch1', 'old_label': '48.ix1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ix1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 165832256
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '27.b1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 27, 'diagramx': [5172, -1, 6184, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 25430664104, 1321086788252, 1078117201, 30235], 'label': '20736.hv.54.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.a1', 'projective_image': '20736.hv', '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': '192.1147'}
  • id: 165832257
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '27.b1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 27, 'diagramx': [1886, -1, 6238, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 25430664104, 1078117201, 1339292114972, 30235], 'label': '20736.hv.54.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.b1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832258
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '27.b1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 27, 'diagramx': [6753, -1, 6167, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 1078117201, 1339292114972, 30235, 26468500904], 'label': '20736.hv.54.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832259
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '27.b1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 27, 'diagramx': [4502, -1, 6344, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 1321086788252, 1078117201, 30235, 26468500904], 'label': '20736.hv.54.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.d1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832260
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '27.b1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 27, 'diagramx': [7321, -1, 6865, -1], 'generators': [1078120744, 16687, 1321086809218, 126937858924800, 25514092800, 1078116480, 1078146715, 26468500904], 'label': '20736.hv.54.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.e1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832261
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '27.b1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 27, 'diagramx': [4483, -1, 6848, -1], 'generators': [1078120744, 16687, 126937858924800, 25514092800, 1321086788252, 1078116480, 1078146715, 26468500904], 'label': '20736.hv.54.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832262
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '27.b1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 27, 'diagramx': [1937, -1, 6420, -1], 'generators': [25514092800, 126937858924800, 26468479846, 16687, 1078116480, 1078146715, 1078120744, 1321086788252], 'label': '20736.hv.54.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832263
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1', '27.b1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 27, 'diagramx': [4674, -1, 6458, -1], 'generators': [25514092800, 126937858924800, 1321086809218, 26468479846, 16687, 1078116480, 1078146715, 1078120744], 'label': '20736.hv.54.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832264
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.i1', '6.j1'], 'contains': ['24.cv1', '24.cx1', '24.cy1', '24.dx1', '24.dy1', '36.r1', '36.bh1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4309, -1, 5397, -1], 'generators': [134983133510400, 26468479846, 16687, 25514092800, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.12.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.y1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1', 'subgroup_fusion': None, 'weyl_group': '50000.bs'}
  • id: 165832265
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1', '27.b1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [1916, -1, 6382, -1], 'generators': [25514092800, 126937858924800, 1339292114972, 25430664104, 721, 30235, 16687, 4985], 'label': '20736.hv.54.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 165832266
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1', '27.b1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [4522, -1, 6815, -1], 'generators': [721, 16687, 4985, 126937858924800, 25514092800, 25430664104, 1321086788252, 30235], 'label': '20736.hv.54.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832267
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '27.b1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [1843, -1, 5384, -1], 'generators': [721, 16687, 4985, 126937858924800, 25514092800, 1321086788252, 30235, 26468500904], 'label': '20736.hv.54.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832268
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '27.b1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [6725, -1, 6832, -1], 'generators': [25514092800, 26468500904, 126937858924800, 1339292114972, 721, 30235, 16687, 4985], 'label': '20736.hv.54.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.l1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832269
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.j1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 54, 'diagramx': [4190, -1, 3905, -1], 'generators': [721, 16687, 4985, 25514092800, 9683982604800, 1321086788252, 30235, 26468500904], 'label': '20736.hv.54.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.m1', 'old_label': '54.m1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832270
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '27.a1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [126, -1, 114, -1], 'generators': [16687, 4985, 25514092800, 41876802358141, 1078117201, 1078116480, 1078146715, 26468500904], 'label': '20736.hv.54.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.n1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 165832271
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '27.a1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [252, -1, 171, -1], 'generators': [16687, 4985, 8395548138806, 9248646718801, 9248646718080, 9690289822080, 67235063236861, 9248646748315], 'label': '20736.hv.54.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.o1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 165832272
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '27.a1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [75, -1, 103, -1], 'generators': [9248646718801, 9248646718080, 67235063236861, 16687, 4985, 9248646748315, 1321086788252, 9690289822080], 'label': '20736.hv.54.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.p1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 165832273
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1', '27.b1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [2104, -1, 5525, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078117201, 1078116480, 1078146715, 26468500904], 'label': '20736.hv.54.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.q1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832274
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '27.b1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [4078, -1, 6148, -1], 'generators': [133937077482806, 16687, 4985, 126937858924800, 87302033280, 1078117201, 1078116480, 1078146715], 'label': '20736.hv.54.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.r1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832275
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.i1', '6.l1'], 'contains': ['24.cw1', '24.cy1', '24.cz1', '36.bi1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5660, -1, 6585, -1], 'generators': [134983133510400, 25430643046, 16687, 25514092800, 112608921600, 2647090246018, 30235, 4264, 9360177523200], 'label': '20736.hv.12.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.z1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1', 'subgroup_fusion': None, 'weyl_group': '1152.43028'}
  • id: 165832276
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1', '27.b1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 27, 'diagramx': [1285, -1, 5827, -1], 'generators': [25514092800, 126937858924800, 1078117201, 16687, 4985, 1078116480, 1078146715, 1321086788252], 'label': '20736.hv.54.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.s1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832277
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.e1', '32.a1', '32.b1', '32.c1'], 'contains': ['192.A', '256.a1'], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [199, -1, 185, -1], 'generators': [134983133510400, 16687, 112608921600, 46036847791741, 30235, 9360177523200], 'label': '20736.hv.64.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '64.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 165832278
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.f1', '16.g1', '32.d1'], 'contains': ['256.a1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [148, -1, 82, -1], 'generators': [134983133510400, 29514, 112608921600, 46036847791741, 21769, 9360177523200], 'label': '20736.hv.64.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.d1', 'old_label': '64.b1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '216.95'}
  • id: 165832279
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.h1', '16.i1', '32.e1'], 'contains': ['256.a1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [256, -1, 447, -1], 'generators': [134983133510400, 721, 4985, 112608921600, 46036847791741, 9360177523200], 'label': '20736.hv.64.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.e1', 'old_label': '64.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
  • id: 165832280
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '16.f1', '16.h1', '32.f1', '32.g1', '32.h1'], 'contains': ['192.B', '256.a1'], 'core': '192.B', 'coset_action_label': None, 'count': 32, 'diagramx': [52, -1, 48, -1], 'generators': [134983133510400, 26428580635, 1078133167, 112608921600, 46036847791741, 9360177523200], 'label': '20736.hv.64.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '64.d1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 165832281
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '16.f1', '16.i1', '32.k1'], 'contains': ['256.a1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [96, -1, 117, -1], 'generators': [134983133510400, 26428572169, 1078145994, 112608921600, 46036847791741, 9360177523200], 'label': '20736.hv.64.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.k1', 'old_label': '64.e1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1', 'subgroup_fusion': None, 'weyl_group': '648.703'}
  • id: 165832282
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '16.g1', '16.h1', '32.j1'], 'contains': ['256.a1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [222, -1, 510, -1], 'generators': [134983133510400, 26428555385, 1078117201, 112608921600, 46036847791741, 9360177523200], 'label': '20736.hv.64.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.j1', 'old_label': '64.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': '648.704'}
  • id: 165832283
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.g1', '16.i1', '32.i1'], 'contains': ['256.a1'], 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [74, -1, 64, -1], 'generators': [134983133510400, 112608921600, 46036847791741, 1078140940, 26428567087, 9360177523200], 'label': '20736.hv.64.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.i1', 'old_label': '64.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1', 'subgroup_fusion': None, 'weyl_group': '648.705'}
  • id: 165832284
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '16.j1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': [115, -1, 100, -1], 'generators': [134983133510400, 2628844643915, 112608921600, 46036847768960, 26468506671, 9360177523200], 'label': '20736.hv.64.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.h1', 'old_label': '64.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 165832285
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '16.f1', '16.g1', '16.h1', '16.i1'], 'contains': ['256.a1'], 'core': '768.A', 'coset_action_label': None, 'count': 128, 'diagramx': [170, -1, 133, -1], 'generators': [134983133510400, 1078121465, 112608921600, 46036847791741, 25514093521, 9360177523200], 'label': '20736.hv.64.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.i1', 'old_label': '64.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1', 'subgroup_fusion': None, 'weyl_group': '324.160'}
  • id: 165832286
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.h1', '6.m1'], 'contains': ['24.cw1', '24.da1', '24.dc1', '36.bj1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6603, -1, 6445, -1], 'generators': [134983133510400, 25430643046, 16687, 25514092800, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.12.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.ba1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1', 'subgroup_fusion': None, 'weyl_group': '4000.fh'}
  • id: 165832287
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '36.cp1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1615, -1, 1224, -1], 'generators': [126937858924800, 1078117201, 4985, 25514109487, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.72.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 165832288
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '36.ch1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4628, -1, 2737, -1], 'generators': [133937077482806, 721, 4985, 126937858924800, 25514092800, 9683982604800, 24460], 'label': '20736.hv.72.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.b1', 'projective_image': '20736.hv', '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': '48.51'}
  • id: 165832289
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '36.ch1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4511, -1, 3193, -1], 'generators': [721, 4985, 126937858924800, 25514092800, 9683982604800, 24460, 133937077497420], 'label': '20736.hv.72.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.c1', 'projective_image': '20736.hv', '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': '48.51'}
  • id: 165832290
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '36.cp1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1528, -1, 1207, -1], 'generators': [1078117201, 9360177523200, 4985, 25514109487, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.72.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.d1', 'projective_image': '20736.hv', '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': '36.10'}
  • id: 165832291
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '36.cp1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3832, -1, 1534, -1], 'generators': [25514092800, 126937858924800, 1078117201, 4985, 1078116480, 1078146715, 5324705527680], 'label': '20736.hv.72.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.e1', 'projective_image': '20736.hv', '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': '36.10'}
  • id: 165832292
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '36.a1', '36.cl1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5329, -1, 3513, -1], 'generators': [721, 4985, 25514092800, 24460, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.72.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '72.f1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832293
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '36.b1', '36.cl1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5276, -1, 4193, -1], 'generators': [721, 4985, 25514092800, 24460, 112608921600, 2646966489420, 9360177523200], 'label': '20736.hv.72.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1', 'old_label': '72.g1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832294
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.g1', '36.a1', '36.b1', '36.co1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6117, -1, 4212, -1], 'generators': [721, 2628761162700, 4985, 25514092800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.72.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.h1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832295
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '36.a1', '36.b1', '36.cp1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5250, -1, 2637, -1], 'generators': [1078121465, 25514092800, 1078133167, 1078117201, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.72.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.i1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 165832296
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.ch1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3550, -1, 3119, -1], 'generators': [87302049967, 134983133510400, 721, 4985, 24460, 2646966474806, 9360177523200], 'label': '20736.hv.72.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.j1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 165832297
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.i1', '6.k1'], 'contains': ['24.cx1', '24.cz1', '24.dd1', '36.bk1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6827, -1, 6690, -1], 'generators': [134983133510400, 26468479846, 16687, 25514092800, 112608921600, 2647090246018, 30235, 4264, 9360177523200], 'label': '20736.hv.12.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165832298
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.ch1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3581, -1, 3081, -1], 'generators': [133937077482806, 721, 4985, 25514109487, 126937858924800, 9683982604800, 24460], 'label': '20736.hv.72.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.k1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 165832299
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.cl1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4878, -1, 4173, -1], 'generators': [721, 4985, 25514109487, 24460, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.72.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.br1', 'old_label': '72.l1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832300
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.i1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7593, -1, 6799, -1], 'generators': [20063, 126937858924800, 25514092800, 9683982604800, 24460, 133913559622018, 26468500904], 'label': '20736.hv.72.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.m1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832301
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.i1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8049, -1, 6708, -1], 'generators': [20063, 126937858924800, 25514092800, 9683982604800, 133913559627364, 24460, 26468500904], 'label': '20736.hv.72.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.n1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832302
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '36.br1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6814, -1, 7880, -1], 'generators': [25514109487, 126937858924800, 1078116480, 112608921600, 1078146715, 19342, 26468500904], 'label': '20736.hv.72.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.br1', 'old_label': '72.o1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832303
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '36.bq1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5501, -1, 7515, -1], 'generators': [25514109487, 1078116480, 112608921600, 1078146715, 19342, 26468500904, 9360177523200], 'label': '20736.hv.72.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bq1', 'old_label': '72.p1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832304
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.c1', '36.t1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8778, -1, 8339, -1], 'generators': [20063, 25514092800, 24460, 112608921600, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.72.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.q1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832305
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.d1', '36.t1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9041, -1, 8302, -1], 'generators': [25514092800, 26468500904, 2628844644964, 24460, 9360177523200, 20063, 112608921600], 'label': '20736.hv.72.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.r1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832306
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.l1', '36.c1', '36.d1', '36.v1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8947, -1, 9263, -1], 'generators': [20063, 25514092800, 24460, 112608921600, 2647090246018, 26468500904, 9360177523200], 'label': '20736.hv.72.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.s1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832307
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.m1', '36.c1', '36.d1', '36.z1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8907, -1, 9032, -1], 'generators': [25430669871, 20063, 25514092800, 24460, 112608921600, 2647090246018, 9360177523200], 'label': '20736.hv.72.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.t1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832308
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.h1', '6.k1'], 'contains': ['24.cx1', '24.db1', '24.dc1', '36.bl1'], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5544, -1, 6645, -1], 'generators': [134983133510400, 26468479846, 16687, 25514092800, 112608921600, 2647090225052, 30235, 4264, 9360177523200], 'label': '20736.hv.12.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1', 'subgroup_fusion': None, 'weyl_group': '50000.bc'}
  • id: 165832309
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '36.c1', '36.ba1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8428, -1, 9246, -1], 'generators': [25430669871, 20063, 25514092800, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.72.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.u1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832310
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1', '36.d1', '36.ba1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8669, -1, 8990, -1], 'generators': [25430669871, 20063, 25514092800, 24460, 112608921600, 2628844644964, 9360177523200], 'label': '20736.hv.72.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.v1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832311
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '36.bq1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7117, -1, 8078, -1], 'generators': [1078121465, 25514109487, 126937858924800, 1078133167, 5324705527680, 1078140940, 26468500904], 'label': '20736.hv.72.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bq1', 'old_label': '72.w1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832312
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '36.e1', '36.bn1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1592, -1, 1618, -1], 'generators': [1078135822, 25514092800, 1078117201, 24460, 112608921600, 2647090220514, 9360177523200], 'label': '20736.hv.72.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.x1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832313
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '36.e1', '36.f1', '36.bp1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1481, -1, 1639, -1], 'generators': [1078135822, 25514092800, 1078117201, 24460, 9360177523200, 2628844618652, 112608921600], 'label': '20736.hv.72.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.y1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832314
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1', '36.f1', '36.bn1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2126, -1, 2138, -1], 'generators': [1078135822, 25514092800, 1078117201, 24460, 112608921600, 2647090225052, 9360177523200], 'label': '20736.hv.72.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.z1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832315
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '36.c1', '36.d1', '36.br1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8795, -1, 8604, -1], 'generators': [1078121465, 25514109487, 126937858924800, 1078133167, 112608921600, 1078140940, 26468500904], 'label': '20736.hv.72.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ba1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832316
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '36.c1', '36.d1', '36.bt1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8927, -1, 9067, -1], 'generators': [1078136543, 2646966471087, 25514092800, 1078116480, 112608921600, 1078140940, 9360177523200], 'label': '20736.hv.72.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.bb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832317
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '36.c1', '36.e1', '36.bu1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7419, -1, 7960, -1], 'generators': [1078136543, 25514092800, 1078116480, 112608921600, 1078140940, 2628844639618, 9360177523200], 'label': '20736.hv.72.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.bc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832318
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.w1', '36.d1', '36.f1', '36.bu1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7457, -1, 8434, -1], 'generators': [1078136543, 25514092800, 1078116480, 112608921600, 1078140940, 2628844644964, 9360177523200], 'label': '20736.hv.72.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.bd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832319
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.d1', '6.n1'], 'contains': ['24.ba1', '24.bo1', '24.bp1', '24.ct1', '24.dd1', '24.de1', '24.fi1', '24.fq1', '36.bm1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6926, -1, 5721, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 2628761148086, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.12.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165832320
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.x1', '36.e1', '36.f1', '36.bx1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1421, -1, 1698, -1], 'generators': [1078136543, 25514092800, 1078116480, 112608921600, 1078140940, 2628844618652, 9360177523200], 'label': '20736.hv.72.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.be1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832321
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '36.t1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8137, -1, 7287, -1], 'generators': [25514109487, 25514097064, 24460, 112608921600, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.72.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1', 'old_label': '72.bf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832322
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '36.i1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7477, -1, 6624, -1], 'generators': [25514109487, 126937858924800, 25514097064, 9683982604800, 24460, 133913559622018, 26468500904], 'label': '20736.hv.72.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.bg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832323
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '36.i1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7497, -1, 6642, -1], 'generators': [134983133510400, 1321086809218, 25514109487, 25514097064, 24460, 26468500904, 9360177523200], 'label': '20736.hv.72.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.bh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832324
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1', '36.bc1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6912, -1, 7593, -1], 'generators': [25514109487, 25514097064, 24460, 112608921600, 123775784, 2628844618652, 9360177523200], 'label': '20736.hv.72.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '72.bi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1', 'subgroup_fusion': None, 'weyl_group': '288.880'}
  • id: 165832325
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '36.bm1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7576, -1, 5938, -1], 'generators': [7879101314486, 1078117201, 24460, 9360177523200, 25514109487, 26428555385, 112608921600], 'label': '20736.hv.72.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bm1', 'old_label': '72.bj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832326
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1', '36.cp1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1687, -1, 1494, -1], 'generators': [126937858924800, 19342, 1078117201, 25514109487, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.72.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.bk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 165832327
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '36.ci1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1504, -1, 1785, -1], 'generators': [4985, 126937858924800, 9683982604800, 24460, 15966, 2628844618652, 89377906464000], 'label': '20736.hv.72.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1', 'old_label': '72.bl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832328
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1', '36.ci1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1570, -1, 1895, -1], 'generators': [2628844614114, 4985, 126937858924800, 9683982604800, 24460, 15966, 89377906464000], 'label': '20736.hv.72.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1', 'old_label': '72.bm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832329
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bb1', '36.cp1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1898, -1, 1477, -1], 'generators': [25514109487, 1078117201, 1078116480, 112608921600, 1078146715, 19342, 9360177523200], 'label': '20736.hv.72.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.bn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 165832330
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.e1', '6.o1'], 'contains': ['24.q1', '24.s1', '24.by1', '24.cv1', '24.db1', '24.de1', '24.fn1', '24.fr1', '36.bn1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5369, -1, 5370, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 1078117201, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.12.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.be1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165832331
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bf1', '36.cp1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1401, -1, 1129, -1], 'generators': [4985, 126937858924800, 25514092800, 1078133167, 1078117201, 112608921600, 1078146715], 'label': '20736.hv.72.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.bo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 165832332
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '36.e1', '36.cm1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1440, -1, 1576, -1], 'generators': [4985, 25514092800, 24460, 112608921600, 15966, 2628844618652, 9360177523200], 'label': '20736.hv.72.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.bp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832333
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bd1', '36.e1', '36.f1', '36.cn1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1460, -1, 1679, -1], 'generators': [4985, 25514092800, 24460, 112608921600, 2647090225052, 15966, 9360177523200], 'label': '20736.hv.72.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1', 'old_label': '72.bq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832334
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1', '36.f1', '36.cm1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1549, -1, 1856, -1], 'generators': [2628844614114, 4985, 25514092800, 24460, 112608921600, 15966, 9360177523200], 'label': '20736.hv.72.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.br1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832335
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bf1', '36.e1', '36.f1', '36.cp1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1381, -1, 1190, -1], 'generators': [126937858924800, 25514092800, 1078117201, 1078116480, 112608921600, 1078146715, 19342], 'label': '20736.hv.72.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.bs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 165832336
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1', '36.ci1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1653, -1, 2256, -1], 'generators': [89377906464721, 4985, 126937858924800, 9683982604800, 24460, 89377906480687, 2628844618652], 'label': '20736.hv.72.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1', 'old_label': '72.bt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832337
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1', '36.ci1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1633, -1, 2239, -1], 'generators': [134983133510400, 4985, 25514109487, 1321086788252, 24460, 25514093521, 9360177523200], 'label': '20736.hv.72.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1', 'old_label': '72.bu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832338
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1', '36.cm1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2554, -1, 2699, -1], 'generators': [24460, 25514093521, 9360177523200, 4985, 2628844618652, 25514109487, 112608921600], 'label': '20736.hv.72.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '72.bv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832339
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1', '36.i1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8093, -1, 7152, -1], 'generators': [126937858924800, 25514092800, 9683982604800, 24460, 133913559622018, 4264, 26468500904], 'label': '20736.hv.72.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.bw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832340
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1', '36.i1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7612, -1, 6763, -1], 'generators': [126937858924800, 25514092800, 9683982604800, 24460, 133913559622018, 26468506671, 4264], 'label': '20736.hv.72.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.bx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832341
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.e1', '6.n1'], 'contains': ['24.bq1', '24.cy1', '24.dc1', '24.de1', '36.bo1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5621, -1, 6213, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 1078117201, 112608921600, 2646966474806, 30235, 9360177523200], 'label': '20736.hv.12.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165832342
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1', '36.br1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6684, -1, 7813, -1], 'generators': [126937858924800, 26468500904, 4985, 25514109487, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.72.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.br1', 'old_label': '72.by1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832343
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bn1', '36.bq1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5228, -1, 7420, -1], 'generators': [26468500904, 9360177523200, 4985, 25514109487, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.72.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bq1', 'old_label': '72.bz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832344
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1', '36.g1', '36.t1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9229, -1, 8354, -1], 'generators': [25514092800, 26468500904, 4264, 24460, 9360177523200, 2628844639618, 112608921600], 'label': '20736.hv.72.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ca1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832345
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1', '36.h1', '36.t1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8815, -1, 8321, -1], 'generators': [25514092800, 26468506671, 4264, 24460, 9360177523200, 2628844639618, 112608921600], 'label': '20736.hv.72.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832346
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bj1', '36.g1', '36.h1', '36.v1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9198, -1, 9282, -1], 'generators': [25514092800, 26468506671, 4264, 24460, 9360177523200, 2647090251364, 112608921600], 'label': '20736.hv.72.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832347
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '36.g1', '36.z1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8858, -1, 9155, -1], 'generators': [25430669871, 25514092800, 24460, 112608921600, 4264, 2647090251364, 9360177523200], 'label': '20736.hv.72.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.cd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832348
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bl1', '36.g1', '36.h1', '36.ba1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9123, -1, 9171, -1], 'generators': [25514092800, 25430664104, 24460, 112608921600, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.72.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ce1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832349
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1', '36.h1', '36.z1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8838, -1, 9011, -1], 'generators': [25514092800, 25430664104, 24460, 112608921600, 4264, 2647090251364, 9360177523200], 'label': '20736.hv.72.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.cf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832350
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.br1', '36.bq1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7844, -1, 8092, -1], 'generators': [4985, 126937858924800, 25514092800, 1078116480, 1078146715, 5324705527680, 26468500904], 'label': '20736.hv.72.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bq1', 'old_label': '72.cg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832351
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1', '36.a1', '36.bm1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6737, -1, 4417, -1], 'generators': [1078132446, 1078135822, 2628761162700, 25514092800, 24460, 112608921600, 9360177523200], 'label': '20736.hv.72.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.ch1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832352
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.a1', '8.b1', '8.c1', '12.bw1', '12.bx1', '16.d1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [347, -1, 283, -1], 'generators': [26468500904, 721, 30235, 16687, 9360177523200, 4985, 2628844618652, 134983133510400, 46036847791741, 112608921600], 'label': '20736.hv.4.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '4.b1', 'projective_image': '20736.hv', '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': None}
  • id: 165832353
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.d1', '6.o1'], 'contains': ['24.r1', '24.cz1', '24.da1', '24.de1', '36.bp1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5639, -1, 6197, -1], 'generators': [134983133510400, 16687, 1078121465, 25514092800, 1078117201, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.12.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165832354
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1', '36.b1', '36.bm1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7003, -1, 5544, -1], 'generators': [1078132446, 1078135822, 25514092800, 2628761148086, 24460, 112608921600, 9360177523200], 'label': '20736.hv.72.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.ci1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832355
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bq1', '36.a1', '36.b1', '36.bo1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5969, -1, 4231, -1], 'generators': [1078132446, 1078135822, 25514092800, 24460, 112608921600, 2646966489420, 9360177523200], 'label': '20736.hv.72.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.cj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832356
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.br1', '36.g1', '36.h1', '36.br1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9077, -1, 8620, -1], 'generators': [4985, 25514109487, 126937858924800, 1078133167, 112608921600, 1078140940, 26468500904], 'label': '20736.hv.72.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ck1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832357
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bs1', '36.a1', '36.g1', '36.bt1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6959, -1, 8129, -1], 'generators': [1078120744, 2646966471087, 25514092800, 1078116480, 112608921600, 1078140940, 9360177523200], 'label': '20736.hv.72.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.cl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832358
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bt1', '36.g1', '36.h1', '36.bu1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9177, -1, 9139, -1], 'generators': [1078120744, 25514092800, 1078116480, 112608921600, 1078140940, 2628844639618, 9360177523200], 'label': '20736.hv.72.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832359
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bu1', '36.b1', '36.h1', '36.bt1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6982, -1, 8495, -1], 'generators': [1078120744, 25514092800, 1078116480, 112608921600, 1078140940, 2646966487501, 9360177523200], 'label': '20736.hv.72.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.cn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832360
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bv1', '36.a1', '36.b1', '36.bw1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6016, -1, 4396, -1], 'generators': [1078120744, 25514092800, 1078116480, 112608921600, 2646966474806, 1078140940, 9360177523200], 'label': '20736.hv.72.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.co1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.co1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832361
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '36.t1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7901, -1, 7381, -1], 'generators': [997953704, 25514109487, 24460, 112608921600, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.72.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1', 'old_label': '72.cp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cp1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832362
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '36.i1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7439, -1, 6674, -1], 'generators': [997953704, 126937858924800, 9683982604800, 24460, 89377906480687, 2628844639618, 4264], 'label': '20736.hv.72.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.cq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cq1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832363
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '36.i1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7375, -1, 6690, -1], 'generators': [134983133510400, 997953704, 1321086809218, 25514109487, 24460, 4264, 9360177523200], 'label': '20736.hv.72.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.cr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cr1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832364
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.f1', '6.g1'], 'contains': ['24.b1', '24.p1', '24.t1', '24.bn1', '24.br1', '24.cp1', '24.cq1', '24.cr1', '24.cs1', '24.dh1', '24.eh1', '24.ej1', '24.el1', '24.en1', '24.fa1', '36.bq1', '36.br1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6180, -1, 7644, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 1078116480, 112608921600, 1078146715, 26468500904, 9360177523200], 'label': '20736.hv.12.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832365
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1', '36.bb1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5206, -1, 7574, -1], 'generators': [25514109487, 25430664104, 7865729194652, 24460, 112608921600, 4264, 9360177523200], 'label': '20736.hv.72.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '72.cs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cs1', 'subgroup_fusion': None, 'weyl_group': '288.880'}
  • id: 165832366
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1', '36.bn1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5070, -1, 5187, -1], 'generators': [26428555385, 25514109487, 26428551121, 7865729194652, 24460, 112608921600, 9360177523200], 'label': '20736.hv.72.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bn1', 'old_label': '72.ct1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ct1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832367
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bz1', '36.c1', '36.g1', '36.cy1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9247, -1, 9408, -1], 'generators': [1078136543, 25514092800, 24460, 112608921600, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.72.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832368
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ca1', '36.d1', '36.g1', '36.cy1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9344, -1, 9206, -1], 'generators': [25514092800, 26468500904, 24460, 9360177523200, 2647090251364, 112608921600, 1078136543], 'label': '20736.hv.72.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832369
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cb1', '36.c1', '36.h1', '36.cy1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9158, -1, 9391, -1], 'generators': [1078136543, 25514092800, 24460, 112608921600, 26468506671, 2628844639618, 9360177523200], 'label': '20736.hv.72.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cw1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832370
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cc1', '36.d1', '36.h1', '36.cy1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9267, -1, 9110, -1], 'generators': [1078136543, 25514092800, 24460, 112608921600, 26468506671, 2647090251364, 9360177523200], 'label': '20736.hv.72.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cx1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832371
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cd1', '36.c1', '36.g1', '36.cz1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8972, -1, 9350, -1], 'generators': [25430669871, 1078136543, 25514092800, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.72.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cy1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832372
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ce1', '36.d1', '36.g1', '36.cz1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9327, -1, 9094, -1], 'generators': [25430669871, 1078136543, 25514092800, 24460, 112608921600, 2647090251364, 9360177523200], 'label': '20736.hv.72.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cz1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832373
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cf1', '36.c1', '36.h1', '36.cz1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8890, -1, 9336, -1], 'generators': [1078136543, 25514092800, 25430664104, 24460, 112608921600, 2628844639618, 9360177523200], 'label': '20736.hv.72.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.da1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.da1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832374
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cg1', '36.d1', '36.h1', '36.cz1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9060, -1, 9082, -1], 'generators': [1078136543, 25514092800, 25430664104, 24460, 112608921600, 2647090251364, 9360177523200], 'label': '20736.hv.72.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.db1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.db1', 'subgroup_fusion': None, 'weyl_group': '576.8666'}
  • id: 165832375
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.h1', '6.n1'], 'contains': ['24.u1', '24.bs1', '24.bu1', '24.ct1', '24.dc1', '24.dh1', '24.er1', '24.ey1', '36.bt1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6798, -1, 8428, -1], 'generators': [134983133510400, 1078120744, 16687, 2646966471087, 25514092800, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.12.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165832376
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ch1', '36.c1', '36.g1', '36.da1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9099, -1, 9318, -1], 'generators': [25514092800, 25430664104, 1078133167, 112608921600, 1078146715, 2647090220036, 9360177523200], 'label': '20736.hv.72.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dc1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832377
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ci1', '36.d1', '36.g1', '36.da1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9313, -1, 9189, -1], 'generators': [25514092800, 26468500904, 1078140940, 2647090220036, 9360177523200, 1078116480, 112608921600], 'label': '20736.hv.72.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dd1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832378
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cj1', '36.c1', '36.h1', '36.da1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8875, -1, 9299, -1], 'generators': [25514092800, 1078133167, 112608921600, 1078146715, 2647090220036, 26468500904, 9360177523200], 'label': '20736.hv.72.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.de1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.de1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832379
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ck1', '36.d1', '36.h1', '36.da1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9020, -1, 9050, -1], 'generators': [25514092800, 25430664104, 1078133167, 112608921600, 1078146715, 2628844613636, 9360177523200], 'label': '20736.hv.72.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.df1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.df1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832380
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cl1', '36.c1', '36.g1', '36.db1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9140, -1, 9421, -1], 'generators': [25430643767, 25514092800, 1078116480, 112608921600, 2647090225530, 1078140940, 9360177523200], 'label': '20736.hv.72.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dg1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832381
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cm1', '36.d1', '36.g1', '36.db1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9291, -1, 9227, -1], 'generators': [25514092800, 1078140940, 2647090220036, 25430638000, 9360177523200, 1078116480, 112608921600], 'label': '20736.hv.72.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dh1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832382
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cn1', '36.c1', '36.h1', '36.db1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8998, -1, 9370, -1], 'generators': [25514092800, 2647090225530, 1078140940, 25430638000, 9360177523200, 1078116480, 112608921600], 'label': '20736.hv.72.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.di1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.di1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832383
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.co1', '36.d1', '36.h1', '36.db1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9214, -1, 9127, -1], 'generators': [25430643767, 25514092800, 1078116480, 112608921600, 2647090220036, 1078140940, 9360177523200], 'label': '20736.hv.72.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dj1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832384
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '36.i1', '36.k1', '36.ce1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4902, -1, 5022, -1], 'generators': [134983133510400, 26428580635, 16687, 4985, 5324705527680, 30235, 26468500904], 'label': '20736.hv.72.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.dk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dk1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832385
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '36.m1', '36.bq1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4853, -1, 5702, -1], 'generators': [26428580635, 16687, 4985, 126937858924800, 5324705527680, 30235, 26468500904], 'label': '20736.hv.72.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.dl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dl1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832386
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.i1', '6.o1'], 'contains': ['24.v1', '24.w1', '24.bt1', '24.cv1', '24.cz1', '24.dh1', '24.eu1', '24.ez1', '36.bu1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7288, -1, 8359, -1], 'generators': [134983133510400, 1078120744, 16687, 25514092800, 1078116480, 112608921600, 1078146715, 2628844639618, 9360177523200], 'label': '20736.hv.12.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165832387
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '36.ce1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2001, -1, 3668, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 9683982604800, 30235, 26468500904], 'label': '20736.hv.72.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ce1', 'old_label': '72.dm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832388
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '36.l1', '36.bq1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2835, -1, 4731, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 5324705527680, 30235, 26468500904], 'label': '20736.hv.72.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.dn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dn1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832389
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '36.j1', '36.br1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2862, -1, 4481, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.do1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.do1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832390
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '36.p1', '36.bq1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4742, -1, 6222, -1], 'generators': [26428580635, 16687, 4985, 126937858924800, 25430664104, 5324705527680, 30235], 'label': '20736.hv.72.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.dp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dp1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832391
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '36.n1', '36.br1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4028, -1, 6183, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 25430664104, 112608921600, 30235], 'label': '20736.hv.72.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.dq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dq1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832392
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '36.o1', '36.bq1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3912, -1, 6130, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 25430664104, 5324705527680, 30235], 'label': '20736.hv.72.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.dr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dr1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832393
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '36.i1', '36.q1', '36.ch1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4953, -1, 4981, -1], 'generators': [16687, 126937858924800, 25514092800, 133937077479087, 9683982604800, 30235, 4264], 'label': '20736.hv.72.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.ds1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ds1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832394
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '36.j1', '36.n1', '36.cp1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2233, -1, 2718, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078117201, 112608921600, 30235], 'label': '20736.hv.72.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.dt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 165832395
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '36.i1', '36.r1', '36.ci1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4586, -1, 4915, -1], 'generators': [16687, 126937858924800, 9683982604800, 30235, 2628844639618, 4264, 89377906464000], 'label': '20736.hv.72.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.du1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.du1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832396
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1', '36.q1', '36.r1', '36.ce1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3240, -1, 3307, -1], 'generators': [134983133510400, 26428580635, 16687, 4985, 26468505950, 5324705527680, 30235], 'label': '20736.hv.72.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.dv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dv1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832397
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.h1', '6.i1'], 'contains': ['24.cw1', '24.cx1', '24.df1', '24.dg1', '24.dh1', '24.ep1', '24.eq1', '24.ev1', '24.fa1', '36.bs1', '36.bv1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4839, -1, 5737, -1], 'generators': [134983133510400, 16687, 4985, 25514092800, 1078116480, 112608921600, 1078146715, 25430669150, 9360177523200], 'label': '20736.hv.12.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832398
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1', '36.k1', '36.r1', '36.ch1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3857, -1, 4046, -1], 'generators': [133937077482806, 16687, 126937858924800, 25514092800, 9683982604800, 30235, 4264], 'label': '20736.hv.72.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.dw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dw1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832399
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1', '36.k1', '36.q1', '36.ci1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3305, -1, 3172, -1], 'generators': [16687, 126937858924800, 9683982604800, 30235, 4264, 2628844618652, 89377906464000], 'label': '20736.hv.72.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.dx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dx1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832400
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '36.m1', '36.bs1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4716, -1, 5897, -1], 'generators': [26428580635, 16687, 4985, 126937858924800, 5324705527680, 30235, 25430669150], 'label': '20736.hv.72.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.dy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dy1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832401
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1', '36.p1', '36.bs1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4284, -1, 5105, -1], 'generators': [26428580635, 16687, 4985, 126937858924800, 26468505950, 5324705527680, 30235], 'label': '20736.hv.72.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.dz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dz1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832402
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '36.l1', '36.o1', '36.cp1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2146, -1, 2817, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078117201, 5324705527680, 30235], 'label': '20736.hv.72.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ea1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ea1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 165832403
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1', '36.m1', '36.p1', '36.cp1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4539, -1, 4248, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 1078117201, 112608921600, 30235], 'label': '20736.hv.72.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.eb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 165832404
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1', '36.ce1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1720, -1, 3547, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 9683982604800, 26468505950, 30235], 'label': '20736.hv.72.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ce1', 'old_label': '72.ec1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ec1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832405
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dg1', '36.l1', '36.bs1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3667, -1, 5413, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 5324705527680, 30235, 25430669150], 'label': '20736.hv.72.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ed1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ed1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832406
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1', '36.o1', '36.bs1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2626, -1, 3862, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 26468505950, 5324705527680, 30235], 'label': '20736.hv.72.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ee1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ee1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832407
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1', '36.n1', '36.bv1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2766, -1, 4289, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 112608921600, 26468505950, 30235], 'label': '20736.hv.72.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ef1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ef1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832408
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '6.i1', '6.n1'], 'contains': ['24.bv1', '24.cy1', '24.dd1', '24.dh1', '36.bw1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5686, -1, 6604, -1], 'generators': [25514092800, 16687, 2646966474806, 9360177523200, 134983133510400, 1078116480, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.12.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165832409
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dg1', '36.j1', '36.bv1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3721, -1, 5872, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 112608921600, 30235, 25430669150], 'label': '20736.hv.72.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.eg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eg1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832410
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '36.t1', '36.u1', '36.v1', '36.w1', '36.x1', '36.br1', '36.cj1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7045, -1, 7109, -1], 'generators': [26428580635, 16687, 4985, 126937858924800, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.eh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eh1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832411
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '36.s1', '36.bq1', '36.cj1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3419, -1, 5085, -1], 'generators': [16687, 4985, 25514092800, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.72.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ei1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ei1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832412
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '36.z1', '36.ba1', '36.bb1', '36.bc1', '36.bd1', '36.br1', '36.ck1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6546, -1, 7633, -1], 'generators': [26428580635, 16687, 4985, 126937858924800, 25430664104, 112608921600, 30235], 'label': '20736.hv.72.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.ej1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ej1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832413
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '36.y1', '36.bq1', '36.ck1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4559, -1, 6165, -1], 'generators': [16687, 4985, 25514092800, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '72.ek1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ek1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832414
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '36.s1', '36.y1', '36.cp1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2165, -1, 2774, -1], 'generators': [16687, 4985, 25514092800, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.el1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.el1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 165832415
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '36.t1', '36.z1', '36.be1', '36.bf1', '36.bm1', '36.bt1', '36.cl1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6784, -1, 7070, -1], 'generators': [16687, 2646966471087, 25514092800, 112608921600, 30235, 4264, 9360177523200], 'label': '20736.hv.72.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.em1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.em1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832416
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '36.t1', '36.ba1', '36.bg1', '36.bh1', '36.bn1', '36.bu1', '36.cm1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7022, -1, 6917, -1], 'generators': [16687, 25514092800, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.72.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.en1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832417
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '36.x1', '36.be1', '36.bg1', '36.bi1', '36.bj1', '36.bv1', '36.ck1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6148, -1, 6491, -1], 'generators': [26428580635, 16687, 4985, 126937858924800, 112608921600, 30235, 25430669150], 'label': '20736.hv.72.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.eo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eo1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832418
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1', '36.bd1', '36.bf1', '36.bh1', '36.bk1', '36.bl1', '36.bv1', '36.cj1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5180, -1, 6370, -1], 'generators': [26428580635, 16687, 4985, 126937858924800, 112608921600, 26468505950, 30235], 'label': '20736.hv.72.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ep1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ep1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832419
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '6.h1', '6.o1'], 'contains': ['24.x1', '24.da1', '24.db1', '24.dh1', '36.bx1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5523, -1, 6426, -1], 'generators': [25514092800, 16687, 9360177523200, 2628844618652, 134983133510400, 1078116480, 1078146715, 1078120744, 112608921600], 'label': '20736.hv.12.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165832420
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1', '36.u1', '36.bb1', '36.bh1', '36.bi1', '36.bo1', '36.bw1', '36.cl1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5643, -1, 6898, -1], 'generators': [16687, 25514092800, 112608921600, 2646966474806, 30235, 4264, 9360177523200], 'label': '20736.hv.72.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.eq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eq1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832421
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cz1', '36.v1', '36.z1', '36.bi1', '36.bk1', '36.bp1', '36.bu1', '36.cn1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7221, -1, 7863, -1], 'generators': [16687, 25514092800, 112608921600, 2647090246018, 30235, 4264, 9360177523200], 'label': '20736.hv.72.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.er1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.er1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832422
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1', '36.u1', '36.bc1', '36.bf1', '36.bj1', '36.bp1', '36.bx1', '36.cm1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5993, -1, 6859, -1], 'generators': [16687, 25514092800, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.72.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.es1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.es1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832423
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.db1', '36.w1', '36.bb1', '36.be1', '36.bl1', '36.bn1', '36.bx1', '36.cn1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5526, -1, 6960, -1], 'generators': [16687, 25514092800, 112608921600, 2647090225052, 30235, 4264, 9360177523200], 'label': '20736.hv.72.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.et1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.et1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832424
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1', '36.v1', '36.ba1', '36.bj1', '36.bl1', '36.bo1', '36.bt1', '36.co1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6934, -1, 7897, -1], 'generators': [16687, 25514092800, 112608921600, 30235, 4264, 2628761144367, 9360177523200], 'label': '20736.hv.72.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.eu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eu1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832425
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1', '36.w1', '36.bc1', '36.bg1', '36.bk1', '36.bm1', '36.bw1', '36.co1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7288, -1, 7088, -1], 'generators': [16687, 25514092800, 2628761148086, 112608921600, 30235, 4264, 9360177523200], 'label': '20736.hv.72.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ev1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ev1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832426
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1', '36.x1', '36.bd1', '36.bm1', '36.bn1', '36.bo1', '36.bp1', '36.cp1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5480, -1, 5783, -1], 'generators': [16687, 1078121465, 25514092800, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ew1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ew1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832427
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1', '36.y1', '36.bs1', '36.cj1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3446, -1, 4503, -1], 'generators': [16687, 4985, 25514092800, 112608921600, 26468505950, 30235, 9360177523200], 'label': '20736.hv.72.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ex1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ex1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832428
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dg1', '36.s1', '36.bs1', '36.ck1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4050, -1, 5920, -1], 'generators': [16687, 4985, 25514092800, 112608921600, 30235, 25430669150, 9360177523200], 'label': '20736.hv.72.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '72.ey1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ey1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832429
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dh1', '36.bq1', '36.bs1', '36.cp1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4671, -1, 6148, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078116480, 1078146715, 5324705527680], 'label': '20736.hv.72.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ez1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ez1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 165832430
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1'], 'contains': ['24.dl1', '24.dn1', '24.do1', '24.dr1', '24.dt1', '24.dw1', '24.dy1', '36.by1', '36.bz1', '36.ca1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2767, -1, 3108, -1], 'generators': [997953704, 30235, 25514093521, 16687, 9360177523200, 2628844618652, 25514097785, 134983133510400, 112608921600], 'label': '20736.hv.12.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.bn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1', 'subgroup_fusion': None, 'weyl_group': '1728.39000'}
  • id: 165832431
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dh1', '36.br1', '36.bt1', '36.bu1', '36.bv1', '36.bw1', '36.bx1', '36.cp1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6036, -1, 7499, -1], 'generators': [16687, 4985, 126937858924800, 25514092800, 1078116480, 112608921600, 1078146715], 'label': '20736.hv.72.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.fa1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fa1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832432
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.di1', '36.n1', '36.x1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3948, -1, 5122, -1], 'generators': [126937858924800, 1078117201, 123775784, 30235, 16687, 4985, 112608921600], 'label': '20736.hv.72.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fb1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832433
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1', '36.p1', '36.s1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3622, -1, 5335, -1], 'generators': [997953704, 16687, 4985, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fc1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832434
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1', '36.o1', '36.p1', '36.cj1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3375, -1, 4307, -1], 'generators': [16687, 4985, 126937858924800, 25430664104, 1078117201, 5324705527680, 30235], 'label': '20736.hv.72.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fd1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832435
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1', '36.t1', '36.by1', '36.cq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4153, -1, 5245, -1], 'generators': [997953704, 16687, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.72.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.fe1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fe1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832436
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dm1', '36.o1', '36.s1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2270, -1, 4609, -1], 'generators': [997953704, 16687, 4985, 26428551121, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ff1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ff1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832437
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dn1', '36.n1', '36.by1', '36.cj1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [3285, -1, 3600, -1], 'generators': [16687, 4985, 126937858924800, 26428551121, 112608921600, 123775784, 30235], 'label': '20736.hv.72.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.fg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fg1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832438
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.do1', '36.u1', '36.by1', '36.cq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4078, -1, 4374, -1], 'generators': [997953704, 16687, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.72.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.fh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fh1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832439
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1', '36.ce1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1976, -1, 3495, -1], 'generators': [134983133510400, 16687, 4985, 25430664104, 1078117201, 112608921600, 30235], 'label': '20736.hv.72.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ce1', 'old_label': '72.fi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fi1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832440
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.di1', '36.m1', '36.y1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3793, -1, 4831, -1], 'generators': [16687, 4985, 1078117201, 112608921600, 123775784, 30235, 9360177523200], 'label': '20736.hv.72.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fj1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832441
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1'], 'contains': ['24.dr1', '24.dq1', '24.ds1', '24.du1', '24.dw1', '24.dv1', '24.dx1', '36.cb1', '36.cc1', '36.cd1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3133, -1, 3095, -1], 'generators': [26468500904, 30235, 25514093521, 16687, 9360177523200, 2628844618652, 25514097785, 134983133510400, 112608921600], 'label': '20736.hv.12.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.bo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1', 'subgroup_fusion': None, 'weyl_group': '1728.39000'}
  • id: 165832442
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1', '36.p1', '36.y1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2719, -1, 3778, -1], 'generators': [16687, 4985, 25430664104, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fk1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832443
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dj1', '36.n1', '36.bd1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2794, -1, 3844, -1], 'generators': [16687, 4985, 126937858924800, 25430664104, 1078117201, 112608921600, 30235], 'label': '20736.hv.72.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fl1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832444
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1', '36.j1', '36.bd1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3770, -1, 5390, -1], 'generators': [126937858924800, 997953704, 1078117201, 30235, 16687, 4985, 112608921600], 'label': '20736.hv.72.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fm1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832445
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.di1', '36.m1', '36.o1', '36.ck1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4462, -1, 5001, -1], 'generators': [16687, 4985, 126937858924800, 1078117201, 5324705527680, 123775784, 30235], 'label': '20736.hv.72.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '72.fn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fn1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832446
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dk1', '36.l1', '36.p1', '36.ck1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3747, -1, 5370, -1], 'generators': [997953704, 16687, 4985, 126937858924800, 1078117201, 5324705527680, 30235], 'label': '20736.hv.72.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '72.fo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fo1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832447
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1', '36.i1', '36.bz1', '36.cr1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3175, -1, 4023, -1], 'generators': [997953704, 16687, 126937858924800, 9683982604800, 30235, 2628844639618, 4264], 'label': '20736.hv.72.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.fp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fp1', 'subgroup_fusion': None, 'weyl_group': '192.1358'}
  • id: 165832448
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dl1', '36.i1', '36.ca1', '36.cs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3075, -1, 3419, -1], 'generators': [134983133510400, 997953704, 16687, 1321086809218, 30235, 4264, 9360177523200], 'label': '20736.hv.72.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.fq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fq1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832449
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dn1', '36.bz1', '36.ca1', '36.ce1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2088, -1, 3101, -1], 'generators': [134983133510400, 16687, 4985, 26428551121, 5324705527680, 123775784, 30235], 'label': '20736.hv.72.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.fr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fr1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832450
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dm1', '36.l1', '36.y1', '36.cg1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2501, -1, 4524, -1], 'generators': [997953704, 16687, 4985, 126937858924800, 26428551121, 5324705527680, 30235], 'label': '20736.hv.72.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fs1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832451
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dn1', '36.o1', '36.y1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2212, -1, 3361, -1], 'generators': [16687, 4985, 126937858924800, 26428551121, 5324705527680, 123775784, 30235], 'label': '20736.hv.72.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ft1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ft1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832452
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.j1', '6.k1'], 'contains': ['24.a1', '24.cp1', '24.cq1', '24.cx1', '24.df1', '24.dj1', '24.dn1', '24.dp1', '24.du1', '24.dz1', '24.ea1', '36.ce1', '36.cf1', '36.cj1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2923, -1, 4402, -1], 'generators': [134983133510400, 721, 16687, 4985, 25514092800, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.12.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1', 'subgroup_fusion': None, 'weyl_group': '1728.46671'}
  • id: 165832453
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dm1', '36.j1', '36.n1', '36.ck1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2743, -1, 4459, -1], 'generators': [997953704, 16687, 4985, 126937858924800, 26428551121, 112608921600, 30235], 'label': '20736.hv.72.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '72.fu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fu1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832454
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.do1', '36.k1', '36.ca1', '36.cr1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2890, -1, 2914, -1], 'generators': [997953704, 16687, 126937858924800, 9683982604800, 30235, 4264, 2628844618652], 'label': '20736.hv.72.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.fv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fv1', 'subgroup_fusion': None, 'weyl_group': '192.1358'}
  • id: 165832455
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.do1', '36.k1', '36.bz1', '36.cs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2914, -1, 2934, -1], 'generators': [134983133510400, 997953704, 16687, 1321086788252, 30235, 4264, 9360177523200], 'label': '20736.hv.72.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.fw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fw1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832456
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1', '36.ce1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1767, -1, 3456, -1], 'generators': [134983133510400, 16687, 4985, 1078117201, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ce1', 'old_label': '72.fx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832457
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1', '36.m1', '36.s1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2697, -1, 3761, -1], 'generators': [16687, 4985, 1078117201, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.72.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fy1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832458
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1', '36.j1', '36.x1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2813, -1, 3687, -1], 'generators': [16687, 4985, 126937858924800, 1078117201, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.fz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fz1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832459
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dp1', '36.l1', '36.m1', '36.cj1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3327, -1, 3881, -1], 'generators': [16687, 4985, 126937858924800, 1078117201, 5324705527680, 30235, 26468500904], 'label': '20736.hv.72.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ga1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ga1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832460
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dr1', '36.bz1', '36.cb1', '36.ch1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2990, -1, 2756, -1], 'generators': [133937077482806, 16687, 126937858924800, 9683982604800, 30235, 25514093521, 25514097785], 'label': '20736.hv.72.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gc1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832461
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1', '36.i1', '36.cb1', '36.ct1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3396, -1, 3137, -1], 'generators': [134983133510400, 16687, 1321086809218, 30235, 4264, 26468500904, 9360177523200], 'label': '20736.hv.72.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gb1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832462
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ds1', '36.q1', '36.cb1', '36.cr1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3201, -1, 2838, -1], 'generators': [16687, 126937858924800, 997932646, 9683982604800, 30235, 4264, 2628844618652], 'label': '20736.hv.72.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gd1', 'subgroup_fusion': None, 'weyl_group': '192.1358'}
  • id: 165832463
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.d1', '8.e1', '8.f1', '12.ca1', '16.d1', '16.j1'], 'core': '24.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [87, -1, 123, -1], 'generators': [25514092800, 26468500904, 2647090220036, 48913735030741, 16687, 9360177523200, 134983133510400, 1078116480, 1078146715, 112608921600], 'label': '20736.hv.4.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '4.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 165832464
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.l1', '6.m1'], 'contains': ['24.cr1', '24.cs1', '24.cw1', '24.dg1', '24.di1', '24.dk1', '24.dm1', '24.dz1', '24.ea1', '36.cg1', '36.ck1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3878, -1, 5600, -1], 'generators': [134983133510400, 721, 16687, 4985, 25514092800, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.12.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832465
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dt1', '36.q1', '36.bz1', '36.ct1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2464, -1, 2501, -1], 'generators': [134983133510400, 26468479846, 16687, 1321086788252, 30235, 4264, 9360177523200], 'label': '20736.hv.72.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.ge1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ge1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832466
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dr1', '36.ca1', '36.cc1', '36.ch1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3151, -1, 2521, -1], 'generators': [134983133510400, 87302034001, 16687, 2646966474806, 87302038265, 30235, 9360177523200], 'label': '20736.hv.72.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gi1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832467
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dr1', '36.by1', '36.cd1', '36.cl1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4130, -1, 4104, -1], 'generators': [16687, 112608921600, 2646966474806, 30235, 25514093521, 25514097785, 9360177523200], 'label': '20736.hv.72.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.gg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gj1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832468
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1', '36.i1', '36.cc1', '36.cv1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3468, -1, 3046, -1], 'generators': [16687, 126937858924800, 9683982604800, 133913559622018, 30235, 4264, 26468500904], 'label': '20736.hv.72.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gf1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832469
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1', '36.t1', '36.cd1', '36.cw1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4268, -1, 4664, -1], 'generators': [16687, 112608921600, 30235, 2628844639618, 4264, 26468500904, 9360177523200], 'label': '20736.hv.72.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.gi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gg1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
  • id: 165832470
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dq1', '36.cx1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1360, -1, 2122, -1], 'generators': [134983133510400, 16687, 9683982604800, 30235, 4264, 26468500904, 8371035986818], 'label': '20736.hv.72.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cx1', 'old_label': '72.gj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gh1', 'subgroup_fusion': None, 'weyl_group': '288.631'}
  • id: 165832471
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ds1', '36.q1', '36.cc1', '36.cs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3223, -1, 2802, -1], 'generators': [134983133510400, 16687, 997932646, 1321086788252, 30235, 4264, 9360177523200], 'label': '20736.hv.72.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.gk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gk1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832472
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dt1', '36.q1', '36.ca1', '36.cv1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2382, -1, 2485, -1], 'generators': [26468479846, 16687, 126937858924800, 9683982604800, 133913559601052, 30235, 4264], 'label': '20736.hv.72.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gl1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832473
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ds1', '36.bf1', '36.cd1', '36.cq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4209, -1, 4127, -1], 'generators': [16687, 997932646, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.72.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.gm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gm1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832474
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dt1', '36.bf1', '36.by1', '36.cw1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3931, -1, 3561, -1], 'generators': [26468479846, 16687, 112608921600, 30235, 4264, 2628844618652, 9360177523200], 'label': '20736.hv.72.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.gn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gn1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
  • id: 165832475
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '6.l1', '6.n1'], 'contains': ['24.e1', '24.f1', '24.i1', '24.ct1', '24.cy1', '24.dr1', '24.dz1', '24.eb1', '36.ch1', '36.cl1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4717, -1, 3324, -1], 'generators': [134983133510400, 721, 16687, 4985, 25514092800, 112608921600, 2646966474806, 30235, 9360177523200], 'label': '20736.hv.12.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.br1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832476
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dt1', '36.cx1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1270, -1, 1827, -1], 'generators': [134983133510400, 26468479846, 16687, 9683982604800, 8371035965852, 30235, 4264], 'label': '20736.hv.72.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cx1', 'old_label': '72.go1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.go1', 'subgroup_fusion': None, 'weyl_group': '288.631'}
  • id: 165832477
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.du1', '36.cb1', '36.cc1', '36.ce1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2445, -1, 3032, -1], 'generators': [134983133510400, 16687, 4985, 26428551121, 5324705527680, 30235, 26468500904], 'label': '20736.hv.72.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gp1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832478
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.du1', '36.l1', '36.s1', '36.cf1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2305, -1, 3378, -1], 'generators': [16687, 4985, 126937858924800, 26428551121, 5324705527680, 30235, 26468500904], 'label': '20736.hv.72.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.gq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gq1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832479
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dw1', '36.bz1', '36.cc1', '36.ci1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2400, -1, 2328, -1], 'generators': [134983133510400, 16687, 1321086788252, 30235, 25514093521, 25514097785, 9360177523200], 'label': '20736.hv.72.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gw1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832480
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dw1', '36.ca1', '36.cb1', '36.ci1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2108, -1, 2370, -1], 'generators': [89377906464721, 16687, 126937858924800, 9683982604800, 89377906468985, 30235, 2628844618652], 'label': '20736.hv.72.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gx1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832481
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.du1', '36.j1', '36.cd1', '36.cj1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [3351, -1, 3646, -1], 'generators': [16687, 4985, 126937858924800, 26428551121, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gr1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832482
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dw1', '36.by1', '36.cd1', '36.cm1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4005, -1, 3272, -1], 'generators': [16687, 112608921600, 30235, 25514093521, 2628844618652, 25514097785, 9360177523200], 'label': '20736.hv.72.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.gu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gy1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832483
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dv1', '36.k1', '36.cc1', '36.ct1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2973, -1, 2427, -1], 'generators': [134983133510400, 16687, 1321086788252, 30235, 4264, 26468500904, 9360177523200], 'label': '20736.hv.72.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gs1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832484
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dv1', '36.k1', '36.cb1', '36.cv1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2945, -1, 2467, -1], 'generators': [16687, 126937858924800, 9683982604800, 133913559601052, 30235, 4264, 26468500904], 'label': '20736.hv.72.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gt1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832485
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dv1', '36.u1', '36.cd1', '36.cw1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4106, -1, 4083, -1], 'generators': [16687, 112608921600, 30235, 4264, 26468500904, 2628844618652, 9360177523200], 'label': '20736.hv.72.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.gx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gu1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
  • id: 165832486
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '6.m1', '6.o1'], 'contains': ['24.bc1', '24.be1', '24.bg1', '24.cv1', '24.da1', '24.dw1', '24.dz1', '24.ee1', '36.ci1', '36.cm1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2443, -1, 2786, -1], 'generators': [134983133510400, 721, 16687, 4985, 25514092800, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.12.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1', 'subgroup_fusion': None, 'weyl_group': '1728.46674'}
  • id: 165832487
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dv1', '36.cx1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1340, -1, 1809, -1], 'generators': [134983133510400, 16687, 9683982604800, 8371035965852, 30235, 4264, 26468500904], 'label': '20736.hv.72.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cx1', 'old_label': '72.gy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gv1', 'subgroup_fusion': None, 'weyl_group': '288.631'}
  • id: 165832488
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dx1', '36.r1', '36.cc1', '36.cr1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3124, -1, 2888, -1], 'generators': [16687, 126937858924800, 997932646, 9683982604800, 30235, 2628844639618, 4264], 'label': '20736.hv.72.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.gz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gz1', 'subgroup_fusion': None, 'weyl_group': '192.1358'}
  • id: 165832489
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dy1', '36.r1', '36.bz1', '36.cv1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2482, -1, 2789, -1], 'generators': [26468479846, 16687, 126937858924800, 9683982604800, 133913559622018, 30235, 4264], 'label': '20736.hv.72.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.ha1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ha1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832490
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dx1', '36.bh1', '36.cd1', '36.cq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4179, -1, 4348, -1], 'generators': [16687, 997932646, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.72.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.hb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hb1', 'subgroup_fusion': None, 'weyl_group': '192.1147'}
  • id: 165832491
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dy1', '36.bh1', '36.by1', '36.cw1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3966, -1, 4065, -1], 'generators': [26468479846, 16687, 112608921600, 30235, 2628844639618, 4264, 9360177523200], 'label': '20736.hv.72.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.hc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hc1', 'subgroup_fusion': None, 'weyl_group': '576.7160'}
  • id: 165832492
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dy1', '36.cx1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1303, -1, 1840, -1], 'generators': [134983133510400, 26468479846, 16687, 9683982604800, 30235, 4264, 8371035986818], 'label': '20736.hv.72.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cx1', 'old_label': '72.hd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hd1', 'subgroup_fusion': None, 'weyl_group': '288.631'}
  • id: 165832493
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dx1', '36.r1', '36.cb1', '36.cs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3096, -1, 2863, -1], 'generators': [134983133510400, 16687, 1321086809218, 997932646, 30235, 4264, 9360177523200], 'label': '20736.hv.72.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.he1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.he1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832494
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dy1', '36.r1', '36.ca1', '36.ct1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2182, -1, 2578, -1], 'generators': [134983133510400, 26468479846, 16687, 1321086809218, 30235, 4264, 9360177523200], 'label': '20736.hv.72.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.hf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hf1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832495
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dz1', '36.ce1', '36.ch1', '36.ci1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2423, -1, 2445, -1], 'generators': [721, 16687, 4985, 126937858924800, 25514092800, 9683982604800, 30235], 'label': '20736.hv.72.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.hg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 165832496
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dz1', '36.cf1', '36.cg1', '36.cp1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3262, -1, 2995, -1], 'generators': [721, 16687, 4985, 126937858924800, 25514092800, 112608921600, 30235], 'label': '20736.hv.72.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.hh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 165832497
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '6.l1', '6.o1'], 'contains': ['24.bd1', '24.cz1', '24.db1', '24.dz1', '36.cn1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5250, -1, 6359, -1], 'generators': [134983133510400, 721, 16687, 4985, 25514092800, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.12.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1', 'subgroup_fusion': None, 'weyl_group': '576.8399'}
  • id: 165832498
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dz1', '36.cj1', '36.ck1', '36.cl1', '36.cm1', '36.cn1', '36.co1', '36.cp1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4691, -1, 4649, -1], 'generators': [721, 16687, 4985, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.hi1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hi1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832499
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ea1', '36.cg1', '36.cj1', '36.cq1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [3886, -1, 4684, -1], 'generators': [997953704, 721, 16687, 4985, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.hj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hj1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 165832500
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ea1', '36.ce1', '36.cr1', '36.cs1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2344, -1, 3155, -1], 'generators': [126937858924800, 997953704, 9683982604800, 721, 30235, 16687, 4985], 'label': '20736.hv.72.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.hk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hk1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832501
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ea1', '36.cf1', '36.cg1', '36.ck1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3642, -1, 4961, -1], 'generators': [126937858924800, 997953704, 721, 30235, 16687, 4985, 112608921600], 'label': '20736.hv.72.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '72.hl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hl1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
  • id: 165832502
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eb1', '36.ch1', '36.cr1', '36.ct1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2528, -1, 2408, -1], 'generators': [134983133510400, 721, 16687, 4985, 2646966474806, 30235, 9360177523200], 'label': '20736.hv.72.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.hm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hm1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 165832503
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eb1', '36.ch1', '36.cs1', '36.cv1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2364, -1, 2386, -1], 'generators': [133937077482806, 721, 16687, 4985, 126937858924800, 9683982604800, 30235], 'label': '20736.hv.72.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.hn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hn1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832504
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eb1', '36.cl1', '36.cq1', '36.cw1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3983, -1, 3530, -1], 'generators': [721, 16687, 4985, 112608921600, 2646966474806, 30235, 9360177523200], 'label': '20736.hv.72.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.ho1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ho1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832505
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eb1', '24.ec1', '36.cx1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1253, -1, 1147, -1], 'generators': [134983133510400, 721, 16687, 4985, 8395548138806, 9683982604800, 30235], 'label': '20736.hv.72.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bw1', 'old_label': '72.hp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hp1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 165832506
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ec1', '36.cu1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [670, -1, 295, -1], 'generators': [132523584036480, 721, 30235, 16687, 4985, 46036847791741, 86575308386486], 'label': '20736.hv.72.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1', 'old_label': '72.hq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hq1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 165832507
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ed1', '36.cu1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [511, -1, 277, -1], 'generators': [721, 16687, 4985, 132523584036480, 41876802358141, 30235, 26468500904], 'label': '20736.hv.72.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1', 'old_label': '72.hr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hr1', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
  • id: 165832508
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '6.m1', '6.n1'], 'contains': ['24.g1', '24.dc1', '24.dd1', '24.dz1', '36.co1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6625, -1, 6228, -1], 'generators': [134983133510400, 721, 16687, 4985, 25514092800, 2628761148086, 112608921600, 30235, 9360177523200], 'label': '20736.hv.12.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1', 'subgroup_fusion': None, 'weyl_group': '1728.46672'}
  • id: 165832509
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '36.ce1', '36.ct1', '36.cv1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2025, -1, 2293, -1], 'generators': [134983133510400, 721, 16687, 4985, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.hs1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hs1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832510
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '36.cf1', '36.cj1', '36.cw1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 9, 'diagramx': [3057, -1, 3342, -1], 'generators': [721, 16687, 4985, 126937858924800, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ht1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ht1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832511
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.ed1', '36.cx1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1215, -1, 1111, -1], 'generators': [134983133510400, 721, 16687, 4985, 9683982604800, 30235, 26468500904], 'label': '20736.hv.72.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bx1', 'old_label': '72.hu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hu1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 165832512
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ee1', '36.ci1', '36.cr1', '36.cv1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2068, -1, 2275, -1], 'generators': [721, 16687, 4985, 126937858924800, 9683982604800, 30235, 2628844618652], 'label': '20736.hv.72.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '72.hv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hv1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832513
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ee1', '36.cm1', '36.cq1', '36.cw1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3495, -1, 3253, -1], 'generators': [721, 16687, 4985, 112608921600, 30235, 2628844618652, 9360177523200], 'label': '20736.hv.72.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '72.hw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hw1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 165832514
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ee1', '24.ef1', '24.eg1', '36.cx1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [941, -1, 406, -1], 'generators': [134983133510400, 721, 16687, 4985, 9683982604800, 30235, 2628844618652], 'label': '20736.hv.72.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cx1', 'old_label': '72.hx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hx1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 165832515
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ee1', '36.ci1', '36.cs1', '36.ct1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2047, -1, 2084, -1], 'generators': [134983133510400, 721, 16687, 4985, 1321086788252, 30235, 9360177523200], 'label': '20736.hv.72.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.hy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hy1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 165832516
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ef1', '36.cu1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [275, -1, 259, -1], 'generators': [41876802358141, 132523584036480, 721, 30235, 16687, 4985, 1321086788252], 'label': '20736.hv.72.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bx1', 'old_label': '72.hz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hz1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
  • id: 165832517
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eg1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 24, 'diagramx': [238, -1, 139, -1], 'generators': [132523584036480, 721, 30235, 16687, 4985, 66960592054141, 1321086788252], 'label': '20736.hv.72.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.eg1', 'old_label': '72.ia1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ia1', 'subgroup_fusion': None, 'weyl_group': '864.4017'}
  • id: 165832518
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eh1', '36.j1', '36.m1', '36.bq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4827, -1, 5267, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 5324705527680, 30235, 26468500904], 'label': '20736.hv.72.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ib1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ib1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832519
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1'], 'contains': ['24.dl1', '24.do1', '24.ds1', '24.dx1', '24.ea1', '24.eb1', '24.ee1', '36.cq1', '36.cr1', '36.cs1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3104, -1, 3155, -1], 'generators': [997953704, 721, 30235, 16687, 9360177523200, 4985, 2628844618652, 134983133510400, 112608921600], 'label': '20736.hv.12.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.bv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1', 'subgroup_fusion': None, 'weyl_group': '576.7159'}
  • id: 165832520
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eh1', '36.l1', '36.m1', '36.br1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4928, -1, 5506, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ic1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ic1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832521
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ei1', '36.i1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [7188, -1, 7303, -1], 'generators': [16687, 126937858924800, 25514092800, 133913559596036, 9683982604800, 30235, 26468500904], 'label': '20736.hv.72.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.id1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.id1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832522
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ej1', '36.j1', '36.l1', '36.bq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3694, -1, 5062, -1], 'generators': [26428580635, 16687, 1078121465, 126937858924800, 5324705527680, 30235, 26468500904], 'label': '20736.hv.72.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ie1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ie1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832523
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.el1', '36.n1', '36.p1', '36.bq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4370, -1, 5803, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 25430664104, 5324705527680, 30235], 'label': '20736.hv.72.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.if1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.if1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832524
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.el1', '36.o1', '36.p1', '36.br1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4437, -1, 6026, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 25430664104, 112608921600, 30235], 'label': '20736.hv.72.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ig1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ig1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832525
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.en1', '36.n1', '36.o1', '36.bq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3013, -1, 5290, -1], 'generators': [26428580635, 16687, 1078121465, 126937858924800, 25430664104, 5324705527680, 30235], 'label': '20736.hv.72.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ih1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ih1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832526
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ep1', '36.m1', '36.n1', '36.bs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4486, -1, 4850, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 5324705527680, 30235, 25430669150], 'label': '20736.hv.72.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ii1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ii1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832527
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eq1', '36.j1', '36.p1', '36.bs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4233, -1, 5352, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 26468505950, 5324705527680, 30235], 'label': '20736.hv.72.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ij1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ij1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832528
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ep1', '36.m1', '36.o1', '36.bv1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4802, -1, 5042, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 112608921600, 30235, 25430669150], 'label': '20736.hv.72.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ik1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ik1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832529
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eq1', '36.l1', '36.p1', '36.bv1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4251, -1, 5434, -1], 'generators': [16687, 1078121465, 126937858924800, 25514092800, 112608921600, 26468505950, 30235], 'label': '20736.hv.72.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.il1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.il1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832530
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.j1'], 'contains': ['24.a1', '24.dq1', '24.dt1', '24.dv1', '24.dy1', '24.eb1', '24.ee1', '36.ct1', '36.cv1', '36.cw1', '36.cx1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2471, -1, 2800, -1], 'generators': [26468500904, 721, 30235, 16687, 9360177523200, 4985, 2628844618652, 134983133510400, 112608921600], 'label': '20736.hv.12.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.bw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1', 'subgroup_fusion': None, 'weyl_group': '1728.39000'}
  • id: 165832531
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.es1', '36.i1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [7559, -1, 7845, -1], 'generators': [16687, 126937858924800, 25514092800, 133913559596036, 9683982604800, 26468474800, 30235], 'label': '20736.hv.72.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.im1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.im1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832532
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ev1', '36.l1', '36.n1', '36.bs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2644, -1, 4559, -1], 'generators': [26428580635, 16687, 1078121465, 126937858924800, 5324705527680, 30235, 25430669150], 'label': '20736.hv.72.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.in1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.in1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832533
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ev1', '36.j1', '36.o1', '36.bs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2574, -1, 4543, -1], 'generators': [26428580635, 16687, 1078121465, 112608921600, 30235, 25430669150, 9360177523200], 'label': '20736.hv.72.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.io1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.io1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832534
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eh1', '36.s1', '36.x1', '36.bq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [5124, -1, 5682, -1], 'generators': [16687, 1078121465, 25514092800, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.72.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ip1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ip1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832535
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ei1', '36.t1', '36.cy1', '36.da1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7870, -1, 8567, -1], 'generators': [16687, 25514092800, 112608921600, 2628844613636, 30235, 26468500904, 9360177523200], 'label': '20736.hv.72.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.iq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iq1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832536
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ej1', '36.s1', '36.br1', '36.cy1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6222, -1, 7667, -1], 'generators': [26428580635, 16687, 1078121465, 126937858924800, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ir1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ir1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832537
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ek1', '36.v1', '36.cy1', '36.da1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7774, -1, 8903, -1], 'generators': [16687, 25514092800, 112608921600, 2647090220036, 30235, 26468500904, 9360177523200], 'label': '20736.hv.72.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.is1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.is1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832538
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.el1', '36.y1', '36.bd1', '36.bq1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4652, -1, 6091, -1], 'generators': [16687, 1078121465, 25514092800, 25430664104, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.it1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.it1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832539
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.em1', '36.z1', '36.cz1', '36.da1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7823, -1, 8721, -1], 'generators': [16687, 25514092800, 25430664104, 112608921600, 2647090220036, 30235, 9360177523200], 'label': '20736.hv.72.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.iu1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iu1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832540
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.en1', '36.y1', '36.br1', '36.cz1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6584, -1, 7650, -1], 'generators': [26428580635, 16687, 1078121465, 126937858924800, 25430664104, 112608921600, 30235], 'label': '20736.hv.72.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.iv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iv1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832541
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1'], 'contains': ['24.ec1', '24.ed1', '24.ef1', '36.cu1', '36.cx1', '48.gx1'], 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [661, -1, 299, -1], 'generators': [26468500904, 132523584036480, 9683982604800, 721, 30235, 16687, 4985, 46036847791741, 86599221823772], 'label': '20736.hv.12.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bx1', 'old_label': '12.bx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
  • id: 165832542
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eo1', '36.ba1', '36.cz1', '36.da1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7753, -1, 8751, -1], 'generators': [16687, 25514092800, 25430664104, 112608921600, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.72.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.iw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iw1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832543
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ep1', '36.x1', '36.y1', '36.bs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4764, -1, 5141, -1], 'generators': [16687, 1078121465, 25514092800, 112608921600, 30235, 25430669150, 9360177523200], 'label': '20736.hv.72.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ix1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ix1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832544
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eq1', '36.s1', '36.bd1', '36.bs1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4328, -1, 5452, -1], 'generators': [16687, 1078121465, 25514092800, 112608921600, 26468505950, 30235, 9360177523200], 'label': '20736.hv.72.iy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.iy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iy1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832545
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.er1', '36.bt1', '36.cy1', '36.cz1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8411, -1, 8781, -1], 'generators': [1078120744, 16687, 2646966471087, 25514092800, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.iz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.iz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.iz1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832546
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.es1', '36.t1', '36.cz1', '36.db1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8479, -1, 8586, -1], 'generators': [16687, 25514092800, 26468474800, 112608921600, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.72.ja1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ja1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ja1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832547
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.et1', '36.z1', '36.cy1', '36.db1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8696, -1, 8924, -1], 'generators': [16687, 25514092800, 112608921600, 25430638000, 2647090220036, 30235, 9360177523200], 'label': '20736.hv.72.jb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.jb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jb1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832548
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.eu1', '36.bu1', '36.cy1', '36.cz1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8562, -1, 8766, -1], 'generators': [1078120744, 16687, 25514092800, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.72.jc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.jc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jc1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832549
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ev1', '36.s1', '36.y1', '36.bv1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2594, -1, 4753, -1], 'generators': [26428580635, 16687, 1078121465, 126937858924800, 112608921600, 30235, 25430669150], 'label': '20736.hv.72.jd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.jd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jd1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832550
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ew1', '36.ba1', '36.cy1', '36.db1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8644, -1, 8945, -1], 'generators': [16687, 25514092800, 112608921600, 25430638000, 2628844613636, 30235, 9360177523200], 'label': '20736.hv.72.je1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.je1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.je1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832551
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ex1', '36.v1', '36.cz1', '36.db1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8390, -1, 8968, -1], 'generators': [16687, 25514092800, 26468474800, 112608921600, 2647090220036, 30235, 9360177523200], 'label': '20736.hv.72.jf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.jf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jf1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 165832552
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1'], 'contains': ['24.bz1', '24.ca1', '24.cb1', '24.cc1', '24.ei1', '24.ej1', '24.ek1', '24.er1', '24.et1', '24.eu1', '24.ew1', '36.cy1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8364, -1, 9256, -1], 'generators': [134983133510400, 1078120744, 16687, 25514092800, 112608921600, 30235, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.12.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.by1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832553
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.bq1', '36.br1', '36.da1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6057, -1, 8109, -1], 'generators': [16687, 126937858924800, 25514092800, 1078116480, 112608921600, 1078146715, 26468500904], 'label': '20736.hv.72.jg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.jg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jg1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832554
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ey1', '36.bt1', '36.da1', '36.db1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7711, -1, 8736, -1], 'generators': [16687, 25514092800, 2628761147486, 1078116480, 112608921600, 1078146715, 9360177523200], 'label': '20736.hv.72.jh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.jh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jh1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832555
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ez1', '36.bu1', '36.da1', '36.db1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7730, -1, 8707, -1], 'generators': [16687, 25514092800, 1078116480, 112608921600, 1078146715, 2647090220036, 9360177523200], 'label': '20736.hv.72.ji1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ji1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ji1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832556
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fa1', '36.br1', '36.bs1', '36.db1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6524, -1, 7794, -1], 'generators': [26468479846, 16687, 126937858924800, 25514092800, 1078116480, 112608921600, 1078146715], 'label': '20736.hv.72.jj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.jj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jj1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832557
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fa1', '36.bq1', '36.bs1', '36.bv1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4977, -1, 6469, -1], 'generators': [26468479846, 16687, 126937858924800, 25514092800, 1078116480, 1078146715, 5324705527680], 'label': '20736.hv.72.jk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.jk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 165832558
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fd1', '36.n1', '36.p1', '36.s1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2611, -1, 3927, -1], 'generators': [997953704, 1078117201, 30235, 16687, 9360177523200, 25514097785, 112608921600], 'label': '20736.hv.72.jl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.jl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jl1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832559
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fb1', '36.t1', '36.dc1', '36.dd1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8155, -1, 6418, -1], 'generators': [997953704, 16687, 25514097064, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.72.jm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.jm1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jm1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832560
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fc1', '36.o1', '36.x1', '36.dc1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6094, -1, 5156, -1], 'generators': [16687, 126937858924800, 25430664104, 1078117201, 5324705527680, 30235, 25514097785], 'label': '20736.hv.72.jn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.jn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jn1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832561
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fe1', '36.w1', '36.dc1', '36.dd1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8116, -1, 6332, -1], 'generators': [997953704, 16687, 25514097064, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.72.jo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.jo1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jo1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832562
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ff1', '36.p1', '36.x1', '36.dd1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6394, -1, 5668, -1], 'generators': [26428555385, 997953704, 16687, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.jp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.jp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jp1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832563
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1'], 'contains': ['24.cd1', '24.ce1', '24.cf1', '24.cg1', '24.em1', '24.en1', '24.eo1', '24.er1', '24.es1', '24.eu1', '24.ex1', '36.cz1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8299, -1, 9227, -1], 'generators': [134983133510400, 1078120744, 16687, 25514092800, 25430664104, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.12.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.bz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832564
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fg1', '36.n1', '36.o1', '36.s1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2195, -1, 3730, -1], 'generators': [997953704, 16687, 26428551121, 112608921600, 30235, 25514097785, 9360177523200], 'label': '20736.hv.72.jq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.jq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jq1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832565
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fb1', '36.i1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [7539, -1, 6433, -1], 'generators': [997953704, 16687, 89377906468264, 126937858924800, 9683982604800, 30235, 2628844639618], 'label': '20736.hv.72.jr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.jr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jr1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832566
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fc1', '36.m1', '36.n1', '36.y1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3814, -1, 3899, -1], 'generators': [16687, 126937858924800, 25430664104, 1078117201, 112608921600, 30235, 25514097785], 'label': '20736.hv.72.js1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.js1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.js1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832567
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fd1', '36.j1', '36.p1', '36.y1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2680, -1, 3914, -1], 'generators': [997953704, 16687, 126937858924800, 1078117201, 112608921600, 30235, 25514097785], 'label': '20736.hv.72.jt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.jt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jt1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832568
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fd1', '36.l1', '36.o1', '36.bd1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2662, -1, 4574, -1], 'generators': [997953704, 16687, 126937858924800, 1078117201, 5324705527680, 30235, 25514097785], 'label': '20736.hv.72.ju1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.ju1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ju1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832569
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ff1', '36.m1', '36.p1', '36.bd1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4784, -1, 5469, -1], 'generators': [26428555385, 997953704, 16687, 126937858924800, 1078117201, 112608921600, 30235], 'label': '20736.hv.72.jv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.jv1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jv1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832570
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fg1', '36.l1', '36.n1', '36.y1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2288, -1, 3717, -1], 'generators': [997953704, 16687, 126937858924800, 26428551121, 5324705527680, 30235, 25514097785], 'label': '20736.hv.72.jw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.jw1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jw1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832571
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fg1', '36.j1', '36.o1', '36.y1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2251, -1, 3702, -1], 'generators': [997953704, 16687, 126937858924800, 26428551121, 112608921600, 30235, 25514097785], 'label': '20736.hv.72.jx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.jx1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jx1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832572
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fh1', '36.i1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 36, 'diagramx': [7519, -1, 6402, -1], 'generators': [16687, 126937858924800, 25514097064, 9683982604800, 133913559622018, 30235, 26468500904], 'label': '20736.hv.72.jy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '72.jy1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jy1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832573
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fl1', '36.j1', '36.m1', '36.s1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3037, -1, 4591, -1], 'generators': [16687, 126937858924800, 1078117201, 112608921600, 30235, 26468500904, 25514097785], 'label': '20736.hv.72.jz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.jz1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.jz1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832574
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.g1', '8.h1', '8.i1', '12.cf1', '16.d1'], 'core': '24.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [267, -1, 337, -1], 'generators': [26468500904, 1078117201, 2647090225052, 30235, 16687, 9360177523200, 134983133510400, 26428555385, 112608921600, 48913735030141], 'label': '20736.hv.4.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '4.d1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165832575
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.f1'], 'contains': ['24.b1', '24.ch1', '24.ci1', '24.cj1', '24.ck1', '24.ei1', '24.ek1', '24.em1', '24.eo1', '24.ey1', '24.ez1', '36.da1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8124, -1, 9183, -1], 'generators': [134983133510400, 16687, 25514092800, 1078116480, 112608921600, 1078146715, 2647090220036, 26468500904, 9360177523200], 'label': '20736.hv.12.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.ca1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832576
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fi1', '36.bm1', '36.dc1', '36.de1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8009, -1, 6075, -1], 'generators': [16687, 1078121465, 26428551121, 2628761148086, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.kb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.ka1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kb1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832577
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fh1', '36.t1', '36.de1', '36.df1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7938, -1, 6387, -1], 'generators': [16687, 25514097064, 112608921600, 30235, 2628844639618, 26468500904, 9360177523200], 'label': '20736.hv.72.ka1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.kb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ka1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832578
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fj1', '36.be1', '36.dc1', '36.df1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7314, -1, 6258, -1], 'generators': [16687, 123754726, 25514097064, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.72.kc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.kc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kc1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832579
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fk1', '36.be1', '36.dd1', '36.de1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8030, -1, 6313, -1], 'generators': [25430643046, 16687, 25514097064, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.72.kd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.kd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kd1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832580
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fl1', '36.l1', '36.x1', '36.de1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6077, -1, 5203, -1], 'generators': [16687, 126937858924800, 1078117201, 5324705527680, 30235, 26468500904, 25514097785], 'label': '20736.hv.72.ke1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ke1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ke1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832581
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fn1', '36.bn1', '36.dc1', '36.de1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7966, -1, 5987, -1], 'generators': [16687, 1078121465, 26428551121, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.72.kg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.kf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kg1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832582
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fm1', '36.w1', '36.de1', '36.df1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7679, -1, 6295, -1], 'generators': [16687, 25514097064, 112608921600, 2647090225052, 30235, 26468500904, 9360177523200], 'label': '20736.hv.72.kf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.kg1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kf1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832583
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fo1', '36.bg1', '36.dc1', '36.df1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7651, -1, 6277, -1], 'generators': [16687, 123754726, 25514097064, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.72.kh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.kh1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kh1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832584
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fp1', '36.bg1', '36.dd1', '36.de1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8069, -1, 6350, -1], 'generators': [25430643046, 16687, 25514097064, 112608921600, 30235, 2628844639618, 9360177523200], 'label': '20736.hv.72.ki1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.ki1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ki1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832585
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fq1', '36.bm1', '36.dd1', '36.df1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7631, -1, 6060, -1], 'generators': [26428555385, 16687, 2628761148086, 1078117201, 112608921600, 30235, 9360177523200], 'label': '20736.hv.72.kj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.kj1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kj1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832586
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1'], 'contains': ['24.cl1', '24.cm1', '24.cn1', '24.co1', '24.es1', '24.et1', '24.ew1', '24.ex1', '24.ey1', '24.ez1', '24.fa1', '36.db1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8321, -1, 9274, -1], 'generators': [134983133510400, 16687, 25514092800, 1078116480, 112608921600, 1078146715, 25430638000, 2647090220036, 9360177523200], 'label': '20736.hv.12.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '12.cb1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1', 'subgroup_fusion': None, 'weyl_group': '1728.47887'}
  • id: 165832587
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '36.m1', '36.x1', '36.df1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 9, 'diagramx': [5846, -1, 5562, -1], 'generators': [26428555385, 16687, 126937858924800, 1078117201, 112608921600, 30235, 26468500904], 'label': '20736.hv.72.kk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.kk1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kk1', 'subgroup_fusion': None, 'weyl_group': '576.8418'}
  • id: 165832588
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fr1', '36.bn1', '36.dd1', '36.df1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6843, -1, 5972, -1], 'generators': [26428555385, 16687, 1078117201, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.72.kl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.kl1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kl1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
  • id: 165832589
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.fs1', '36.j1', '36.l1', '36.s1'], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2324, -1, 3745, -1], 'generators': [16687, 126937858924800, 26428551121, 112608921600, 30235, 26468500904, 25514097785], 'label': '20736.hv.72.km1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '72.km1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.km1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
  • id: 165832590
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ft1', '36.e1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1287, -1, 635, -1], 'generators': [2628844614114, 1078135822, 721, 25514092800, 112608921600, 1078140940, 9360177523200], 'label': '20736.hv.72.kn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '72.kn1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kn1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832591
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.fu1', '36.e1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1319, -1, 761, -1], 'generators': [26428580635, 4985, 1078133167, 1078117201, 112608921600, 2628844618652, 9360177523200], 'label': '20736.hv.72.ko1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '72.ko1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ko1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832592
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.fv1', '36.a1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5707, -1, 2621, -1], 'generators': [1078121465, 25514092800, 1078117201, 112608921600, 2646966474806, 1078140940, 9360177523200], 'label': '20736.hv.72.kp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '72.kp1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kp1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832593
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.fw1', '36.a1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5584, -1, 2591, -1], 'generators': [26428580635, 1078121465, 26428551121, 1078133167, 2628761148086, 112608921600, 9360177523200], 'label': '20736.hv.72.kq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '72.kq1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kq1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832594
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.fx1', '36.e1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1234, -1, 461, -1], 'generators': [1078117201, 26428567087, 9360177523200, 2628844618652, 25514097785, 1078146715, 112608921600], 'label': '20736.hv.72.kr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '72.kr1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kr1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832595
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.fy1', '36.e1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1085, -1, 390, -1], 'generators': [26428580635, 1078121465, 1078133167, 112608921600, 2647090225052, 25514093521, 9360177523200], 'label': '20736.hv.72.ks1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1', 'old_label': '72.ks1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ks1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832596
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.fz1', '36.a1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5601, -1, 2606, -1], 'generators': [1078135822, 25514092800, 112608921600, 2646966489420, 15966, 1078140940, 9360177523200], 'label': '20736.hv.72.kt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '72.kt1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.kt1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832597
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['24.fb1', '24.fc1', '24.fe1', '24.fi1', '24.fj1', '24.fn1', '24.fo1', '36.dc1'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7450, -1, 5871, -1], 'generators': [134983133510400, 997953704, 16687, 1078121465, 26428551121, 112608921600, 2647090225052, 30235, 9360177523200], 'label': '20736.hv.12.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.cc1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165832598
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '72.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ga1', '36.a1'], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5423, -1, 2565, -1], 'generators': [26428580635, 721, 4985, 1078133167, 112608921600, 2646966474806, 9360177523200], 'label': '20736.hv.72.ku1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '72.ku1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ku1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 165832599
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '27.a1', '27.b1'], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 81, 'diagramx': [1370, -1, 5654, -1], 'generators': [16687, 4985, 25514092800, 1321086788252, 1078117201, 1078116480, 1078146715, 26468500904], 'label': '20736.hv.81.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '20736.hv', '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': '64.202'}
  • id: 165832600
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '96.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1', '48.fj1', '48.ft1', '48.gm1', '48.gu1', '48.gy1'], 'contains': ['192.A'], 'core': '96.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6936, -1, 2772], 'generators': [134983133510400, 16687, 112608921600, 30235, 26468500904, 9360177523200], 'label': '20736.hv.96.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': ['24.a1', '24.b1', '24.c1'], 'normal_contains': ['192.A'], 'normalizer': '1.a1', 'old_label': '96.a1.N', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.A', 'subgroup_fusion': None, 'weyl_group': '10000.da'}
  • id: 165832601
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '192.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '96.A'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6538, -1, 3606], 'generators': [134983133510400, 16687, 112608921600, 30235, 9360177523200], 'label': '20736.hv.192.A', 'mobius_quo': 1, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': ['48.a1', '48.b1', '48.c1', '96.A'], 'normal_contains': ['768.A', '5184.A'], 'normalizer': '1.a1', 'old_label': '192.a1.N', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.A', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 165832602
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '192.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.d1'], 'contains': [], 'core': '192.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 4521, -1, 6877], 'generators': [134983133510400, 26428580635, 1078133167, 112608921600, 9360177523200], 'label': '20736.hv.192.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '192.B', 'normal_contained_in': ['48.b1'], 'normal_contains': ['768.A'], 'normalizer': '1.a1', 'old_label': '192.b1.N', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.B', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 165832603
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.c1', '64.d1', '64.g1', '64.e1', '64.f1', '64.i1'], 'contains': ['768.A'], 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [134983133510400, 112608921600, 46036847791741, 9360177523200], 'label': '20736.hv.256.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.h1', 'old_label': '256.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 165832604
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '768.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.a1'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6165, -1, 4056], 'generators': [134983133510400, 112608921600, 9360177523200], 'label': '20736.hv.768.A', 'mobius_quo': -1, 'mobius_sub': None, 'normal_closure': '768.A', 'normal_contained_in': ['192.A', '192.B'], 'normal_contains': ['20736.a1'], 'normalizer': '1.a1', 'old_label': '768.a1.N', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.A', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 165832605
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '1296.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': [], 'core': '1296.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 8418, -1, 1948], 'generators': [721, 16687, 4985, 30235], 'label': '20736.hv.1296.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '1296.A', 'normal_contained_in': ['48.a1'], 'normal_contains': ['5184.A'], 'normalizer': '1.a1', 'old_label': '1296.a1.N', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.A', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 165832606
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '5184.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': [], 'core': '5184.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6911, -1, 3156], 'generators': [16687, 30235], 'label': '20736.hv.5184.A', 'mobius_quo': -1, 'mobius_sub': None, 'normal_closure': '5184.A', 'normal_contained_in': ['192.A', '1296.A'], 'normal_contains': ['20736.a1'], 'normalizer': '1.a1', 'old_label': '5184.a1.N', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.A', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 165832607
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '20736.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': [], 'core': '20736.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6538, -1, 3606], 'generators': [], 'label': '20736.hv.20736.a1', 'mobius_quo': 1, 'mobius_sub': None, 'normal_closure': '20736.a1', 'normal_contained_in': ['768.A', '5184.A'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '20736.a1.N', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20736.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 165832608
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['24.fb1', '24.fe1', '24.ff1', '24.fk1', '24.fp1', '24.fq1', '24.fr1', '36.dd1'], 'core': '48.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [7475, -1, 5929, -1], 'generators': [997953704, 1078117201, 2647090225052, 30235, 16687, 9360177523200, 134983133510400, 26428555385, 112608921600], 'label': '20736.hv.12.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.cd1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165832609
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['24.fi1', '24.fh1', '24.fk1', '24.fl1', '24.fn1', '24.fm1', '24.fp1', '36.de1'], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7499, -1, 5907, -1], 'generators': [134983133510400, 16687, 1078121465, 26428551121, 112608921600, 2647090225052, 30235, 26468500904, 9360177523200], 'label': '20736.hv.12.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.ce1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165832610
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.b1'], 'contains': ['24.c1', '24.fh1', '24.fj1', '24.fm1', '24.fo1', '24.fq1', '24.fr1', '36.df1'], 'core': '24.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [7324, -1, 5850, -1], 'generators': [26468500904, 1078117201, 2647090225052, 30235, 16687, 9360177523200, 134983133510400, 26428555385, 112608921600], 'label': '20736.hv.12.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.cf1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1', 'subgroup_fusion': None, 'weyl_group': '1728.46611'}
  • id: 165832611
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.a1', '8.b1', '8.c1'], 'contains': ['48.a1', '48.fr1', '48.fs1', '64.a1', '64.b1', '64.c1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [305, -1, 224, -1], 'generators': [134983133510400, 721, 16687, 4985, 112608921600, 46036847791741, 30235, 9360177523200], 'label': '20736.hv.16.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.a1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '1728.12469'}
  • id: 165832612
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.d1', '8.e1', '8.f1'], 'contains': ['48.b1', '64.a1', '64.d1', '64.f1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [87, -1, 63, -1], 'generators': [134983133510400, 16687, 25514092800, 1078116480, 112608921600, 46036847791741, 1078146715, 9360177523200], 'label': '20736.hv.16.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.b1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '2304.oh'}
  • id: 165832613
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.g1', '8.h1', '8.i1'], 'contains': ['48.c1', '64.a1', '64.g1', '64.e1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [220, -1, 347, -1], 'generators': [134983133510400, 26428555385, 16687, 1078117201, 112608921600, 46036847791741, 30235, 9360177523200], 'label': '20736.hv.16.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.c1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 165832614
    {'ambient': '20736.hv', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20736.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.c1', '4.d1'], 'contains': ['32.a1', '32.b1', '32.c1', '48.gu1', '48.gx1', '64.h1'], 'core': '96.A', 'coset_action_label': None, 'count': 16, 'diagramx': [244, -1, 247, -1], 'generators': [134983133510400, 46036847792341, 16687, 112608921600, 2628844613636, 30235, 26468500904, 9360177523200], 'label': '20736.hv.16.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '16.d1', 'projective_image': '20736.hv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '1296.1790'}